New approaches to the direct search of BSM physics with Codex-b and LHCb experiments

INTERNATIONAL DOCTORAL SCHOOL OF THE USC Saúl López Soliño PhD Thesis New approaches to the direct search of BSM physics with Codex-b and LHCb experiments. Santiago de Compostela, 2024 Doctoral Programme in Nuclear and Particles Physics DOCTORAL THESIS NEW APPROACHES TO THE DIRECT SEARCH OF BSM PHYSICS WITH CODEX-B AND LHCB EXPERIMENTS Author Saúl López Soliño Supervisor/s: Xabier Cid Vidal, Carlos Vázquez Sierra Tutor: Xabier Cid Vidal PHD PROGRAMME IN NUCLEAR AND PARTICLE PHYSICS SANTIAGO DE COMPOSTELA iii “I didn’t choose this town, I dream of getting out.” Taylor Swift “And I cry, it’s not fair.” Chappell Roan “These are what they call hard feelings.” Lorde iv Abstract This work presents studies in Beyond Standard Model Physics, using two different experiments, LHCb and future CODEX-b. Asearchfor DarkMatterfrom Λ𝑏 decays is performedwithintheLHCbexperiment during the LHC Run II at a center of mass energy of √𝑠=13 TeV. Two dark matter operators are studied, 𝒪𝑐𝑑(¯ 𝑏→𝜓DM𝑐𝑑) and 𝒪𝑐𝑠(¯ 𝑏→𝜓DM𝑐𝑠) with 0.940 GeV/c2< 𝑚(𝜓DM)<4.430 GeV/c2 , respectively. The Λ𝑏 baryons originate in Σ(∗) 𝑏 decays. Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾) and Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾) are the final observed states. No signal is observed in any of the studied decay modes and the following upper limits are set for the first time: ℬ(𝒪𝑐𝑠(¯ 𝑏→𝜓DM𝑐𝑠)) <8.96 ×10−5−6.23 ×10−4 for 0.940 GeV/c2<𝑚(𝜓DM)<3.0GeV/c2 and ℬ(𝒪𝑐𝑑(¯ 𝑏→𝜓DM𝑐𝑑)) <2.45 ×10−4− 8.25 ×10−5for 0.940 GeV/c2<𝑚(𝜓DM)<3.5GeV/c2at 95% CL. Within the CODEX-b, some studies for potential long lived particles searches are performed. A generator level efficiency for three different production modes (inclusive, Higgs-strahlung and weak-boson fusion) is computed in the framework of the CODEX-b experiment assuming a minimal Higgs portal model. These Higgs production modes are the dominant ones, while the Higgs portal decay models show a minimal decay model that would allow for future searches within the CODEX framework. This two experiments could also work together for collaborative searches, as showcased in this work. v Limiar Este traballo presenta estudos de física alén do modelo estándar, usando dous experimentos diferentes, LHCb e o futuro CODEX-b. Realizouse unha busca de materia escura a partir de desintegracións de Λ𝑏 recollidas polo experimento LHCb durante a Run II do LHC a unha enerxía no centro de masas de √𝑠=13 TeV. Estudáronse dous operadores de materia escura, 𝒪𝑐𝑑(¯ 𝑏→ 𝜓DM𝑐𝑑) e 𝒪𝑐𝑠(¯ 𝑏→𝜓DM𝑐𝑠) , con masas 0.940 GeV/c2<𝑚(𝜓DM)<4.430 GeV/c2 , respectivamente. Os barións Λ𝑏 orixínanse en desintegracións de Σ(∗) 𝑏 . Λ𝑏→ 𝜓DM𝐾(𝐷→𝜋𝜋𝐾) e Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾) son os estados finais observados. Non se observou sinal en ningún dos modos de desintegración estudados e establécense por primeira vez os seguintes límites superiores: ℬ(𝒪𝑐𝑠(¯ 𝑏→𝜓DM𝑐𝑠)) <8.96 ×10−5− 6.23 ×10−4 para 0.940 GeV/c2<𝑚(𝜓DM)<3.0GeV/c2 e ℬ(𝒪𝑐𝑑(¯ 𝑏→𝜓DM𝑐𝑑)) < 2.45 ×10−4−8.25 ×10−5para 0.940 GeV/c2<𝑚(𝜓DM)<3.5GeV/c2ao 95% CL. Nomarcode CODEX-b, realízanseestudos para potenciaisbúsquedasde partículas de vida media longa. Calculouse unha eficiencia a nivel de xerador para tres modos de produción diferentes (inclusivo, Higgs-strahlung e fusión de bosóns débiles) no marco do experimento CODEX-b supoñendo un modelo mínimo de portal de Higgs. Estes mecanismos de produción do Higgs representan os dominantes, mentres que os modelos portais de Higgs amosan un modelo mínimo que permitiría búsquedas destas partículas no detector CODEX-b. Estes dous experimentos tamén poderían utilizarse conxuntantamente para realizar diferentes búsquedas, como se amosa neste traballo. vi Resumen Este trabajo presenta estudios de física más allá del modelo estándar, usando dos experimentos diferentes, LHCb y el futuro CODEX-b. Se realiza una búsqueda de materia oscura a partir de desintegraciones de Λ𝑏 recogidas por el experimento LHCb durante el Run II del LHC a una energía en el centro de masa de √𝑠=13 TeV. Se estudian dos operadores de materia oscura, 𝒪𝑐𝑑(¯ 𝑏→𝜓DM𝑐𝑑) y 𝒪𝑐𝑠(¯ 𝑏→𝜓DM𝑐𝑠) con 0.940 GeV/c2<𝑚(𝜓DM)<4.430 GeV/c2 , respectivamente. Los bariones Λ𝑏 se originan en desintegraciones de Σ(∗) 𝑏 . Λ𝑏→ 𝜓DM𝐾(𝐷→𝜋𝜋𝐾) y Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾) son los estados finales observados. No se observa señal en ninguno de los modos de desintegración estudiados y se establecen los siguientes límites superiores por primera vez: ℬ(𝒪𝑐𝑠(¯ 𝑏→𝜓DM𝑐𝑠)) < 8.96 ×10−5−6.23 ×10−4 para 0.940 GeV/c2<𝑚(𝜓DM)<3.0GeV/c2 y ℬ(𝒪𝑐𝑑(¯ 𝑏→ 𝜓DM𝑐𝑑)) <2.45 ×10−4−8.25 ×10−50.940 GeV/c2<𝑚(𝜓DM)<3.5GeV/c2 al 95% CL. Se calcula la eficiencia a nivel de generador para tres modos de producción diferentes (inclusivo, Higgs-strahlung y fusión de bosón débil) en el marco del experimento CODEX-b asumiendo un modelo de portal de Higgs mínimo. Estos mecanismos de producción de Higgs representan los dominantes, mientras que los modelos portales de Higgs suponen un modelo mínimo que permitiría búsquedas de estas partículas en el detector CODEX-b. Estos dos experimentos también podrían utilizarse conjuntamente para realizar diferentes búsquedas, como se muestra en este trabajo. vii Acknowledgements A cantidade de xente que me levo destes anos roza o inumerable, pero creo que comezar cos meus pais, Muchi e Camilo, é o mellor punto, xa que sen o seu apoio e educación, e contra vento e marea, sería imposible que eu puidese escribir isto. Agradecer tamén aos meus directores, Xabi e Carlos, pola guía neste traballo, así tamén aos meus titores na sombra Adrián e Alexandre, sen os cales non podería nunca ter feito esta tese; e Emilio e Miguel, polo código compartido. Por suposto incluir tamén a inestimable axuda académica e persoal de todos os compañeiros do despacho 26: Moncho, Pablo e Asier (o compi de piso máis chill que ninguén podería desexar) que acompañaron todos estes anos e aos achegados, que tiveron a sorte de rematar antes: Dulla, Gabis, Gonzalo e Marcos. E ás persoas que aguantaron o verán en Suíza, facendo del algo máis ameno: Eloi e Erl. Tampouco isto sería posible sen os descansos para os cafés, que comezaron cun grupo modesto e rematou por ser un grupo de amizades do que sigo e seguirei a desfrutar: Clara, Juan, Martina, Miguel e especialmente Arnau; e ás novas fichaxes que toman o relevo: Bea, David, Fran e Carmen. Julián, Alicia, Martín e Xoán, tamén abonados aos cafés pero tamén a moitas mais cousas fóra, moitas grazas por todos estes anos ao voso carón, así como para os que non estaban nos cafés pero si en todo o demáis: Carol, Cris, Antía, Sergio, Mar, Diego, Tomás, Juanma, Rocío, Kiara, Iago, Aitor, Eugenia, María, Pedrito, Saruki, Sampi... e persoas que inevitablemente estou a olvidar e pido desculpas por iso. No ámbito persoal e non académico, Xabi, mereces unha mención máis especial xa que penso que confiaches máis en min durante estes anos máis do que eu o fixen; grazas por iso. E ás dúas persoas que mais me apoiaron e nas que máis me apoiei durante todos estes anos, Verónica e Carlos, os meus pronomes favoritos, non teño palabras para plasmar aquí todo que sinto por vos, a moita felicidade que me produce cada intre que pasamos xuntos e o moi querido que me sinto. Sodes unhas persoas totalmente excepcionais e o agradacemento que sinto é infinito. Por último, á persoa que me quixo nas últimas etapas máis duras e insufribles, onde cada día era peor que o anterior excepto por ti, que pinta todo dunha cor máis bonita e que sempre pensou que podía conseguir todo, ainda que non fose así ás veces, grazas, por todo, Fermín. viii List of Figures 1.1 SM transition of a 𝑠 quark to a 𝑢 quark via 𝑊− emission. The full decay would be Λ→𝑝𝜇−¯ 𝜈𝜇........................ 2 1.2 Diagram of the proposed model and how it ensures the Sakharov conditions. The figure has been adapted from [18]. . . . . . . . . . . 6 1.3 The two decays that will be studied in this work. Any of them could be enough to a successful explanation of the model provided that its BR is large enough. The first one is the one associated with the 𝒪𝑐𝑑 operator whereas the second is related to 𝒪𝑐𝑠.............. 8 1.4 Current limits on inclusive Br( 𝐵→ ℬ𝜓DMℳ ) as a function of the DM particle 𝜓DM constrained by the recast of a search conducted by ALEPH as well as indirect searches from ATLAS and CMS for particles similar to the propagator of the model (TeV-scales colortriplet scalars). The excluded area would be the lightest coloured one. Figure obtained from [18] under Creative Commons license. . . . . 10 1.5 ℒ ⊃ 𝐴𝑆𝑆𝐻†𝐻 associated diagram where the parameter 𝐴𝑆 has already been substituted by a mixing angle and the 𝑆 field identified with the 𝐴0 particle has inherited the fermionic decay of the SM Higgs. 12 1.6 Main production modes of the SM Higgs: Higgs-strahlung (left), weak-boson fusion (right) and gluon-gluon fusion (bottom). . . . . 13 1.7 Diagram of potential physics cases covered by current, proposed and future experiments depending on the LLP mass, lifetime or allowedCenter-of-Massenergy. Reproducedfrom[33]underCreative Commonslicense.............................. 14 3.1 Diagram ofa potential locationforthe CODEX-b detectorin relationto the LHCb detector. Reproduced from [33] under Creative Commons license. ................................... 18 3.2 Cern accelerator complex diagram taken from [61] under Creative Commons licensing. Many of the experiments of the institution are also shown in this diagram. . . . . . . . . . . . . . . . . . . . . . . . 20 3.3 Diagram of the LHCb detector with the described components. Taken from [80] under Creative Commons License. . . . . . . . . . . . . . 22 ix 3.4 Schedule of the LHC data taking periods. LHC Run 1 took place from 2011 to 2013 and Run 2 from 2015 to 2018. Taken from [81] under Creative Commons License. . . . . . . . . . . . . . . . . . . . 23 5.1 Efficiencies plot for all detection modes described. Both axes are in logarithmic scale, and no event with both 𝐴0in CODEX is found. . 31 5.2 Efficiencies plot for the detection modes described for the Higgsstrahlung production. Both axes are in logarithmic scale. . . . . . . 32 5.3 Efficiencies plot for the described detection modes for the jets associated production mode. Both axes are in logarithmic scale. Note that almost no events with two jets in CODEX are produced since the requirements of detection are very tough. . . . . . . . . . . . . . . . 33 5.4 Efficiencies plot (right) and expected events (left) to be detected at the CODEX-b experiment for a ℒ=300 fb−1. ............. 34 6.1 Diagram of the Run 2 trigger configuration. Taken from [106] under Creative Commons License. . . . . . . . . . . . . . . . . . . . . . . . 45 6.2 Histogram with the importance of each of the features used in the first iteration of the BDT in the Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾)) decay. No Σ±(∗) 𝑏 tagging particles are used in the BDT. piminus1,2 and Kplus variables are related to the 𝐷 daughters, and the Ksoft variables refer to the Λ𝑏 daughter. A 𝑚(𝜓DM)=940 MeV MC sample isused. ................................... 48 6.3 Distributions of signal and background variables of every feature used in the classifier. The label on top of each subplot indicates the variable plotted in each one. Every plot has arbitrary units on the y-axis..................................... 49 6.4 Correlation matrix for the most relevant variables used to train the BDT for the Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾)) decay using a 𝑚(𝜓DM)=940 MeV............................. 50 6.5 Histogram with the importance of each of the features used in the second iteration of the BDT for the Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→ 𝜋𝜋𝐾)) decay using a 𝑚(𝜓DM)=940 MeV. ............... 51 6.6 Performance of the classifier for the train/test samples for the Σ±(∗) 𝑏→ 𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾)) decay using a 𝑚(𝜓DM)=940 MeV. . . 52 6.7 ROC curve obtained for the BDT using a train/test method for the Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾)) decay using a 𝑚(𝜓DM)=940 MeV...................................... 52 6.8 Effect of different BDT cuts over the background of this analysis. No fake peaking structures appear for a wide range of this classifier cut. 53 xvi 6.1 Generator level cuts imposed over the particles of the Σ±(∗) 𝑏→ 𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾)) . The subindex in each particle indicates the mother of the semi-stable particles. 𝜂 is the pseudorapidity of the particle, this requirement is imposed due to LHCb being a forward region detector [100]. An additional condition of truth matching via TRUEID [101] is applied. This is, the MC flag for the ID of the particle is required to be the same in the reconstructed and in the generated decays. This is something not achievable in the real reconstruction. 37 6.2 Generator level cuts imposed over the particles of the Σ±(∗) 𝑏→ 𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) and Σ±∗ 𝑏→𝜋±(Λ𝑏→Λ0𝜋(𝐷→𝐾𝜋𝜋)) . The subindex in each particle indicates the mother of the semi-stable particles. All particles are truth matched. . . . . . . . . . . . . . . . 38 6.3 Generator level cuts imposed over the particles of the Σ±∗ 𝑏→𝜋± ( Λ𝑏→ 𝜋(Λ𝑐→𝑝𝐾𝜋) ). The subindex in each particle indicates the mother of the semi-stable particles. Every particle is truth matched. . . . . . 38 6.4 Generator level efficiencies of every signal mode. The normalisation channel generator level efficiency is independent of the DM particle mass. The masses are given in GeV. Only one mass has been generated so far for the Σ± 𝑏 decays, and that is the one used in the whole analysis. 39 6.5 Reconstruction efficiency table for the Σ±∗ 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→ 𝜋𝜋𝐾)) and Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) decay modes. It is clear that a mass dependency exists in this case. . . . . . . . . . . . . 40 6.6 Stripping line for Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾) , LambdaDecaysDMLambdaToDKLine . The subindex of the 𝐾 and 𝜋 particles indicates its direct ascendant. As mentioned, the cuts for Stripping34r0p3 are also those for Stripping29r2p3 and Stripping28r2p3 . The misalignment in the cuts is expected to not affect much, the difference in value is not big and does not affect many variables, in fact it only affects three of them (four in reality, since there are two 𝜋− 𝐷): 𝜋− 𝐷(𝑝𝑇), Λ0 𝑏(IP𝜒2OWNPV) and 𝐾+ 𝐷(𝑝𝑇). . 41 6.7 Stripping line for Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾) , LambdaDecaysDMLambdaToDPiLine . The subindex of the 𝐾 and 𝜋 particles indicates its direct ascendant. As mentioned, the cuts for Stripping34r0p3 are also those for Stripping29r2p3 and Stripping28r2p3 . As shown in this table, no misalignment had to be fixed for this line in particular. . . . . . . . . . . . . . . . . . . . . 42 6.8 Stripping efficiency table for the Σ±∗ 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→ 𝜋𝜋𝐾)) and Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) decay modes. It is clear that a mass dependency exists in this case. . . . . . . . . . . . . 43 xvii 6.9 Efficiencies table for the Σ±∗ 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) decay mode. The three trigger stages requirements are TOS. The efficiencies are calculated in a sequential way, this being, the HLT1 efficiencies are calculated over the events that passed the L0 selection, this also applies to the HLT2 efficiency with respect to the HLT1 efficiency. . 47 6.10 Efficiencies table for the Σ±∗ 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾)) decay mode. The three trigger stages requirements are TOS. The efficiencies are calculated in a sequential way, this being, the HLT1 efficiencies are calculated over the events that passed the L0 selection, this also applies to the HLT2 efficiency with respect to the HLT1 efficiency. . 47 6.11 Scoresobtained usinga k-foldcross-validationmethod for the Σ±(∗) 𝑏→ 𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾)) decay using a 𝑚(𝜓DM)=940 MeV. . . 50 6.12 Scoresobtained usinga k-foldcross-validationmethod for the Σ±(∗) 𝑏→ 𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) decay using a 𝑚(𝜓DM)=940 MeV. . . 51 6.13 Efficiencies table for the Σ±∗ 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾)) and Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) decay modes. The BDT cuts are applied in a sequential way, this being, the BDT efficiencies are calculated over the events that passed the stripping and trigger selection. .................................. 60 6.14 Efficiencies table for the Σ±∗ 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾)) and Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) decay modes. . . . . . . . . . 60 6.15 Efficiencies table for the Σ±∗ 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾)) and Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) decay modes. The 𝑑>0 cuts are applied in a sequential way, this being, the 𝑑>0 efficiencies are calculated over the events that passed the stripping, the trigger selection and the BDT cut. . . . . . . . . . . . . . . . . . . . . . . . . 62 6.16 Efficiencies table for the Σ±∗ 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾)) and Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) decay modes. The 𝑚min cuts are applied in a sequential way, this being, the 𝑚min efficiencies are calculated over the events that passed the stripping, the trigger selection, the BDT cut and the tagging cut. . . . . . . . . . . . . . . . 63 6.17 Table with the fit results of the Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→ 𝜋𝜋𝐾)) decay mode. The model used for the signal is the one shown in Equation (6.11) extended to the events of the simulation, so the integral over the full model does not add to one but to the 𝑁sig parameterinstead.............................. 68 xviii 6.18 Table with the fit results of the Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→ 𝜋𝜋𝐾)) decay mode. The model used for the signal is the one shown in Equation (6.11) extended to the events of the simulation, so the integral over the full model does not add to one but to the 𝑁sig parameterinstead.............................. 69 6.19 Table with the fit results of the Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→ 𝜋𝜋𝐾)) decay mode. The full model is taken into account as shown in Equation (6.16). The tail parameters are those in Table 6.17. Different amounts of the signal to background ratio are studied, and it is shown that the fitter shows a better convergence consistency when 𝑁sig 𝑁bkg ≈1. 70 6.20 Table with the fit results of the Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→ 𝜋𝜋𝐾)) decay mode. The full model is taken into account as shown in Equation (6.16). The tail parameters are those in Table 6.18. Different amounts of the signal to background ratio are studied, and it is shown that the fitter shows a better convergence consistency when 𝑁sig 𝑁bkg ≈1. 71 6.21 Results of the fits performed to a gaussian of all the pseudoexperiments computed for the Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→ 𝜋𝜋𝐾)) decay................................. 72 6.22 Results of the fits performed to a gaussian of all the pseudoexperiments computed for the Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→ 𝜋𝜋𝐾)) decay. In this case some higher and lower limits of 𝑁fit were studied to check if some dependency around this input arose, butitdidnot................................. 73 6.23 Generator level cuts imposed over the particles of the Σ±∗ 𝑏→𝜋± ( Λ𝑏→ 𝜋(Λ𝑐→𝑝𝐾𝜋) ). The subindex in each particle indicates the mother of the semi-stable particles. An additional condition of truth matching via TRUEID [101] is applied. . . . . . . . . . . . . . . . . . . . . . . . 74 6.24 Scores obtained using a k-fold cross-validation method for the normalisation decay classifier. . . . . . . . . . . . . . . . . . . . . . . . . 76 6.25 Results of the full model fit performed to an exponential background modulated by a power law to describe the background and two relativistic Breit-Wigner describing the two components of the signal. 84 6.26 Computed expected limit for both decay modes and every mass. . . 85 6.27 Calculated values of ℬsignal for each mass and decay mode. . . . . . 86 6.28 Calculated values of ℬsignal for each mass and decay mode adjusted toluminosity................................. 88 7.1 Table with all of the efficiencies computed for the Σ±(∗) 𝑏→𝜋±(Λ𝑏→ 𝜓DM𝐾(𝐷→𝜋𝜋𝐾)) Dark matter and B-mesogenesis LHCb search. . 89 xix 7.2 Table with all of the efficiencies computed for the Σ±(∗) 𝑏→𝜋±(Λ𝑏→ 𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) Dark matter and B-mesogenesis LHCb search. . 90 7.3 Calculated values of ℬsignal for each mass and decay mode extrapolated to total luminosity. . . . . . . . . . . . . . . . . . . . . . . . . . 90 7.4 Number of events expected for all detection modes described for every studied production mode. Lifetimes are given in terms of 𝑐𝜏 andinmeters. ............................... 90 B.1 Desintegracións máis lixeiras e diferencias de masas obtidas no modelo. Para cada operador particular as fraccións de desintegración que esperamos atopar son similares, xa que o espazo fásico é similar. Máis mesóns lixeiros poderían aparecer nos estados finais, unicamente cambiando a diferencia de masa e cunha supresión na fracción de desintegración. Adaptado de [18]. . . . . . . . . . . . . . . . . . . . . 107 B.2 Eventos esperados para todos os modos de produción e detección descritos. As vidas medias 𝑐𝜏están en metros. . . . . . . . . . . . . 112 B.3 Resultados obtidos para todas as masas para o modo de desintegración de Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)). . . . . . . . . . . . 115 B.4 Resultados obtidos para todas as masas para o modo de desintegración de Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾)). . . . . . . . . . . . 116 B.5 Resultados obtidos da canle de normalización. . . . . . . . . . . . . 116 B.6 Valores de ℬsignal para todas as masas e modos de desintegración. . 116 B.7 Táboa con todas as eficiencias da desintegración Σ±(∗) 𝑏→𝜋±(Λ𝑏→ 𝜓DM𝐾(𝐷→𝜋𝜋𝐾)). ............................ 118 B.8 Táboa con todas as eficiencias da desintegración Σ±(∗) 𝑏→𝜋±(Λ𝑏→ 𝜓DM𝜋(𝐷→𝜋𝜋𝐾)). ............................ 118 xx Contents Abstract iv Limiar v Resumen vi Acknowledgements vii 1 Introduction 1 1.1 The Standard Model of Particle Physics . . . . . . . . . . . . . . . . . . 1 1.2 CKMmatrix ................................. 2 1.3 Dark Matter and B-mesogenesis . . . . . . . . . . . . . . . . . . . . . . 4 1.3.1 Foundations of the 𝐵-mesogenesis ................ 6 1.3.2 Formal description and kinematic constraints . . . . . . . . . . 7 1.3.3 Dark matter operators and allowed decays . . . . . . . . . . . 8 1.3.4 Current experimental status . . . . . . . . . . . . . . . . . . . . 9 1.4 BSM long lived particles . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4.1 Simplified models studied . . . . . . . . . . . . . . . . . . . . . 11 1.4.2 State-of-the-art on BSM LLP searches . . . . . . . . . . . . . . 13 2 Objectives 15 3 Experimental setup 17 3.1 CODEX-bexperiment............................ 17 3.1.1 CODEX-bdetector ......................... 17 3.2 LHCbexperiment.............................. 19 3.2.1 The Large Hadron Collider . . . . . . . . . . . . . . . . . . . . 19 3.2.2 The LHCb experiment . . . . . . . . . . . . . . . . . . . . . . . 20 The LHCb subdetectors . . . . . . . . . . . . . . . . . . . . . . 21 Stripping............................... 23 Simulation.............................. 23 4 Methodology 25 xxi 4.1 LHCbsearch................................. 25 4.2 CODEXefficiency.............................. 27 5 CODEX-b studies 29 5.1 MonteCarlosamples............................ 29 5.2 Generator level efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . 30 5.2.1 Inclusive production . . . . . . . . . . . . . . . . . . . . . . . . 30 5.2.2 Higgs-strahlung........................... 31 5.2.3 Weak-boson fusion . . . . . . . . . . . . . . . . . . . . . . . . . 32 5.3 Results .................................... 33 6 Dark matter and B-mesogenesis 35 6.1 Data and Monte Carlo Samples . . . . . . . . . . . . . . . . . . . . . . 35 6.1.1 Recorded data samples . . . . . . . . . . . . . . . . . . . . . . . 35 6.1.2 MCsamples............................. 36 6.2 Selection ................................... 38 6.2.1 Generator level selection . . . . . . . . . . . . . . . . . . . . . . 38 6.2.2 Reconstruction............................ 39 6.2.3 Stripping Selection . . . . . . . . . . . . . . . . . . . . . . . . . 40 StrippingVariables ......................... 43 6.2.4 TriggerSelection........................... 44 Trigger independent of signal / Trigger on Signal . . . . . . . 44 L0Trigger .............................. 45 HLT1Trigger ............................ 46 HLT2Trigger ............................ 46 6.2.5 Multivariate Classifier . . . . . . . . . . . . . . . . . . . . . . . 46 6.2.6 Totalefficiencies........................... 55 6.3 Tagging.................................... 61 6.3.1 Mathematical description . . . . . . . . . . . . . . . . . . . . . 61 6.3.2 Taggingefficiency.......................... 62 6.3.3 𝑚min computation.......................... 62 6.4 Massfit.................................... 64 6.4.1 Mathematical description . . . . . . . . . . . . . . . . . . . . . 64 6.4.2 Fittingbasis ............................. 65 6.4.3 Massmodel ............................. 66 6.4.4 Signalfit ............................... 68 6.4.5 Fullmodelfit ............................ 69 6.4.6 Toys.................................. 71 6.5 Normalisation channel . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 6.5.1 Generator level selection . . . . . . . . . . . . . . . . . . . . . . 74 6.5.2 Reconstruction and stripping . . . . . . . . . . . . . . . . . . . 74 6.5.3 Trigger ................................ 75 xxii 6.5.4 Multivariate classifier . . . . . . . . . . . . . . . . . . . . . . . . 75 6.5.5 Fit for normalisation channel . . . . . . . . . . . . . . . . . . . 82 6.5.6 𝑁(Σ±(∗) 𝑏)computation........................ 83 6.6 Limits..................................... 84 6.6.1 Branching ratio limit . . . . . . . . . . . . . . . . . . . . . . . . 86 6.7 Backgrounds................................. 86 6.8 Results .................................... 88 7 Results and discussion 89 7.1 Dark matter and B-mesogensis results . . . . . . . . . . . . . . . . . . 89 7.2 Long lived particles results . . . . . . . . . . . . . . . . . . . . . . . . . 90 7.3 Discussion .................................. 91 8 Conclusions 93 Appendices 95 A Appendix Analysis 97 A.1 Mass distributions for every dark matter mass . . . . . . . . . . . . . 97 A.2 Signal fits for every dark matter mass . . . . . . . . . . . . . . . . . . . 97 A.3 Pull plots for every dark matter mass . . . . . . . . . . . . . . . . . . . 101 B Resumo 103 B.1 Introdución.................................. 103 B.1.1 MatrizCKM............................. 104 B.1.2 Materia escura e B-mesoxénese . . . . . . . . . . . . . . . . . . 105 Bases da B-mesoxénese . . . . . . . . . . . . . . . . . . . . . . . 105 Descripción formal e restricións cinemáticas . . . . . . . . . . 105 Operadores de materia escura e desintegracións permitidas . 106 Estado experimental actual . . . . . . . . . . . . . . . . . . . . 107 B.1.3 Partículas de vida media longa . . . . . . . . . . . . . . . . . . 108 Modelos de vida media longa . . . . . . . . . . . . . . . . . . . 109 Estado experimental actual . . . . . . . . . . . . . . . . . . . . 109 B.2 Obxectivos.................................. 109 B.3 Montaxe experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 B.3.1 Experimento CODEX-b . . . . . . . . . . . . . . . . . . . . . . . 110 B.3.2 Experimento LHCb . . . . . . . . . . . . . . . . . . . . . . . . . 110 B.4 Metodoloxía ................................. 111 B.5 Partículas de vida media longa . . . . . . . . . . . . . . . . . . . . . . 111 B.6 Materia escura e B-mesoxénese . . . . . . . . . . . . . . . . . . . . . . 112 B.6.1 Datos e Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . 112 B.6.2 Selección............................... 113 xxiii Selección de Stripping . . . . . . . . . . . . . . . . . . . . . . . 113 Selección do disparador . . . . . . . . . . . . . . . . . . . . . . 113 Clasificador multivariante . . . . . . . . . . . . . . . . . . . . . 113 B.6.3 Etiquetado.............................. 114 B.6.4 Axusteámasa............................ 115 B.6.5 Canle de normalización . . . . . . . . . . . . . . . . . . . . . . 115 B.6.6 Límites................................ 116 B.6.7 Fondos................................ 117 B.7 Resultados e discusión . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 B.7.1 Resultados da materia escura e B-mesoxénese . . . . . . . . . . 117 B.7.2 Resultados das partículas de vida media longa . . . . . . . . . 118 B.7.3 Discusión............................... 118 B.8 Conclusións ................................. 119 1 Chapter 1 Introduction 1.1 The Standard Model of Particle Physics The Standard Model of particle physics (SM) [1 – 4] has proven itself to be an exceptionally effective theory to describe and predict the observed subatomic particles and how they interact with each other. Numerous testing has been performed at different particles colliders and no physics beyond it has been found yet. On the other hand, evidence from astrophysics and cosmology supports the standard cosmological model: this theory suggests that the intensely hot early Universe [5] was preceded by a period of rapid inflationary growth [6,7], offering an explanation for the early stages of the Universe and its subsequent development. These two very successful models are inconsistent with each other and common ground does not seem to be found at first glance, indicating the necessity for new physics phenomena beyond the Standard Model (BSM). Up-to-date precise measurements of the cosmos indicate that approximately 16% of the universe’s matter is composed of ordinary (baryonic) matter [8,9], with the remaining 84% being attributed to an as-yet unidentified component known as dark matter (DM) [8,9]. The SM of particle physics has not been able to provide any potential dark matter candidate, nor a mechanism for its production [10 – 12]. Additionally, the Standard Model fails to account for the observed asymmetry between matter and antimatter in the universe. According to SM predictions, a universe originating from a hot Big Bang and governed solely by SM physics should contain less different amounts of matter and antimatter. This discrepancy necessitates the proposal of an alternative mechanism, commonly referred to as baryogenesis (or mesogenesis when specifically discussing mesons), to explain the imbalance. Both terms, baryogenesis and mesogenesis, revolve around the same fundamental concept aimed at addressing this critical issue. This observation arises due to the 𝐶 and 𝑃 operators. The 𝐶 operator, or charge operator, changes every particle by its anti-particle, while the 𝑃 operator, or parity operator, changes the sign of the position quantity: ® 𝑥→ −® 𝑥 . The 𝐶𝑃 is the product of these two operators and due to some particles not being eigenstates of it, a matter-antimatter asymmetry arises. 8Chapter 1. Introduction Figure 1.3: The two decays that will be studied in this work. Any of them could be enough to a successful explanation of the model provided that its BR is large enough. The first one is the one associated with the 𝒪𝑐𝑑 operator whereas the second is related to 𝒪𝑐𝑠. 1.3.3 Dark matter operators and allowed decays As mentioned, for 𝐵→ ℬ𝜓DMℳ to exist a BSM TeV-scale bosonic mediator is required [18]. This 𝑌 mediator would be a colour-triplet scalar that couples the dark sector to the SM sector. An effective Lagrangian for this kind of coupling can be written as follows: ℒeff =𝒪𝑢𝑖𝑑𝑗 𝑦𝑖𝑦𝑗 𝑀2 𝑌 ,(1.16) where Einstein summation convention has been used, and 𝑦𝑖𝑦𝑗 is the product of the coupling referred to the 𝑖 -quark and 𝑗 -quark. This kind of Lagrangian allows for four different possible operators 𝒪𝑖𝑗 that can act over any 𝑏-quark: 𝒪𝑢𝑑 =𝜓DM 𝑏 𝑢 𝑑, (1.17a) 𝒪𝑢𝑠 =𝜓DM 𝑏 𝑢 𝑠, (1.17b) 𝒪𝑐𝑑 =𝜓DM 𝑏 𝑐 𝑑, (1.17c) 𝒪𝑐𝑠 =𝜓DM 𝑏 𝑐 𝑠. (1.17d) These operator would allow the decay of anti𝑏 quarks contained by the 𝐵 mesons and baryons to decay into two lighter quarks and a dark antibaryon ¯ 𝜓DM . The lightest possible hadronic decays allowed by the introduction of this operator are listed in Table 1.1. It is important to note that in this work only 𝒪𝑐𝑑 and 𝒪𝑐𝑠 are being studied, and due to some considerations that will be discussed later, a heavier case will be the chosen one for 𝒪𝑐𝑑. In particular, the search in this work will be performed over the decays in Figure 1.3. Note that one of them is not the lightest search one can perform. 1.3. Dark Matter and B-mesogenesis 9 Operator and Decay Initial state Final state ∆M (MeV) 𝐵𝑑𝜓DM +𝑛(𝑢𝑑𝑑)4340.1 𝒪𝑢𝑑 =𝜓DM 𝑏 𝑢 𝑑 𝐵𝑠𝜓DM +Λ(𝑢𝑑𝑠)4251.2 ¯ 𝑏→𝜓DM 𝑢 𝑑 𝐵+𝜓DM +𝑝(𝑑𝑢𝑢)4341.0 Λ𝑏¯ 𝜓DM +𝜋05484.5 𝐵𝑑𝜓DM +Λ(𝑢𝑠𝑑)4164.0 𝒪𝑢𝑠 =𝜓DM 𝑏 𝑢 𝑠 𝐵𝑠𝜓DM +Σ0(𝑢𝑠𝑠)4025.0 ¯ 𝑏→𝜓DM 𝑢 𝑠 𝐵+𝜓DM +Σ+(𝑢𝑢𝑠)4090.0 Λ𝑏¯ 𝜓DM +𝐾05121.9 𝐵𝑑𝜓DM +Λ𝑐+𝜋−(𝑐𝑑𝑑)2853.6 𝒪𝑐𝑑 =𝜓DM 𝑏 𝑐 𝑑 𝐵𝑠𝜓DM +Σ0 𝑐(𝑐𝑑𝑠)2895.0 ¯ 𝑏→𝜓DM 𝑐 𝑑 𝐵+𝜓DM +Λ+ 𝑐(𝑑𝑐𝑢)2992.9 Λ𝑏¯ 𝜓DM +𝐷03754.7 𝐵𝑑𝜓DM +Σ0 𝑐(𝑐𝑠𝑑)2807.8 𝒪𝑐𝑠 =𝜓DM 𝑏 𝑐 𝑠 𝐵𝑠𝜓DM +Ω𝑐(𝑐𝑠𝑠)2671.7 ¯ 𝑏→𝜓DM 𝑐 𝑠 𝐵+𝜓DM +Σ+ 𝑐(𝑐𝑠𝑢)2810.4 Λ𝑏¯ 𝜓DM +𝐷−+𝐾+3256.2 Table 1.1: Lightest decay processes and their mass differences that would allow baryogenesis and dark matter production. It must be noted that, given a particular operator, the decay rate for each of the allowed modes is expected to be similar since no big differences in phase space suppression are present. More light mesons would be allowed in final states and different quark groups may be studied, this would only translate into a proportional phase space suppression depending on the Δ𝑀 of the new final states proposed. Adapted from [18] under Creative Commons license. To wrap up this introduction, the two searches that will be conducted are Λ0 𝑏→𝜓DM𝜋+(𝐷−→𝜋−𝜋−𝐾+) (second lightest decay for 𝒪𝑐𝑑 , not a big suppression to be expected, if any), and Λ0 𝑏→𝜓DM𝐾+(𝐷−→𝜋−𝜋−𝐾+)(lightest decay for 𝒪𝑐𝑑). 1.3.4 Current experimental status Not many direct searches of the particular signatures mentioned have been performed at colliders or 𝐵 -factories. As a matter of fact, at the present moment, this is the second work that searches for these signatures in general, being the first one conducted by the BaBar Collaboration. 10 Chapter 1. Introduction Figure 1.4: Current limits on inclusive Br( 𝐵→ ℬ𝜓DMℳ ) as a function of the DM particle 𝜓DM constrained by the recast of a search conducted by ALEPH as well as indirect searches from ATLAS and CMS for particles similar to the propagator of the model (TeV-scales color-triplet scalars). The excluded area would be the lightest coloured one. Figure obtained from [18] under Creative Commons license. One direct search of 𝐵→Λ𝜓DM has been performed by BaBar collaboration finding a nonsignificant signal sensitivity and setting a limit to the branching fraction from 0.13 to 5.2×10−5 for 1.0<𝑚𝜓DM <4.2GeV/c2 at a 90% CL [26]. The BaBar collaboration also performed another direct search of 𝐵+→𝜓DM +𝑝 where no significant signal is found and limits to the branching fraction in the range from 10−7 to 10−5 for 1.0<𝑚𝜓DM <4.3GeV/c2 at a 90% CL [27] are set. These two searches set a constraint to one of the four operators allowed by this model. Indirect searches from CMS [28] and ATLAS [29], as well as recasts from ALEPH [30] allow to set some upper limits of around 10−3 to the other three operators mentioned in this work. The summary from these works are the limits shown in Figure 1.4 1.4. BSM long lived particles 11 1.4 BSM long lived particles Other extensions proposed to the Standard Model are those involving long lived particles (LLPs), which are defined as particles with lifetimes (usually measured in terms of 𝑐𝜏 ) larger than most of those within the SM. It is important to note that not every LLP is a Beyond Standard Model particle, since some of the most studied mesons in colliders are LLPs, such as 𝜇± , 𝜋± or 𝜋0 , or even the neutron, 𝑛 , with a 𝑐𝜏∼1011 m, among others. It is possible to extend the Standard Model in many directions, and some of these extensions require of new LLPs to work. Notably, some supersymmetric models may hint towards the existence of these particles, such as those with decouples supersymmetric scalars or decays to gravitino (the proposed supersymmetric partner of the graviton) suppressed by SUSY-breaking scale [31,32]. Other models, such as the ones studied in this work, are the so-called hidden sector models, accessible via Higgs-portal, that allows Higgs bosons to decay into a whole new zoo of particles. 1.4.1 Simplified models studied As mentioned, LLPs may arise from different theoretical models, since the landscape for this field is vast and rich, with a significant amount of theories proposing BSM LLPs from different mechanisms. In this work, one possibility is studied, this being a certain minimal model, a Higgs-portal model. In this case the SM Higgs, 𝐻0 is allowed to decay to a new BSM Higgs sector particles, in this work, a new scalar long-lived particle, 𝐴0[33]. An Allowed minimal operator describing this could be: 𝑆𝐻𝐻† , 𝑆2𝐻𝐻† where H is the SM Higgs field doublet and S is the new scalar particle field, that can be identified with the 𝐴0 field. Requiring the lagrangian density to be gauge invariant imposes the following form of the lagrangian: ℒ ⊃ 𝐴𝑆𝑆𝐻†𝐻+𝜆 2𝑆2𝐻†𝐻+... (1.18) wherearbitraryhigherdimensionoperatorswouldbeallowedbutwouldnotdominate the branching ratios. The LHCb experiment has constrained this model [34,35] and CODEX-b could potentially probe regions with smaller coupling constant and longer lifetimes. By replacing 𝐴𝑆 with a mixing angle sin 𝜃 of Higgs field with the new scalar field, it inherits every SM Higgs coupling [36], allowing it to decay to, for example, two muons, as it will be studied in this work. Every SM coupling would be suppressed by small enough values of sin 𝜃 . The SM couplings contribute to potential decays 12 Chapter 1. Introduction Figure 1.5: ℒ ⊃ 𝐴𝑆𝑆𝐻†𝐻 associated diagram where the parameter 𝐴𝑆 has already been substituted by a mixing angle and the 𝑆 field identified with the 𝐴0 particle has inherited the fermionic decay of the SM Higgs. of the S field and to its production cross-section. [37,38] The decays allowed by this mechanism and presented in this work can be seen in the diagram in Figure 1.5. In order to study this mechanism, three different Higgs production mechanism will be studied [39–41]: • inclusive production: widely dominated by gluon-gluon fusion, but every possible production cross-section predicted by the SM is considered. In this mechanism two different cases will be studied: a single detection of one 𝐴0 in the CODEX volume, and a second case where one 𝐴0 is detected in the CODEX volume while the other is detected in the LHCb. The gluon-gluon fusion diagram can be found in Figure 1.6 (bottom). • Higgs-strahlung: associated production mechanism of the Higgs boson with a gauge boson. The signature of this events is the detection of one 𝐴0 in the CODEX volume while a 𝜇 generated in the decay of the 𝑍0 or 𝑊± and it is detected in LHCb. The associated Feynman diagram is shown in Figure 1.6 (left). • weak-boson fusion: in this production mechanism, two vector bosons ( 𝑊±𝑊∓ or 𝑍0𝑍0 ) merge into a Higgs boson, which is produced together with hadronic jets. The signature of this mechanism is the detection of one 𝐴0 in CODEX and one jet in LHCb. The associated Feynman diagram is shown in Figure 1.6 (right). Data samples for these decay modes, as well as a generator level efficiency study is performed in this work. 1.4. BSM long lived particles 13 Figure 1.6: Main production modes of the SM Higgs: Higgs-strahlung (left), weak-boson fusion (right) and gluon-gluon fusion (bottom). 1.4.2 State-of-the-art on BSM LLP searches The main CERN experiments, even though the search of LLPs is not their main topic, have shown some results in studying some physics cases for LLPs [42,43]. Accessing some regions of the parameter space at low LLP masses becomes very challenging for the main CERN detectors, due to the presence of an overwhelming background component populating the forward region. Some other beam dump experiments such as SHiP [44] or NA62 [45], or forward experiments like FASER [46] have access to said regions by using shielding that removes most of the SM background while having access to more boosted LLPs in a narrower cone. This allows great searches in the low mass region of the space parameter but the higher masses are extremely suppressed due to lower √𝑠 , this also has the additional drawback of not allowing any physics case of LLPs through heavy portals (LLPs that arise from heavy particles such as Higgs or W/Z bosons). The last case are transverse shielded detectors such as CODEX or ANUBIS, which both are expected to have great shielding that would allow to remove most of the SM background allowing for low mass LLPs searches by having a smaller solid angle, which drastically reduces the luminosity available. On the other hand, very high √𝑠 of proton-proton collisions at CERN would allow this experiments to probe many 14 Chapter 1. Introduction Figure 1.7: Diagram of potential physics cases covered by current, proposed and future experiments depending on the LLP mass, lifetime or allowed Center-of-Mass energy. Reproduced from [33] under Creative Commons license. portal physics through Higgs or Z decays. To sum up, the expected regions are those shown in Figure 1.7. 15 Chapter 2 Objectives This thesis has two main objectives: 1. Provide a brand new measurement for some dark matter decay modes described in Section 1.3.3 and aiming for a world-first measurement of these modes. For this the branching fraction of two decays will be measured: ℬ(Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾))) (2.1) ℬ(Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾))),(2.2) which are related to the 𝒪𝑐𝑠 and 𝒪𝑐𝑑 respectively. The introduction of the Σ𝑏 decay head is a new approach to these kind of measurements where a loss of signal efficiency is to be expected in a tradeoff for a significantly better background discrimination. In case of finding no significative signal over the background, an upper limit to thebranchingratioswillbeset, which isexpectedtobea worldbestmeasurement at the moment of writing. This is framed within the LHCb experiment at CERN, since its detectors and data will be used throughout most of the work. 2. The other main objective is to provide a generator level efficiency to some Higgs portal model, as stated in Sections 1.4 and 1.4.1. This is made within the CODEX-b collaboration, which is a project of a detector to be installed detector aiming to be a candidate to potentially study SM and BSM long lived particles, as it will be described in the experimental section. 17 Chapter 3 Experimental setup 3.1 CODEX-b experiment Current LHC experiments have shown immense ability and future potential in discovering new particles such as the Higgs boson [47,48] and its characterisation [40], or the discoveries of new and exotic resonances such as bound states of five quarks [49] and in general many other short range physics cases [50,51]. Not only SM searches have been done at the LHC but also some BSM physics have been studied, setting new limits to other physics cases [52]. All of these experiments excel at searches of SM and BSM signatures of particles with very short lifetimes [53 – 55]. Even though steps are being made, no change in the state of the art in the beyond standard model physics has been found in any of these experiments. A more novel approach some physicists are currently following is the search for long lived particles. These are, in general, BSM particles characterised by the wide variance that is present in their masses and lifetimes, providing current experiments of an almost impossible challenge of discovery. For this purpose new detectors have been proposed, such as the one that will be studied in this work, CODEX-b [33,56] but not exclusively since others exist such as Mathusla [57] or Anubis [58]. In the case of CODEX-b, it is expected to be a very general purpose detector for LLPs, being able to prove different physics cases such as: Abelian hidden sector, Scalar-Higgs portal (the one studied in this work), Axion-like particles... The physics cases studied by this experiment are expected to be out of reach for most of current detectors. Classical examples of SM LLP searches can also be probed at CODEX, such as 𝐾0 𝐿,𝜋, neutron and muon decays. 3.1.1 CODEX-b detector The proposed CODEX location is the room next to the LHCb experiment. About 25 meters from the interaction point of the LHCb. It would be formed by a volume of 10 m × 10 m × 10 m. Resistive Plate Chambers (RPCs) are the main tracking technology of the experiment [56]. Modules of RPCs (in the demonstrator two modules of 2 m × 24 Chapter 3. Experimental setup EvtGen is utilised to specifically induce the decay of certain particles into desired final states, which is crucial for studying rare decays. The interaction of particles with the detector’s described layers is modeled using Geant4, and the detector’s response is digitised. This information is then processed by software that simulates the Level 0 (L0) trigger response and applies the trigger decisions similar to those used on actual data, ensuring that both real and simulated data maintain a structurally comparable format. During Run 2, the simulation framework version known as Sim09 was in use, but it was updated to Sim10 in 2022, with the primary change being an upgrade from Geant4 version 9 to version 10. 25 Chapter 4 Methodology 4.1 LHCb search On the one hand, missing energy analyses are not the most popular ones at LHCb [82] due to not being a hermetic detector. As an immediate consequence of this, the total energy of an event is not a variable we can access. On the other hand, LHCb is an extremely suitable experiment to produce and study Λ0 𝑏 decays. This is due to the fact that 𝑏 -particles are produced at the impact point of the LHCb and decay within the VELO [83]. The Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾) and Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾) upper limits to the branching ratios will be obtained using as input the Run 2 data of 5.4fb −1 . Two stripping lines have been written in order to process the data from the collisions taken during 2016, 2017, and 2018. Each line corresponds to each one of the two decay modes that will be studied. One additional decay mode is considered: Λ𝑏→𝜋(Λ𝑐→𝑝𝐾𝜋) . This decay is used as a normalisation channel to measure the amount of Λ𝑏 produced, so the branching ratios can be computed as: ℬ(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) ∼ 𝑁(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) 𝑁(Λ𝑏),(4.1a) ℬ(Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾)) ∼ 𝑁(Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾)) 𝑁(Λ𝑏).(4.1b) Moreover, the searches that will be performed are Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→ 𝜋𝜋𝐾)) and Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾)) . This allows for a mass fit to a double crystal ball (DCB) [84] probability distribution function (PDF) and a better background discrimination. The downside to this methodology [85 – 88] is that many statistic is lost due to two main features: not all Λ𝑏 are produced in a Σ𝑏 decay, and one additional particle must be reconstructed (the 𝜋 from the Σ𝑏 ). This will be expanded in a latter section of this work. 26 Chapter 4. Methodology Bearing all of the above in mind, the analysis strategy can be described by the following steps: 1. Generate Monte Carlo (MC) samples of the signal decay modes, as well as from the normalisation channel that will be used in order to compute the DM branching ratios as previously stated. 2. Apply the selection described in the Section 6.2.3 to all the generated Monte Carlo (MC). The objective is suppressing all peaking backgrounds and an important amount of the combinatorial. 3. Apply a different selection to the normalisation channel since it has been obtained from an older stripping campaign. 4. Apply a full trigger-on-signal (or TOSTOSTOS) trigger selection in both signal channels as well as in the normalisation channel. 5. Perform a multivariate analysis (MVA) in both signal and normalistaion decays in order to be able to obtain a clean mass peak. 6. Obtain the kinematic variables associated with the methodology described in [85–88] and in Section 6.3 for the Σ(∗) 𝑏in the signal decays. 7. Reconstruct potential Σ(∗) 𝑏 candidates in the signal and normalisation decay modes using the selected data after stripping and trigger selection from steps 3 and 4 and having performed the MVA described in step 5. 8. Compute all the efficiencies associated to the signal and normalisation decays (𝜀NORM) to be able to compute the 𝑁(Σ𝑏). 9. Fit normalisation channel to obtain 𝑁(Σ(∗) 𝑏) to a multicomponent signal and background extended fit. 10. Compute 𝑁(Σ𝑏) by using the result of the extended fit and the value of all the computed efficiencies mentioned. 11. Fit the signal MC and background to obtain a signal PDF to perform a hypothesis test over the date. 12. Compute the expected limit using the computed numbers mentioned above and the PDF of the signal. 13. Use the b-inclusive MC to study potential peaking backgrounds that could appear using the Σ𝑏tagging methodology and be confused with signal. 4.2. CODEX efficiency 27 It is important to note that Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾)) and Σ±(∗) 𝑏→ 𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) have been used indistinctly without indicating the charge of the particles since both charged modes will be used since one is just the 𝒞 -conjugation of the other and no differences in its BR is to be expected according to the model. 4.2 CODEX efficiency In this case, the proceeding is as follows: 1. Generate MC samples of the described decay modes for the Higgs portal for several Higgs production modes. 2. Parametrise every counting experiment done to compute the generator level efficiency. 3. Apply the conditions obtained in the previous step to the samples produced in step 1. 4. Compute the generator level efficiency. In this case, no background is taken into account for this. 29 Chapter 5 CODEX-b studies 5.1 Monte Carlo samples LHC events were generated in PYTHIA8 [89] at a center of mass energy of √𝑠 = 14 TeV, since this is the energy at which both the CODEX-b detector and the CODEX𝛽 demonstrator will acquire the data [33]. In this case, as mentioned in Section 1.4.1, three different Higgs production modes are studied, the inclusive Higgs production, where all bosons are produced according to the known production cross-sections [90]. It must be noted that no detector effects such as pile-up, material interactions or any other non-ideality are considered in this work. The efficiencies presented in this text should be interpreted in an analogous way to those presented in Sections 6.2.1 and 6.5.1. This being, as an efficiency that could be implemented in a CODEX dedicated simulation software, analogous to the LHCb Gauss [91,92]. The characterisation of the data samples generated can be found in Table 5.1. In this case, no previous selection is applied, and Monte Carlo is generated according to the known SM distributions [93–95]. Production mode Cross section Events generated Inclusive 58151 4000000 Higgs-strahlung 2479 6000000 Weak-boson fusion 4260 16112103 Table 5.1: Production cross sections and amounts of events generated for each of the Higgs production modes studied. The cross section is given in fb−1 30 Chapter 5. CODEX-b studies Particle prod-x prod-y prod-z 𝑝𝑇𝜂 𝜇− 1∈ (25750,35750) ∈ (−5000,5000) ∈ (5000,15000)>0.25 ∈ (2,5) 𝜇+ 1∈ (25750,35750) ∈ (−5000,5000) ∈ (5000,15000)>0.25 ∈ (2,5) 𝜇− 2∈ (25750,35750) ∈ (−5000,5000) ∈ (5000,15000)>0.25 ∈ (2,5) 𝜇+ 2∈ (25750,35750) ∈ (−5000,5000) ∈ (5000,15000)>0.25 ∈ (2,5) Table 5.2: Potential constraints imposed over the 𝜇 for the counting experiment performed for the Higgs inclusive production. Distances are in mm and 𝑝𝑇are in GeV. 5.2 Generator level efficiency The proceedings followed to obtain the efficiencies for each production mode, as well as the different detection cases and the constraints imposed for each case are described. For every production mode the generated decay is 𝑝𝑝 →𝐻0→ (𝐴0→ 𝜇+𝜇−)(𝐴0→𝜇+𝜇−), and only the production mode of the 𝐻0changes. 5.2.1 Inclusive production In this case, no production mode is imposed and the 𝐻0 is allowed to be generated freely according to SM production cross-sections. With all the Monte Carlo events a counting experiment is performed. The condition for counting +1 event that fulfills the requirements of a CODEX detection is the 𝐴0 decaying within its volume. This is equivalent to requiring that at least one of the 𝜇 of the described decay is generated in the detector volume, this means that at least one row of the Table 5.2 must be met, excluding the 𝑝𝑇and pseudorapidity 𝜂conditions. We studied two additional cases: one of them being that two of the 𝐴0 decay in CODEX, this would be met if one of the 𝜇1and one of the 𝜇2were produced within the CODEX volume. In terms of conditions this would be true if at least one row from each subtable in Table 5.2 happened. Once again no 𝑝𝑇nor 𝜂criteria are required. The other case is that at least one 𝐴0 decays within the CODEX volume while the other decays in the LHCb volume. In this case, the counting experiment would be successful if at least one of 𝜇1 or one of the 𝜇2 were produced in the CODEX volume, while the others must meet the 𝑝𝑇 and 𝜂 requirements. This happens when the spatial production requirements of at least one of the rows from one subtable of Table 5.2 happens while both 𝑝𝑇 and 𝜂 requirements of the other subtable are true, this one must also be produced in prod-z∈ (0,15000). The obtained efficiencies are shown in Table 5.3 and Figure 5.1. 5.2. Generator level efficiency 31 Detector 0.1 m 1 m 10 m 100 m 1000 m One CODEX 2.13 ×10−574.2×10−522.8×10−52.13 ×10−50.2×10−5 Two CODEX 0 0 0 0 0 CODEX & LHCb 5.25 ×10−60.5×10−60 0 0 Table 5.3: Efficiencies computed for all detection modes described. Lifetimes are given in terms of 𝑐𝜏and in meters. 10−1100101102103 cτ[m] 10−6 10−5 10−4 Efficiency @ 14TeV A0in codex two A0in codex A0in codex and in LHCb Figure 5.1: Efficiencies plot for all detection modes described. Both axes are in logarithmic scale, and no event with both 𝐴0 in CODEX is found. 5.2.2 Higgs-strahlung In this case only the Higgs-strahlung (also known as associated boson production) will be the allowed production mode of the SM Higgs. In this case, the counting experiment consists of one of the 𝐴0 decaying within the CODEX volume while the 𝑊/𝑍0 are assumed to decay into their leptonic modes, these being: 𝑊→𝜇𝜈 and 𝑍0→𝜇+𝜇− , and one charged lepton with very high 𝑝𝑇 is required to be found in the LHCb experiment. So this counting experience rests over the future capability of CODEX and LHCb interplay, otherwise no difference from the previous case is to be expected. In this case the explicit conditions would be, that the 𝜇1 or 𝜇2 have their production coordinates within the CODEX volume (see Table 5.2) while one 𝜇 from a vector boson must meet the three following constraints: 𝜂∈ (2,5) , 𝑝𝑇>20 GeV and prod-z <15000 , with the last one being trivially met since the 𝑊 and 𝑍 bosons have short lifetimes. The obtained efficiencies are shown in Table 5.4 and Figure 5.2. 32 Chapter 5. CODEX-b studies Detector 0.1 m 1 m 10 m 100 m 1000 m CODEX 3.13 ×10−560.5×10−520.8×10−52.37 ×10−50.18 ×10−5 CODEX & LHCb 6.67 ×10−7453 ×10−7237 ×10−72.67 ×10−71.67 ×10−7 Table 5.4: Efficiencies computed for all detection modes described. Lifetimes are given in terms of 𝑐𝜏and in meters. 10−1100101102103 cτ[m] 10−6 10−5 10−4 Efficiency @ 14TeV A0in codex A0in codex and µin LHCb Figure 5.2: Efficiencies plot for the detection modes described for the Higgs-strahlung production. Both axes are in logarithmic scale. 5.2.3 Weak-boson fusion The last study case is weak-boson fusion (also known as jet associated production), and this is the only allowed production mode for the SM Higgs. The counting experiment in this case is positive when one 𝐴0 decays within the CODEX volume while a hadronisation of a quark into a jet is detected in the LHCb experiment. This counting experiment differs a bit from the previous ones, since now there is one additional layer that is reconstructing and clusterising the hadrons of the jet into an object that LHCb understands as a jet. In order to perform the clusterisation, every stable and semi-stable particle ( 𝑝, 𝜇, 𝐾, 𝜋, 𝑒 ) detected by the VELO [96,97] is clusterised into a jet according to the anti𝑘𝑡 jet clustering algorithm [98] with a radius of 0.5 as the input parameter. In this case the explicit conditions for this counting experiments are that, either the 𝜇1 or 𝜇2 must decay within CODEX volume as in the Higgs-strahlung production. On the other hand, the VELO particles must meet the following conditions: 𝜂∈ (2,5) , 𝑝𝑇>0.25 GeV, 𝜌 < 38 mm and prod-z ∈ (0,800) mm; where 𝜌=p𝑥2+𝑦2 , and the final clusterised jet must have 𝑝𝑇>20 GeV. The results of this methodology can be found in Table 5.5 and in Figure 5.3. 5.3. Results 33 Detector 0.1 m 1 m 10 m 100 m 1000 m CODEX 3.98 ×10−577.1×10−524.5×10−53.02 ×10−50.27 ×10−5 CODEX & LHCb 1.74 ×10−624.1×10−66.64 ×10−60.87 ×10−60.12 ×10−6 CODEX & 1 LHCb 1.74 ×10−624.1×10−66.58 ×10−60.81 ×10−60.12 ×10−6 CODEX & 2 LHCb 06.21 ×10−86.21 ×10−86.21 ×10−80 Table 5.5: Efficiencies computed for all detection modes described for weak boson fusion production mode. Lifetimes are given in terms of 𝑐𝜏 and in meters. 10−1100101102103 cτ[m] 10−7 10−6 10−5 10−4 Efficiency @ 14 TeV A0in codex A0in codex and jet in LHCb A0in codex and one jet in LHCb A0in codex and two jets in LHCb Figure 5.3: Efficiencies plot for the described detection modes for the jets associated production mode. Both axes are in logarithmic scale. Note that almost no events with two jets in CODEX are produced since the requirements of detection are very tough. 5.3 Results By collecting all the results for the three studied production modes and their respective cross-sections [41]: •inclusive production: 58151 fb−1. •Higgs-strahlung: 2479 fb−1. •weak-boson fusion: 4260 fb−1. we can compute the expected events for 300 fb −1 of integrated luminosity. The results are shown in Table 5.6 and Figure 5.4. 40 Chapter 6. Dark matter and B-mesogenesis 0.94 GeV 1.5 GeV 2.0 GeV 2.4 GeV 3.0 GeV 3.5 GeV 𝒪cs 0.23342 0.22065 0.21871 0.20379 0.19550 NOPHSP 𝒪cd 0.25776 0.24652 0.22866 0.21989 0.19740 0.18820 Table 6.5: Reconstruction efficiency table for the Σ±∗ 𝑏→𝜋±(Λ𝑏→ 𝜓DM𝐾(𝐷→𝜋𝜋𝐾)) and Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) decay modes. It is clear that a mass dependency exists in this case. 6.2.3 Stripping Selection Thisanalysis usesseveralstrippinglines andstrippingcampaigns asalready described in Section 6.1.1. The definition of the variables used, the reason to use these variables as well as the collection of values will be presented in this section for every line and campaign used during the analysis. This means that the stripping for Stripping28r2p1 will not be discussed in here. This analysis uses three stripping lines, all from the stream BhadronCompleteEvent5: •LambdaDecaysDMLambdaToDPiLine : signal line used to select Λ𝑏→𝜓DM𝜋(𝐷→ 𝜋𝜋𝐾) candidates. An additional 𝜋± tagged with the candidates coming from the stripping. The combination is required to have a somehow good enough vertex reconstruction, (VFASPF(VCHI2/VDOF)< 10) is imposed over every Σ±(∗) 𝑏 candidate in this analysis. The variables used in these stripping line as well as the cuts imposed over said variables can be found in Table 6.7. •LambdaDecaysDMLambdaToDKLine : signal line used to select Λ𝑏→𝜓DM𝐾(𝐷→ 𝜋𝜋𝐾) candidates. The same proceeding over 𝜋± in order to reconstruct Σ±(∗) 𝑏 candidates is followed in this case. The condition over the vertex of the Σ±(∗) 𝑏 is also imposed. The variables used in this stripping line as well as the cuts imposed over said variables can be found in Table 6.6. •Lb2LcPiNoIPLc2PKPiBeauty2CharmLine : normalisation line used to select Λ𝑏→𝜋(Λ𝑐→𝑝𝐾𝜋) candidates. In this case, Σ±(∗) 𝑏 candidates are also reconstructed following the same procedure as in the other two lines. The same condition over the vertex reconstruction is imposed. This stripping lines were 5 A fullDST stream is required, such as BhadronCompleteEvent is required since the stripping lines, as it will be shown, only have requirements over the Λ𝑏 and its descents. This implies that the analysis will require fullDST lines in order to be able to reconstruct Σ±(∗) 𝑏 candidates, tagging the Λ𝑏 candidates coming from the stripping with 𝜋± living in the StdAllNoPIDsPions , only accessible within complete events. 6.2. Selection 41 not written for this analysis, and a deeper description and usage can be found in [109,110]. Particle (Variable) Cut(Stripping34r0p2) Cut(Stripping34r0p3) Λ0 𝑏(𝑝𝑇)>2000 MeV >2000 MeV Λ0 𝑏(DOCA) <0.5mm <0.5mm Λ0 𝑏(DOCA𝜒2)<8<8 Λ0 𝑏(FD𝜒2OWNPV) >30 >30 Λ0 𝑏(Isolation) >0.6>0.6 Λ0 𝑏(M) 1100 <𝑀<5700 MeV 1100 <𝑀<5700 MeV Λ0 𝑏(V𝜒2/DOF) <8<8 Λ0 𝑏(IP𝜒2OWNPV) >20 >25 𝐾+ 𝐷(𝑝𝑇)>800 MeV >250 MeV 𝐾+ 𝐷(ProbNNghost) <0.1<0.1 𝐾+ 𝐷(ProbNNk) >0.8>0.8 𝜋− 𝐷(𝑝𝑇)>800 MeV >250 MeV 𝜋− 𝐷(ProbNNghost) <0.1<0.1 𝜋− 𝐷(ProbNN𝜋)>0.8>0.8 𝐾+ Λ(𝑝𝑇)>250 MeV >250 MeV 𝐾+ Λ(ProbNNghost) <0.2<0.2 𝐾+ Λ(ProbNNk) >0.7>0.7 𝐾+ Λ(IP𝜒2OWNPV) >20 >20 𝐷−(DOCA) <0.4mm <0.4mm 𝐷−(FD𝜒2OWNPV) >50 >50 𝐷−(M) 1840 <𝑀<1900 MeV 1840 <𝑀<1900 MeV 𝐷−(𝑝𝑇)>2000 MeV >2000 MeV 𝐷−(V𝜒2/DOF) <6<6 Table 6.6: Stripping line for Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾) , LambdaDecaysDMLambdaToDKLine . The subindex of the 𝐾 and 𝜋 particles indicates its direct ascendant. As mentioned, the cuts for Stripping34r0p3 are also those for Stripping29r2p3 and Stripping28r2p3 . The misalignment in the cuts is expected to not affect much, the difference in value is not big and does not affect many variables, in fact it only affects three of them (four in reality, since there are two 𝜋− 𝐷): 𝜋− 𝐷(𝑝𝑇), Λ0 𝑏(IP𝜒2OWNPV) and 𝐾+ 𝐷(𝑝𝑇). 42 Chapter 6. Dark matter and B-mesogenesis Particle (Variable) Cut(Stripping34r0p2) Cut(Stripping34r0p3) Λ0 𝑏(𝑝𝑇)>3000 MeV >3000 MeV Λ0 𝑏(DOCA) <0.3mm <0.3mm Λ0 𝑏(DOCA𝜒2)<7<7 Λ0 𝑏(FD𝜒2OWNPV) >30 >30 Λ0 𝑏(Isolation) >0.6>0.6 Λ0 𝑏(M) 1100 <𝑀<5700 MeV 1100 <𝑀<5700 MeV Λ0 𝑏(V𝜒2/DOF) <8<8 Λ0 𝑏(IP𝜒2OWNPV) >20 >20 𝐾+ 𝐷(𝑝𝑇)>800 MeV >800 MeV 𝐾+ 𝐷(ProbNNghost) <0.1<0.1 𝐾+ 𝐷(ProbNNk) >0.9>0.9 𝜋− 𝐷(𝑝𝑇)>800 MeV >800 MeV 𝜋− 𝐷(ProbNNghost) <0.1<0.1 𝜋− 𝐷(ProbNN𝜋)>0.8>0.8 𝜋+ Λ(𝑝𝑇)>400 MeV >400 MeV 𝜋+ Λ(ProbNNghost) <0.2<0.2 𝜋+ Λ(ProbNN𝜋)>0.8>0.8 𝜋+ Λ(IP𝜒2OWNPV) >20 >20 𝐷−(DOCA) <0.4mm <0.4mm 𝐷−(FD𝜒2OWNPV) >50 >50 𝐷−(M) 1840 <𝑀<1900 MeV 1840 <𝑀<1900 MeV 𝐷−(𝑝𝑇)>2000 MeV >2000 MeV 𝐷−(V𝜒2/DOF) <6<6 Table 6.7: Stripping line for Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾) , LambdaDecaysDMLambdaToDPiLine . The subindex of the 𝐾 and 𝜋 particles indicates its direct ascendant. As mentioned, the cuts for Stripping34r0p3 are also those for Stripping29r2p3 and Stripping28r2p3 . As shown in this table, no misalignment had to be fixed for this line in particular. The selections shown in Tables 6.6 and 6.7 aim to minimise the combinatorial background as much as possible, but they also look forward to completely suppress any potential peaking background. This is achieved with the isolation and primary vertex (PV) variables, these being topological variables, which are the most important ones for this analysis. All the other kinematic variables affect background and signal 6.2. Selection 43 0.94 GeV 1.5 GeV 2.0 GeV 2.4 GeV 3.0 GeV 3.5 GeV 𝒪cs 0.05578 0.05283 0.04888 0.04528 0.02763 NOPHSP 𝒪cd 0.03944 0.03853 0.03659 0.03258 0.02478 0.00868 Table 6.8: Stripping efficiency table for the Σ±∗ 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→ 𝜋𝜋𝐾)) and Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) decay modes. It is clear that a mass dependency exists in this case. in a very similar way, but these are required to have a low enough rate and being able to achieve the disk usage quota. The variables used, as mentioned, have different natures, topological if they are related to how the tracks are positioned in the space, where they point at, how close they are to one another... Or kinematic, if they are related to momentum, mass... There is also a third kind, which are the so-called probNN, that are the probabilities assigned by a neural network to a particle to be of a certain kind, as explained in Section 6.2.3. ApplyingtheselectionsdescribedinTables6.6 and 6.7 to the MCsamplesdescribed in Section 6.1.2 the efficiencies in Table 6.8 are computed. Stripping Variables • probNN: the variables named probNN, i.e.: probNNk, probNN 𝜋 , are predictions of neural networks using information coming from different LHCb subdetectors. This information is used to assign a probability to each track of being associated to a specific specie of particle. There is a different probNN variable, the so-called probNNghost, that assigns to each “track” the probability of it not being a real track by a particle, but instead being hits in the tracking misidentified as a track [111,112]. •𝑝𝑇 : the transverse momentum is one of the most relevant kinematic variables at LHCb since it is a forward spectrometer. It is useful to get a better trigger efficiency, since the L0 Trigger is unable to process low transverse momentum tracks. It is defined as: 𝑝𝑇=q𝑝2 𝑥+𝑝2 𝑦(6.1) • DOCA: acronym for Distance Of Closest Approach (DOCA) of two or more tracks associated to the descendants of a given particle. It is the minimum separation between every track, calculated in pairs. •DOCA𝜒2: the value of the DOCA significance in units of 𝜒2. 44 Chapter 6. Dark matter and B-mesogenesis • FD 𝜒2 OWNPV: flight distance (FD) of a given particle in units of 𝜒2 from its own primary vertex (OWNPV), this being the point where it is originated, to the point where it decays. • Isolation: variable that measures how isolated is a certain track from any other given track. It takes into account for the computation every track that falls within a cone defined from the track that is calculated, the radius of the cone is an input set as 𝑅2=0.62. The variable is defined as ISO =𝑝𝑇 𝑝𝑇+𝑝CONE 𝑇 (6.2) this means that the isolation variable will always be a number between 0 and 1, if the particle is entirely isolated we will have 𝑝CONE 𝑇=0 and therefore ISO =1 . On the other hand, the less isolated the particle is, the bigger 𝑝CONE 𝑇 will be, and consequently ISO →0. • V 𝜒2 /DOF: the vertex 𝜒2 is a way of measuring the quality of the fit for the position of the decay vertex of a certain particle. In this case, it is normalised taking into account the degrees of freedom of the fit. • IP 𝜒2 OWNPV: the value of impact parameter (IP) in units of 𝜒2 . The impact parameter is the shortest distance between the track of a particle and a given vertex. 6.2.4 Trigger Selection This section describes the trigger aspects of the analysis, performing an efficiency study over the 2018 Σ±∗ 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾)) and Σ±∗ 𝑏→𝜋±(Λ𝑏→ 𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) samples described in Section 6.1.2 that allow for a better selection of Σ±∗ 𝑏. Trigger independent of signal / Trigger on Signal In the LHCb experiment candidates are categorised as TIS (Trigger independent of signal) or TOS (Trigger on signal) depending on the trigger decision. A candidate is said to be TOS if it has been selected by the trigger due to itself, while it is defined as TIS if the trigger selection is not conditioned by the candidate. This means, that removing a TOS candidate from the event, changes the trigger state, while doing the same with a TIS does not. This analysis is, as already stated, based on TOS candidates. 6.2. Selection 45 Figure 6.1: Diagram of the Run 2 trigger configuration. Taken from [106] under Creative Commons License. L0 Trigger The Level Zero (L0) trigger of the LHCb experiment is a critical component designed to manage the vast amount of data generated by proton collisions. It reduces the data rate from the full bunch crossing rate of 40 MHz to about 1 MHz, as seen in Figure 6.1, making it possible to record the data for offline analysis. This reduction is achieved through a system of field-programmable gate arrays (FPGAs) with a fixed latency, utilising information from the electromagnetic calorimeter, hadronic calorimeter, and muon stations in separate L0 trigger lines [113]. The LHCb trigger system, including the L0 trigger, plays a pivotal role in enabling the experiment to capture data on particles containing b and c quarks, essential for its physics program. This trigger is the most determinant for this analysis, since the topological lines written for the High Level Trigger 2 (HLT2) and the TrackMVA lines for the High Level Trigger 1 (HLT1) have higher efficiencies overall. Due to the nature of the studied decays in this analysis, the most efficient L0 line is L0HadronDecision applied over the Σ𝑏 particle, since this is the head of the decay. 46 Chapter 6. Dark matter and B-mesogenesis HLT1 Trigger The HLT1 stage of the LHCb trigger system is responsible for an inclusive selection of events. This selection is based on criteria such as the presence of one or two-track signatures, muon tracks displaced from primary vertices, or dimuon combinations within an event. Selected events by HLT1 are temporarily stored in disk storage within the online system for further processing during inter-fill periods or for detector calibration and alignment before proceeding to HLT2, where a full event reconstruction occurs [113]. The HLT1 lines found to be the most efficient ones are Hlt1TrackMVADecision and Hlt1TwoTrackMVADecision , applied again over the Σ𝑏 . These lines are selected as an OR operation between them (this is, only one is required simultaneously) and with an AND operator with the L0 line (a L0 positive trigger decision is always required, this is the reason for the efficiencies to be calculated in a sequential way). HLT2 Trigger The HLT2 stage in the LHCb trigger system is where full event reconstruction occurs. After HLT1 has made an initial selection, HLT2 processes these events comprehensively, allowing for a wide range of inclusive and exclusive final states to trigger events. This stage enables the fine-tuning of data selection, preparing it for detailed physics analysis without the need for further offline processing. This sophisticated triggering allows for efficient data handling and significantly contributes to the experiment’s ability to perform real-time analyses [113]. The HLT2 lines found to be the most efficient ones in this analysis are Hlt2Topo2BodyDecision , Hlt2Topo3BodyDecision and Hlt2Topo4BodyDecision , which are different examples of “topological” trigger lines [114]. Once again an OR operator is applied between the different HLT2 lines and an AND one is required between previous trigger levels. Taking into account the results in Tables 6.9 and 6.10 it is clear that the L0 trigger is, in general, the most determinant one, with the HLT2 requirements being also important at high DM masses, this is due to the fact that the tracks and hits recorded in the different subdetectors are associated with a smaller transverse momentum, lowering the efficiency of the L0 and HLT2 trigger requirements [113]. The mass dependency is more relevant in the HLT2 stage than in the L0 Trigger. 6.2.5 Multivariate Classifier Using a Boosted Decision Tree (BDT) algorithm, namely a Gradient Boosting Classifier [115,116], from the scikit-learn [117] python library is a usual method [118] in high energy physics (HEP) to obtain a better signal to background discrimination. The classifier optimises a loss function for binary classification. A metric that will be 6.2. Selection 47 0.94 GeV 1.5 GeV 2.0 GeV 2.4 GeV 3.0 GeV 3.5 GeV L0 0.213837 0.197694 0.178280 0.165681 0.134211 0.145561 HLT1 0.998306 1.0 0.999212 0.998071 1.0 1.0 HLT2 0.684389 0.580994 0.471609 0.389372 0.287582 0.174888 𝜀Trigger 0.146100 0.114859 0.084012 0.064387 0.038597 0.025457 Table 6.9: Efficiencies table for the Σ±∗ 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→ 𝜋𝜋𝐾)) decay mode. The three trigger stages requirements are TOS. The efficiencies are calculated in a sequential way, this being, the HLT1 efficiencies are calculated over the events that passed the L0 selection, this also applies to the HLT2 efficiency with respect to the HLT1 efficiency. 0.94 GeV 1.5 GeV 2.0 GeV 2.4 GeV 3.0 GeV L0 0.227932 0.209320 0.180461 0.169569 0.124025 HLT1 0.996573 0.994700 0.998859 0.997297 0.993711 HLT2 0.669087 0.612789 0.470588 0.371274 0.161392 𝜀Trigger 0.151982 0.1275892 0.084826 0.062786 0.019891 Table 6.10: Efficiencies table for the Σ±∗ 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→ 𝜋𝜋𝐾)) decay mode. The three trigger stages requirements are TOS. The efficiencies are calculated in a sequential way, this being, the HLT1 efficienciesare calculatedoverthe eventsthat passedtheL0 selection, this also applies to the HLT2 efficiency with respect to the HLT1 efficiency. used to evaluate the quality of this tool is the receiver operating characteristic (ROC) curve [119 – 122]. Different classifiers were tried out and no significant differences were found. The classifier is trained using the MC samples in Section 6.1.2 as a signal proxy and a small data sample as background, the 4.55% (2.275% for the Σ±(∗) 𝑏→𝜋±(Λ𝑏→ 𝜓DM𝜋(𝐷→𝜋𝜋𝐾))decay mode) of the total available luminosity. A first iteration of the BDT is trained with all the relevant topological and kinematic variables, and a features importance algorithm is executed in order to select a smaller sample of features to create the BDT. In light of the results of this proceeding, and according to Figure 6.2 the selected variables for the second iteration of the BDT will be: piminus1IPCHI2OWNPV, piminus2PT, piminus2IPCHI2OWNPV, KplusIPCHI2OWNPV, KsoftPT, KsoftIPCHI2OWNPV, DminusPT, DminusIPCHI2OWNPV, DminusFDOWNPV, DminusFDCHI2OWNPV, Lambdab0IPCHI2OWNPV, Lambdab0DIRAOWNPV, Lambdab0DOCA and Lambdab0ISOLATIONSTRIPPING. 48 Chapter 6. Dark matter and B-mesogenesis 0 5 10 15 20 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 piminus1 PT piminus1 IPCHI2 OWNPV piminus2 PT piminus2 IPCHI2 OWNPV Kplus PT Kplus IPCHI2 OWNPV Ksoft PT Ksoft IPCHI2 OWNPV Dminus PT Dminus IPCHI2 OWNPV Dminus FD OWNPV Dminus FDCHI2 OWNPV Dminus DIRA OWNPV Dminus VCHI2PERDOF Lambda b0 VCHI2PERDOF Lambda b0 PT Lambda b0 IPCHI2 OWNPV Lambda b0 FD OWNPV Lambda b0 OWNPV CHI2 Lambda b0 DIRA OWNPV Lambda b0 FDCHI2 OWNPV Lambda b0 DOCA Lambda b0 DOCACHI2 Lambda b0 ISOLATION STRIPPING Figure 6.2: Histogram with the importance of each of the features used in the first iteration of the BDT in the Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→ 𝜋𝜋𝐾)) decay. No Σ±(∗) 𝑏 tagging particles are used in the BDT. piminus1,2 and Kplus variables are related to the 𝐷 daughters, and the Ksoft variables refer to the Λ𝑏 daughter. A 𝑚(𝜓DM)=940 MeV MC sample is used. Note that FD stands for flight distance, and OWNPV means that the variable is referred to the primary vertex of the given particle. Finally, when a variable has CHI2 in the name, it means that is measured in units of 𝜒2. The isolation and vertex variables of the Λ𝑏 are the most relevant for the classifier, 6.2. Selection 49 1000 2000 3000 0.0000 0.0005 piminus1 PT 1000 2000 3000 4000 0.000 0.001 0.002 piminus1 IPCHI2 OWNPV 1000 2000 3000 0.0000 0.0005 piminus2 PT 1000 2000 3000 4000 0.000 0.001 0.002 piminus2 IPCHI2 OWNPV MC BKG 1000 2000 3000 0.00000 0.00025 0.00050 Kplus PT 1000 2000 0.000 0.002 Kplus IPCHI2 OWNPV 1000 2000 3000 4000 5000 0.00000 0.00025 0.00050 Ksoft PT 1000 2000 3000 0.000 0.002 Ksoft IPCHI2 OWNPV 4000 6000 8000 0.0000 0.0001 0.0002 Dminus PT 500 1000 1500 0.0000 0.0025 0.0050 Dminus IPCHI2 OWNPV 20 40 0.00 0.02 0.04 Dminus FD OWNPV 10000 20000 30000 0.0000 0.0002 Dminus FDCHI2 OWNPV −0.5 0.0 0.5 0 5 10 Dminus DIRA OWNPV 1 2 0.00 0.25 0.50 Dminus VCHI2PERDOF 0 1 2 0 1 2 Lambda b0 VCHI2PERDOF 2500 5000 7500 10000 12500 0.0000 0.0001 Lambda b0 PT 200 400 600 0.000 0.005 0.010 Lambda b0 IPCHI2 OWNPV 10 20 30 0.00 0.05 0.10 Lambda b0 FD OWNPV 20 40 60 0.00 0.01 0.02 Lambda b0 OWNPV CHI2 −0.5 0.0 0.5 0 5 Lambda b0 DIRA OWNPV 2500 5000 7500 10000 0.0000 0.0005 0.0010 Lambda b0 FDCHI2 OWNPV 0.01 0.02 0.03 0.04 0 20 40 Lambda b0 DOCA 0 1 2 0 1 2 Lambda b0 DOCACHI2 0.6 0.7 0.8 0.9 1.0 0 2 4 Lambda b0 ISOLATION STRIPPING Figure 6.3: Distributions of signal and background variables of every feature used in the classifier. The label on top of each subplot indicates the variable plotted in each one. Every plot has arbitrary units on the y-axis. as it was expected due to the nature of the decay. The different distributions of all the relevant features are shown in Figure 6.3 and their correlations may be found in Figure 6.4. The distributions are consistent with the result of the second iteration of the features importance histogram as seen in Figure 6.5. The overtraining of the BDT is checked by using a k-fold cross-validation technique [123] with 5 folds. Each of them is validated separately by obtaining the area under the ROC curve and using a train/test sample. The scores are shown in Table 6.11, the ROC curve and the performance of BDT can be found in Figure 6.6 and Figure 6.7. The BDT does not produce artificial peaking structures on the background as it Figure 6.8 shows. The last check is to see that the BDT response is similar in any given mass bin, both for background and for potential signal regions. This check is shown in Figure 6.9. This proceeding is repeated for every mass and both decay modes. The results can be found in Figures 6.10 to 6.17 and table 6.12. 56 Chapter 6. Dark matter and B-mesogenesis piminus1 IPCHI2 OWNPV piminus2 PT piminus2 IPCHI2 OWNPV Kplus IPCHI2 OWNPV piplus PT piplus IPCHI2 OWNPV Dminus PT Dminus IPCHI2 OWNPV Dminus FD OWNPV Dminus FDCHI2 OWNPV Dminus VCHI2PERDOF Lambda b0 IPCHI2 OWNPV Lambda b0 OWNPV CHI2 Lambda b0 DIRA OWNPV Lambda b0 DOCA Lambda b0 ISOLATION STRIPPING piminus1 IPCHI2 OWNPV piminus2 PT piminus2 IPCHI2 OWNPV Kplus IPCHI2 OWNPV piplus PT piplus IPCHI2 OWNPV Dminus PT Dminus IPCHI2 OWNPV Dminus FD OWNPV Dminus FDCHI2 OWNPV Dminus VCHI2PERDOF Lambda b0 IPCHI2 OWNPV Lambda b0 OWNPV CHI2 Lambda b0 DIRA OWNPV Lambda b0 DOCA Lambda b0 ISOLATION STRIPPING 1.00 0.02 0.44 0.62 0.08 0.21 0.02 0.49 0.38 0.53 -0.00 0.46 -0.03 0.03 -0.07 0.03 0.02 1.00 -0.01 -0.01 0.03 0.02 0.61 -0.02 0.09 0.04 0.01 -0.01 0.03 0.00 -0.01 0.03 0.44 -0.01 1.00 0.50 0.06 0.17 0.02 0.53 0.34 0.50 -0.01 0.45 -0.04 0.03 -0.05 0.02 0.62 -0.01 0.50 1.00 0.04 0.20 0.01 0.69 0.28 0.44 0.01 0.69 -0.03 -0.01 -0.03 0.00 0.08 0.03 0.06 0.04 1.00 0.04 0.04 0.01 0.10 0.10 -0.00 -0.02 -0.02 0.16 -0.36 0.12 0.21 0.02 0.17 0.20 0.04 1.00 0.03 0.16 0.25 0.22 -0.00 0.16 -0.02 0.02 -0.04 0.03 0.02 0.61 0.02 0.01 0.04 0.03 1.00 -0.02 0.11 0.08 0.04 -0.02 0.07 0.00 -0.03 0.01 0.49 -0.02 0.53 0.69 0.01 0.16 -0.02 1.00 0.20 0.44 0.00 0.92 -0.04 -0.03 -0.01 0.01 0.38 0.09 0.34 0.28 0.10 0.25 0.11 0.20 1.00 0.52 -0.07 0.15 -0.17 0.14 -0.12 0.09 0.53 0.04 0.50 0.44 0.10 0.22 0.08 0.44 0.52 1.00 0.01 0.33 -0.04 0.05 -0.08 0.01 -0.00 0.01 -0.01 0.01 -0.00 -0.00 0.04 0.00 -0.07 0.01 1.00 0.00 0.08 -0.04 0.01 -0.09 0.46 -0.01 0.45 0.69 -0.02 0.16 -0.02 0.92 0.15 0.33 0.00 1.00 -0.03 -0.06 0.00 0.01 -0.03 0.03 -0.04 -0.03 -0.02 -0.02 0.07 -0.04 -0.17 -0.04 0.08 -0.03 1.00 -0.13 0.08 -0.27 0.03 0.00 0.03 -0.01 0.16 0.02 0.00 -0.03 0.14 0.05 -0.04 -0.06 -0.13 1.00 -0.30 0.08 -0.07 -0.01 -0.05 -0.03 -0.36 -0.04 -0.03 -0.01 -0.12 -0.08 0.01 0.00 0.08 -0.30 1.00 -0.07 0.03 0.03 0.02 0.00 0.12 0.03 0.01 0.01 0.09 0.01 -0.09 0.01 -0.27 0.08 -0.07 1.00 Correlation Matrix of Features −0.2 0.0 0.2 0.4 0.6 0.8 1.0 Figure 6.12: Correlation matrix for the most relevant variables used to train the BDT for the Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) decay using a𝑚(𝜓DM)=940 MeV. 6.2. Selection 57 0 2 4 6 8 10 12 14 0.00 0.05 0.10 0.15 0.20 0.25 piminus1 IPCHI2 OWNPV piminus2 PT piminus2 IPCHI2 OWNPV Kplus IPCHI2 OWNPV piplus PT piplus IPCHI2 OWNPV Dminus PT Dminus IPCHI2 OWNPV Dminus FD OWNPV Dminus FDCHI2 OWNPV Dminus VCHI2PERDOF Lambda b0 IPCHI2 OWNPV Lambda b0 OWNPV CHI2 Lambda b0 DIRA OWNPV Lambda b0 DOCA Lambda b0 ISOLATION STRIPPING Figure 6.13: Histogram with the importance of each of the features used in the second iteration of the BDT for the Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→ 𝜋𝜋𝐾)) decay using a 𝑚(𝜓DM)=940 MeV. which applied to every decay mode and mass in this analysis the values in Table 6.14 are computed. 58 Chapter 6. Dark matter and B-mesogenesis 0.2 0.4 0.6 0.8 bdt response 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 AU signal train signal test bkg train bkg test Figure 6.14: Performance of the classifier for the train/test samples for the Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) decay using a 𝑚(𝜓DM)=940 MeV. 0.0 0.2 0.4 0.6 0.8 1.0 False Positive Rate 0.0 0.2 0.4 0.6 0.8 1.0 True Positive Rate test sample train sample Figure 6.15: ROC curve obtained for the BDT using a train/test method for the Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) decay using a 𝑚(𝜓DM)= 940 MeV. 6.2. Selection 59 2500 3000 3500 4000 4500 5000 5500 Σbmass 0.0000 0.0001 0.0002 0.0003 0.0004 BDT >0.5 BDT >0.7 BDT >0.8 BDT >0.9 Figure 6.16: Effect of different BDT cuts over the background of this analysis. No fake peaking structures appear for a wide range of this classifier cut for the Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) decay using a𝑚(𝜓DM)=940 MeV. 0.6 0.7 0.8 0.9 BDT 0.0 0.5 1.0 1.5 2.0 2.5 3.0 signal region mass bin 1 mass bin 2 0.6 0.7 0.8 0.9 BDT 0.0 0.5 1.0 1.5 2.0 2.5 3.0 right sideband mass bin 1 mass bin 2 Figure 6.17: BDT response for different mass bins for a potential signal region (left) and for a guaranteed background region (right) for the Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) decay using a 𝑚(𝜓DM)=940 MeV. 60 Chapter 6. Dark matter and B-mesogenesis 0.0 0.2 0.4 0.6 0.8 1.0 BDT cut 0.0 0.2 0.4 0.6 0.8 1.0 FOM normalised 940 MeV 2000 MeV 3500 MeV 0.0 0.2 0.4 0.6 0.8 1.0 BDT cut 0.0 0.2 0.4 0.6 0.8 1.0 FOM normalised 940 MeV 2000 MeV 3000 MeV Figure 6.18: Normalised FOM computation for the Σ±(∗) 𝑏→𝜋±(Λ𝑏→ 𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) (left) and for the Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→ 𝜋𝜋𝐾)) (right) decay using three different masses: the lightest available by theory, the heaviest allowed by phase space, and an intermediate one of 2GeV proposed as the benchmark by [18]. 0.94 GeV 1.5 GeV 2.0 GeV 2.4 GeV 3.0 GeV 3.5 GeV 𝒪cs 0.55111 0.63768 0.29369 0.70072 0.54901 NOPHSP 𝒪cd 0.45041 0.31227 0.22241 0.52109 0.38636 0.87179 Table 6.13: Efficiencies table for the Σ±∗ 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→ 𝜋𝜋𝐾)) and Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) decay modes. The BDT cuts are applied in a sequential way, this being, the BDT efficiencies are calculated over the events that passed the stripping and trigger selection. 0.94 GeV 1.5 GeV 2.0 GeV 2.4 GeV 3.0 GeV 3.5 GeV 𝒪cs 6.39×10−55.45×10−51.53×10−52.54×10−50.327×10−5NOPHSP 𝒪cd 4.95×10−52.77×10−51.17×10−51.68×10−50.424×10−50.210×10−5 Table 6.14: Efficiencies table for the Σ±∗ 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→ 𝜋𝜋𝐾)) and Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) decay modes. 6.3. Tagging 61 6.3 Tagging As described in Section 4.1 a tagging strategy is performed over the Λ𝑏 baryons where its mother, a Σ±(∗) 𝑏 , is reconstructed by tagging the original baryon to a 𝜋± pointing towards the primary vertex, as done in other works [85 – 88]. In this section the mathematical proceeding of the tagging will be shown, as well as some additional strategies and selections that improve the signal to background discrimination. 6.3.1 Mathematical description By imposing the tagging requirement, the following kinematic calculation can be done: 𝑚2 Λ𝜋=©« 𝐸Λ 0 0 q𝐸2 Λ−𝑚Λ 2ª®®®®¬ +©« p𝑝2 𝜋+𝑚2 𝜋 𝑝𝜋sin 𝜃 0 𝑝𝜋cos 𝜃ª®®®¬  2 = =𝐸Λ+q𝑝2 𝜋+𝑚2 𝜋2 −𝑝2 𝜋sin2𝜃−q𝐸2 Λ−𝑚2 Λ+𝑝𝜋cos 𝜃2 = =2𝐸Λ𝐸𝜋+𝑚2 𝜋+𝑝2 𝜋(1−sin2𝜃)+𝑚2 Λ−2𝑝𝜋cos 𝜃q𝐸2 Λ−𝑚2 Λ−𝑝2 𝜋cos2𝜃, (6.5) where 𝜃is the angle between the Λtrack and the 𝜋track. By rearranging the terms in the previous expression one can write: 0=𝐸2 Λ(4(𝐸2 𝜋−𝑝2 𝜋cos2𝜃))+𝐸Λ(−4𝐸𝜋Δ2)+4𝑚2 Λ𝑝2 𝜋cos2𝜃+Δ4,(6.6) where Δ2=𝑚2 Λ𝜋−𝑚2 Λ−𝑚2 𝜋 has been defined for shorter expressions, since it is a known constant. It is important to note that every variable in the previous equation is measured in the described experimental setup, except for 𝐸Λ. The Λ𝑏 direction of flight can be determined based on the primary and secondary vertex positions, allowing for a reconstruction of its direction even though it is not a fully reconstructed particle. For this derivation the Λ𝑏 direction of flight is chosen as the 𝑧 -axis without any loss of generality. By solving the quadratic equation in 𝐸Λtwo possible solutions appear: 𝐸Λ=Δ2 2𝐸𝜋 1 1−(𝑝𝜋/𝐸𝜋)2cos2𝜃[1±√𝑑],(6.7) with 62 Chapter 6. Dark matter and B-mesogenesis 𝑑=𝑝𝜋 𝐸𝜋 cos 𝜃2 −4𝑚2 Λ𝑝2 𝜋cos2𝜃 Δ4 1−𝑝𝜋 𝐸𝜋 cos 𝜃2!.(6.8) 6.3.2 Tagging efficiency It is clear then that 𝑑>0 is a required constraint for solutions to exist and imaginary solutions are not taken into account and must be discarded. When taking into account the existence of two solutions, about 90% of the time the lowest one is the correct one and choosing the incorrect one adds close to no noise into the proceeding [85,87]. This imposes a new requirement in the analysis and in the selection, this being 𝑑>0 . Let us call this the tagging requirement. The efficiency of this reconstruction is shown in Table 6.15. 0.94 GeV 1.5 GeV 2.0 GeV 2.4 GeV 3.0 GeV 3.5 GeV 𝒪cs 0.72301 0.71818 0.74790 0.81521 0.76364 NOPHSP 𝒪cd 0.76867 0.84782 0.78698 0.74519 0.64286 0.84375 Table 6.15: Efficiencies table for the Σ±∗ 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→ 𝜋𝜋𝐾)) and Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) decay modes. The 𝑑>0 cuts are applied in a sequential way, this being, the 𝑑>0 efficiencies are calculated over the events that passed the stripping, the trigger selection and the BDT cut. 6.3.3 𝑚min computation A related quantity is the minimum mass of the Λ𝜋 pair. This would be equivalent to taking the quadratic discriminant, setting it to zero and solving for the mass. The expression of this new quantity is: 𝑚min =r𝑚2 Λ+𝑚2 𝜋+2𝑚Λq𝑝2 𝜋sin2𝜃+𝑚2 𝜋.(6.9) This observable allows for a rectangular cut to be imposed over it, allowing for further background to signal discrimination. This quantity results in a very similar distribution for every decay mode, as it is expected, since it has no relation with the dark matter particle or the decay mode at all. This can be seen in Figures 6.19 and 6.20. The imposition of this cut ( 𝑚min >88 MeV) arises the need for a new efficiency computation, which can be found in Table 6.16. As seen in this table, the efficiency 6.3. Tagging 63 0 50 100 150 200 250 mmin [MeV] 0.0000 0.0025 0.0050 0.0075 0.0100 0.0125 0.0150 0.0175 0.0200 Arbitrary Units Data MC 0 50 100 150 200 250 mmin [MeV] 0.0000 0.0025 0.0050 0.0075 0.0100 0.0125 0.0150 0.0175 0.0200 Arbitrary Units Data MC 0 50 100 150 200 250 mmin [MeV] 0.000 0.005 0.010 0.015 0.020 0.025 Arbitrary Units Data MC Figure 6.19: 𝑚min computation for the Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→ 𝜋𝜋𝐾)) decay using the same three benchmark masses as in Figure 6.18: the lightest available (top left), the 2 GeV benchmark (top right) and the heaviest possible (bottom). Only the stripping selection is applied for these plots since the whole selection has already trimmed down lots of the events and the distributions are not easily seen. 0.94 GeV 1.5 GeV 2.0 GeV 2.4 GeV 3.0 GeV 3.5 GeV 𝒪cs 1.0 1.0 1.0 1.0 1.0 NOPHSP 𝒪cd 1.0 1.0 1.0 1.0 1.0 1.0 Table 6.16: Efficiencies table for the Σ±∗ 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→ 𝜋𝜋𝐾)) and Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) decay modes. The 𝑚min cuts are applied in a sequential way, this being, the 𝑚min efficiencies are calculated over the events that passed the stripping, the trigger selection, the BDT cut and the tagging cut. after the whole selection in this variable is very close to one, since the events that do not pass it are already outliers of the selection. This also applies to background, but some outliers are eliminated in the latter case. 64 Chapter 6. Dark matter and B-mesogenesis 0 50 100 150 200 250 mmin [MeV] 0.0000 0.0025 0.0050 0.0075 0.0100 0.0125 0.0150 0.0175 0.0200 Arbitrary Units Data MC 0 50 100 150 200 250 mmin [MeV] 0.000 0.005 0.010 0.015 0.020 Arbitrary Units Data MC 0 50 100 150 200 250 mmin [MeV] 0.0000 0.0025 0.0050 0.0075 0.0100 0.0125 0.0150 0.0175 0.0200 Arbitrary Units Data MC Figure 6.20: 𝑚min computation for the Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→ 𝜋𝜋𝐾)) decay using the same three benchmark masses as in Figure 6.18: the lightest available (top left), the 2 GeV benchmark (top right) and the heaviest possible (bottom). Only the stripping selection is applied for these plots since the whole selection has already trimmed down lots of the events and the distributions are not easily seen. 6.4 Mass fit In this section the fits performed to describe the background and the signal used are described. 6.4.1 Mathematical description The calculation in Section 6.3 allows the computation of the squared missing mass (𝑚2 miss): 𝑚2 miss =𝑚2 Λ+(𝑚2 𝐷+𝑚2 𝐾+2(𝐸𝐷𝐸𝐾−(® 𝑝𝐷® 𝑝𝐾))−2𝐸Λ(𝐸𝐷+𝐸𝐾)−q𝐸2 Λ−𝑚2 Λ(6.10) and this quantity can be fitted to a double sided crystal ball probability distribution function [84]. This is made by the core of a gaussian function and the tails are 6.4. Mass fit 65 moduled by power-laws. This PDF is described is given by the following expression: 𝑓(𝑚;𝛼𝐿,𝑅, 𝑛𝐿,𝑅,¯ 𝑥, 𝜎)= 𝐴𝐿𝐵𝐿−𝑚−¯ 𝑥 𝜎−𝑛𝐿,for 𝑚−¯ 𝑥<−𝛼𝐿𝜎 exp −(𝑚−¯ 𝑥)2 2𝜎2,for −𝛼𝐿𝜎≤𝑚−¯ 𝑥≤𝛼𝑅𝜎 𝐴𝑅𝐵𝑅−𝑚−¯ 𝑥 𝜎−𝑛𝑅,for 𝑚−¯ 𝑥> 𝛼𝑅𝜎 (6.11) where the coefficients are: 𝐴𝑖=𝑛𝑖 |𝛼𝑖|𝑛𝑖 ·exp −|𝛼𝑖|2 2 𝐵𝑖=𝑛𝑖 |𝛼𝑖|−|𝛼𝑖|. The parameters that describe this PDF are: •𝛼𝐿.𝑅 : parameter that defines the left and right points of transition from the Gaussian core to the power-law tails. •𝑛𝐿.𝑅: parameter that defines the left and right tails of the PDF. •¯ 𝑥: the mean of the Gaussian core. •𝜎: the standard deviation of the Gaussian core. 6.4.2 Fitting basis For every fit in this analysis a minimisation of a negative log-likelihood will be used. The negative log-likelihood (NLL) function is a fundamental concept in statistical modeling and inferential statistics, particularly in the context of maximum likelihood estimation (MLE). It serves as a criterion for evaluating the fit of a statistical model to observed data by quantifying the discrepancy between the observed data and the model’s predictions [125]. The log-likelihood function is derived from the likelihood function, which expresses the probability of observing the given data under a specific statistical model. For a set of independent and identically distributed observations {𝑥1, 𝑥2, ..., 𝑥𝑛} with a PDF 𝑓(𝑥, 𝜃) dependent on parameters 𝜃 , the likelihood function 𝐿(𝜃) is defined as: 𝐿(𝜃)= 𝑛 Ö 𝑖=1 𝑓(𝑥𝑖,𝜃).(6.12) Thelog-likelihoodfunction ℒ(𝜃) isthe natural logarithm of the likelihoodfunction: 72 Chapter 6. Dark matter and B-mesogenesis 600 800 1000 1200 1400 signal pdf data m2 miss −m2 teo (GeV/c2) −5 0 5 Pulls 1500 2000 2500 signal pdf data m2 miss −m2 teo (GeV/c2) −5 0 5 Pulls Figure6.25: Fullmodelfitsperformedforboth decaymodes(left: Σ±(∗) 𝑏→ 𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾)) , right: Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→ 𝜋𝜋𝐾)) ) for a 𝑚(𝜓DM)=2 GeV. The distance in 𝜎 between the fit and the data is shown in the plot below the fits. Same as Figure 6.24 but signal and background histograms are not shown explicitly. 𝑁fit 𝜇 𝜎 0.94 GeV 2399.66 -0.0616 1.0310 1.5 GeV 2399.79 -0.0884 1.0550 2.0 GeV 2599.63 -0.0858 1.0547 2.4 GeV 2000.00 -0.0573 1.0225 3.0 GeV 1800.01 -0.0332 1.0114 3.5 GeV 2000.00 -0.0298 0.9323 Table 6.21: Results of the fits performed to a gaussian of all the pseudoexperiments computed for the Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) decay. as in the full fit are allowed to float. A Gaussian distribution with a mean of 0 and a standard deviation of 1 is expected when 𝑛fit−𝑛poisson 𝜎 is computed for a sufficiently large number of pseudo-experiments. In this case, 𝑛fit is the obtained value of the number of signal events, and 𝑛poisson is the input parameter representing the number of events to be generated in the pseudoexperiment. Approximately 2000 pseudo-experiments were generated for each mass and decay mode. This ensures that the distribution of these Poisson-distributed quantities approaches a Gaussian distribution [130,131]. The results of applying this methodology can be found in Tables 6.21 and 6.22 and Figure 6.26. These tables and figures demonstrate that the obtained mass model in Section 6.4.5 is valid. 6.5. Normalisation channel 73 𝑁fit 𝜇 𝜎 0.94 GeV 2000.00 -0.0317 1.0381 1.5 GeV 1000.04 -0.1165 1.0206 2.0 GeV 2000.00 -0.0908 1.0090 2.4 GeV 3799.86 -0.0922 1.0971 3.0 GeV 2200.60 0.0063 0.9598 3.5 GeV NOPHSP NOPHSP NOPHSP Table 6.22: Results of the fits performed to a gaussian of all the pseudoexperiments computed for the Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) decay. In this case some higher and lower limits of 𝑁fit were studied to check if some dependency around this input arose, but it did not. −3−2−1 0 1 2 3 (nfit −npoisson)/σ 0 20 40 60 80 100 120 Entries/(0.15) fit Sig1 data −3−2−1 0 1 2 3 (nfit −npoisson)/σ 0 25 50 75 100 125 150 175 Entries/(0.15) fit Sig1 data Figure 6.26: Pull plots obtained for both decay modes (left: Σ±(∗) 𝑏→ 𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾)) , right: Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→ 𝜋𝜋𝐾)) ). The 𝑚(𝜓DM) used here is 2 GeV as it is the benchmark proposed in the model. 6.5 Normalisation channel A very similar proceeding to that in Section 6.2 is followed to study the decay that will act as the normalisation channel of this analysis: Λ𝑏→𝜋(Λ𝑐→𝑝𝐾𝜋) . The proceeding is very similar. 1. MC was generated privately, as stated in Section 6.1. 2. The selection shown in Section 6.1.1 is applied to both MC and 2018 data. 3. The same trigger selection shown in Section 6.2.4 is applied. 4. A multivariate analysis is performed over this channel. 74 Chapter 6. Dark matter and B-mesogenesis Particle Cut 𝐾Λ𝑐𝑝𝑇>0.1GeV& 1.9< 𝜂 < 5.0 𝑝Λ𝑐𝑝𝑇>0.1GeV& 1.9< 𝜂 < 5.0 𝜋Λ𝑐,𝜋,Σ𝑝𝑇>0.1GeV& 1.9< 𝜂 < 5.0 Table 6.23: Generator level cuts imposed over the particles of the Σ±∗ 𝑏→ 𝜋± ( Λ𝑏→𝜋(Λ𝑐→𝑝𝐾𝜋) ). The subindex in each particle indicates the mother of the semi-stable particles. An additional condition of truth matching via TRUEID [101] is applied. 5. A similar tagging proceeding as the one in Section 6.3 is done. 6. The efficiency of each step is computed. 7. Finally, a fit is performed to obtain the number of Σ± 𝑏and Σ±∗ 𝑏. 6.5.1 Generator level selection As in Section 6.2.1 a very soft selection is applied at generator level to speed up the simulation, and waste a smaller amount of disk space. The pseudorapidity cut ( 1.9< 𝜂 < 5.0 ) is applied over every semi-stable particle at generator level. The cuts can be found in Table 6.3 in Section 6.5.1. The efficiency of these cuts is: 𝜀gen =0.10221 as shown in Table 6.4. 6.5.2 Reconstruction and stripping In this case, since the stripping lines to this normalisation channel were not expressly written for this analysis, the reconstructed MC already has the stripping applied so the reconstruction and stripping efficiencies are not factorised separately, but just one factor has been computed. The obtained reconstruction and stripping efficiency is: e 𝜀rec+sel =𝜀rec𝜀sel =0.03611. Even though the efficiencies have been computed at once, they still factorise. 6.5. Normalisation channel 75 6.5.3 Trigger The same trigger selection has been applied to the normalisation channel and the signal ones, already described in Section 6.2.4. By applying the same lines an efficiency of: 𝜀trig =0.71416 has been computed. 6.5.4 Multivariate classifier The proceeding shown in Section 6.2.5 has been applied again over the normalisation channel signal MC and background in order to obtain better discrimination of signal over background. A first iteration of the BDT was trained over the topological and kinematic variables. A feature importance algorithm is used to select a smaller sample of features to train the final version of the BDT. The results obtained are shown in Figure 6.27, from where the variables chosen are: piminusIPCHI2OWNPV, piplusIPCHI2OWNPV, pplusPT, KminusPT, LambdacplusPT, LambdacplusFDOWNPV, LambdacplusDIRAOWNPV, LambdacplusIPOWNPV, Lambdab0PT, Lambdab0IPCHI2OWNPV, Lambdab0DIRAOWNPV, Lambdab0FDCHI2OWNPV, Lambdab0ISOLATIONSTRIPPING, Lambdab0VCHI2PERDOF. Even though not all variables are as relevant as Lambdab0IPCHI2OWNPV , for example, at least the most relevant one from each particle has been chosen. The distribution of all features can be found in Figure 6.28, and the correlation of the most relevant ones is presented in Figure 6.30. The distributions are consistent with the result of the second iteration of features importance histogram shown in Figure 6.29. The overtraining of the BDT is checked by using a k-fold cross-validation technique as in Section 6.2.5. As before, 5 folds are used, each of them validated separately by computing the area under the ROC curve using different train/test samples. The scores are those presented in Table 6.24, while the ROC curve and the performance of the classifier can be found in Figures 6.31 and 6.32. As in Section 6.2.5, the search of peaking structures for different BDT cuts is performed, obtaining no results as seen in Figure 6.34. One can finally check the BDT response in similar mass bins, as in Section 6.2.5 we checked over background and signal regions, obtaining the results shown in Figure 6.33. The FOM from Equation (B.10) is once again used to choose the definitive BDT cut, as that maximising the FOM. This cut is BDT > 0.9 as seen in Figure 6.35. By imposing 76 Chapter 6. Dark matter and B-mesogenesis 0 5 10 15 20 25 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 piminus IPCHI2 OWNPV piminus PT piplus IPCHI2 OWNPV piplus PT pplus IPCHI2 OWNPV pplus PT Kminus IPCHI2 OWNPV Kminus PT Lambda cplus PT Lambda cplus P Lambda cplus IPCHI2 OWNPV Lambda cplus FD OWNPV Lambda cplus OWNPV CHI2 Lambda cplus DIRA OWNPV Lambda cplus FDCHI2 OWNPV Lambda cplus IP OWNPV Lambda b0 PT Lambda b0 IPCHI2 OWNPV Lambda b0 FD OWNPV Lambda b0 OWNPV CHI2 Lambda b0 DIRA OWNPV Lambda b0 FDCHI2 OWNPV Lambda b0 ISOLATION STRIPPING Lambda b0 VCHI2PERDOF Lambda b0 IP OWNPV Lambda b0 DOCA Lambda b0 DOCACHI2 Figure 6.27: Histogram with the importance of each of the features used in the first iteration of the BDT for the normalisation channel. As in Figures 6.2 and 6.10, no Σ±(∗) 𝑏particles are used in the BDT. Fold 1 Fold 2 Fold 3 Fold 4 Fold 5 BDT accuracy 0.93042 0.92566 0.93033 0.92500 0.92262 Table 6.24: Scores obtained using a k-fold cross-validation method for the normalisation decay classifier. 6.5. Normalisation channel 77 2000 4000 0.000 0.001 0.002 piminus IPCHI2 OWNPV 2000 4000 6000 8000 10000 0.0000 0.0002 0.0004 piminus PT 500 1000 1500 0.0000 0.0025 0.0050 piplus IPCHI2 OWNPV 1000 2000 3000 0.0000 0.0005 piplus PT MC DATA 500 1000 1500 0.000 0.002 0.004 pplus IPCHI2 OWNPV 2000 4000 6000 0.0000 0.0002 pplus PT 500 1000 1500 0.0000 0.0025 0.0050 Kminus IPCHI2 OWNPV 1000 2000 3000 4000 0.00000 0.00025 0.00050 Kminus PT 5000 10000 0.0000 0.0001 0.0002 Lambda cplus PT 50000 100000 150000 200000 0 1 ×10−5Lambda cplus P 500 1000 1500 2000 0.000 0.002 Lambda cplus IPCHI2 OWNPV 10 20 30 40 0.00 0.02 0.04 Lambda cplus FD OWNPV 20 40 60 0.00 0.01 0.02 Lambda cplus OWNPV CHI2 0.2 0.4 0.6 0.8 0 10 20 Lambda cplus DIRA OWNPV 2000 4000 6000 8000 0.0000 0.0005 Lambda cplus FDCHI2 OWNPV 0.2 0.4 0.6 0.8 0 1 2 Lambda cplus IP OWNPV 5000 10000 15000 0.0000 0.0001 Lambda b0 PT 2 4 0.0 0.2 0.4 Lambda b0 IPCHI2 OWNPV 10 20 30 40 0.00 0.05 0.10 Lambda b0 FD OWNPV 20 40 60 0.00 0.01 0.02 Lambda b0 OWNPV CHI2 −1.0 −0.5 0.0 0.5 1.0 0 5 10 Lambda b0 DIRA OWNPV 5000 10000 15000 0.00000 0.00025 0.00050 Lambda b0 FDCHI2 OWNPV 0.0 0.2 0.4 0.6 0.8 1.0 0 2 4 Lambda b0 ISOLATION STRIPPING 1 2 3 0 1 2Lambda b0 VCHI2PERDOF 0.01 0.02 0.03 0 20 40 Lambda b0 IP OWNPV 0.01 0.02 0.03 0 20 40 Lambda b0 DOCA 123 0 1 2Lambda b0 DOCACHI2 Figure 6.28: Distribution of signal and background variables of every feature used in the first iteration of the classifier. The label on top of each subplot indicates the variable plotted. The units in the y-axis are arbitrary since every distribution is normalised. this additional selection a new efficiency can be computed for the normalisation channel: 𝜀BDT =0.73647. 78 Chapter 6. Dark matter and B-mesogenesis 0 2 4 6 8 10 12 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 piminus IPCHI2 OWNPV piplus IPCHI2 OWNPV pplus PT Kminus PT Lambda cplus PT Lambda cplus FD OWNPV Lambda cplus DIRA OWNPV Lambda cplus IP OWNPV Lambda b0 PT Lambda b0 IPCHI2 OWNPV Lambda b0 DIRA OWNPV Lambda b0 FDCHI2 OWNPV Lambda b0 ISOLATION STRIPPING Lambda b0 VCHI2PERDOF Figure 6.29: Histogram with the importance of each of the features used in the final iteration of the BDT for the normalisation channel. 6.5. Normalisation channel 79 piminus IPCHI2 OWNPV piplus IPCHI2 OWNPV pplus PT Kminus PT Lambda cplus PT Lambda cplus FD OWNPV Lambda cplus DIRA OWNPV Lambda cplus IP OWNPV Lambda b0 PT Lambda b0 IPCHI2 OWNPV Lambda b0 DIRA OWNPV Lambda b0 FDCHI2 OWNPV Lambda b0 ISOLATION STRIPPING Lambda b0 VCHI2PERDOF piminus IPCHI2 OWNPV piplus IPCHI2 OWNPV pplus PT Kminus PT Lambda cplus PT Lambda cplus FD OWNPV Lambda cplus DIRA OWNPV Lambda cplus IP OWNPV Lambda b0 PT Lambda b0 IPCHI2 OWNPV Lambda b0 DIRA OWNPV Lambda b0 FDCHI2 OWNPV Lambda b0 ISOLATION STRIPPING Lambda b0 VCHI2PERDOF 1.00 0.13 0.05 0.03 0.04 0.25 0.01 0.33 0.00 0.62 0.02 0.56 -0.01 -0.02 0.13 1.00 -0.04 -0.05 -0.03 0.30 0.01 0.50 0.02 0.18 0.01 0.26 -0.05 -0.00 0.05 -0.04 1.00 0.41 0.85 0.06 0.05 -0.15 0.58 -0.04 0.00 0.02 0.24 -0.03 0.03 -0.05 0.41 1.00 0.74 0.06 0.06 -0.15 0.50 -0.04 -0.02 0.02 0.17 -0.00 0.04 -0.03 0.85 0.74 1.00 0.08 0.07 -0.19 0.68 -0.06 -0.01 0.02 0.25 -0.02 0.25 0.30 0.06 0.06 0.08 1.00 0.07 0.49 0.12 0.15 0.02 0.35 -0.04 0.02 0.01 0.01 0.05 0.06 0.07 0.07 1.00 0.00 0.05 -0.00 0.01 0.01 0.07 -0.02 0.33 0.50 -0.15 -0.15 -0.19 0.49 0.00 1.00 -0.08 0.46 0.03 0.40 -0.07 -0.01 0.00 0.02 0.58 0.50 0.68 0.12 0.05 -0.08 1.00 -0.06 0.05 0.01 0.37 -0.06 0.62 0.18 -0.04 -0.04 -0.06 0.15 -0.00 0.46 -0.06 1.00 -0.00 0.26 -0.09 0.02 0.02 0.01 0.00 -0.02 -0.01 0.02 0.01 0.03 0.05 -0.00 1.00 0.01 0.09 -0.04 0.56 0.26 0.02 0.02 0.02 0.35 0.01 0.40 0.01 0.26 0.01 1.00 -0.03 -0.02 -0.01 -0.05 0.24 0.17 0.25 -0.04 0.07 -0.07 0.37 -0.09 0.09 -0.03 1.00 -0.17 -0.02 -0.00 -0.03 -0.00 -0.02 0.02 -0.02 -0.01 -0.06 0.02 -0.04 -0.02 -0.17 1.00 Correlation Matrix of Features 0.0 0.2 0.4 0.6 0.8 1.0 Figure 6.30: Correlation matrix for the most important variables used to train the BDT for the normalisation channel. 0.0 0.2 0.4 0.6 0.8 1.0 False Positive Rate 0.0 0.2 0.4 0.6 0.8 1.0 True Positive Rate test sample train sample Figure 6.31: ROC curve obtained for the BDT using a train/test method for the normalisation channel. 80 Chapter 6. Dark matter and B-mesogenesis 0.2 0.4 0.6 0.8 bdt response 0 2 4 6 8 10 12 14 16 AU signal train signal test bkg train bkg test Figure 6.32: Performance of the classifier for the train/test samples normalisation decay. 0.6 0.7 0.8 0.9 BDT 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 right sideband mass bin 1 mass bin 2 0.6 0.7 0.8 0.9 BDT 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 signal region mass bin 1 mass bin 2 Figure 6.33: BDT response for different mass bins for the signal region (left) and for background region (right) for the normalisation channel. Note that both responses are very similar due to being backgrounddominated, if the full BDT response was plotted, both would peak overwhelmingly as seen in Figure 6.32. 5600 5700 5800 5900 6000 6100 Σbmass 0.0000 0.0005 0.0010 0.0015 0.0020 BDT >0.95 BDT >0.99 BDT >0.8 BDT >0.9 Figure 6.34: Effect of different BDT cuts over the mass spectrum of this decay. No peaking structures arise for a wide range of classifier cuts and the functional form is preserved. 6.5. Normalisation channel 81 0.0 0.2 0.4 0.6 0.8 1.0 BDT cut 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 FOM Figure 6.35: Figure of merit computation for the normalisation channel. The BDT cut of FOM=0.9 is chosen since it is the one that maximises the quantity. 88 Chapter 6. Dark matter and B-mesogenesis •48.48% the 𝐷mother being in the 𝜋soft ascendants list. •40.34% the 𝐷grandmother being in the 𝜋soft ascendants list. •14.05% the 𝐷great-grandmother being in the 𝜋soft ascendants list. In this case, any ascendant of the 𝜋 soft is in the ascendants of the 𝐷 the 63.80% of the times. Itmustbenotedthatthe trendwithineach category isnotmonotonicallyincreasing because ascendants tagged as a hadronising quark or the 𝑝𝑝 collision are not taken into account since it could never act as a peaking background. Within the shown cases, an additional study is performed, and potential peaking backgrounds are checked. This is done by checking if when the any ascendant requirement is met there is a dominant decay mode, and no dominating decay mode is found, being around 50 different decay modes are present with none of it being present more than 5% of the total decays. 6.8 Results By adjusting each value of Table 6.27 by the luminosity factor, the expected limits for the branching ratio for each decay mode and mass can be computed. In order to adjust to the full Run 2 luminosity, the following factors must be taken into account, depending on the decay mode: •ℒcs =√0.44 √5.1 •ℒcd =√0.22 √5.1 The numerators are the used luminosities for the analysis as stated in Section 6.1, and the denominator is the full Run II luminosity as indicated in the same section. By multiplying each row of Table 6.27 by its corresponding factor, Table 6.28 is obtained, being these the expected limits of both decay modes and every mass at a 95% CL, setting a world first and best measurement of these operators. 0.94 GeV 1.5 GeV 2.0 GeV 2.4 GeV 3.0 GeV 3.5 GeV 𝒪cs 8.96 ×10−51.44 ×10−52.43 ×10−41.06 ×10−46.23 ×10−4NOPHSP 𝒪cd 2.45 ×10−43.88 ×10−48.02 ×10−42.91 ×10−42.47 ×10−38.25 ×10−5 Table 6.28: Calculated values of ℬsignal for each mass and decay mode adjusted to luminosity. 89 Chapter 7 Results and discussion This work scope was to prove that searches beyond the Standard Model could be done with current and future experiments, and it has been proven for already taken LHCb data and several potential searches for CODEX-b have been shown. 7.1 Dark matter and B-mesogensis results The most relevant results obtained here are the efficiencies, all of them collected in Tables 7.1 and 7.2, a mass model for the signal and background date, shown in Section 6.4.5 and a first draft of the expected limits shown in Section 6.6.1. It is important to note that the analysis systematic errors have not been computed in this work, so the expected branching ratio limits computed may only be interpreted as a first approach to a result since the systematics may play a crucial role at a later stage. While this is true, the systematics of the analysis should not alter significantly the values computed for the expected limits, shown once again in Table 7.3. 𝜀gen 𝜀reco 𝜀sel 𝜀trig 𝜀BDT 𝜀tag 𝜀𝑚min 0.94 GeV 8.108 0.23342 0.05578 0.151982 0.55111 0.72301 6.39×10−5 1.5 GeV 8.004 0.22065 0.05283 0.1275892 0.63768 0.71818 5.45×10−5 2.0 GeV 7.855 0.21871 0.04888 0.084826 0.29369 0.74790 1.53×10−5 2.4 GeV 7.679 0.20379 0.04528 0.062786 0.70072 0.81521 2.54×10−5 3.0 GeV 7.277 0.19550 0.02763 0.019891 0.54901 0.76364 0.327×10−5 Table 7.1: Table with all of the efficiencies computed for the Σ±(∗) 𝑏→ 𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾)) Dark matter and B-mesogenesis LHCb search. 90 Chapter 7. Results and discussion 𝜀gen 𝜀reco 𝜀sel 𝜀trig 𝜀BDT 𝜀tag 𝜀tot 0.94 GeV 0.09637 0.25776 0.03944 0.146100 0.45041 0.76867 4.95×10−5 1.5 GeV 0.09619 0.24652 0.03853 0.114859 0.31227 0.84782 2.77×10−5 2.0 GeV 0.09527 0.22866 0.03659 0.084012 0.22241 0.78698 1.17×10−5 2.4 GeV 0.09405 0.21989 0.03258 0.064387 0.52109 0.74519 1.68×10−5 3.0 GeV 0.09051 0.19740 0.02478 0.038597 0.38636 0.64286 0.424×10−5 3.5 GeV 0.06873 0.18820 0.00868 0.025457 0.87179 0.84375 0.210×10−5 Table 7.2: Table with all of the efficiencies computed for the Σ±(∗) 𝑏→ 𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) Dark matter and B-mesogenesis LHCb search. 0.94 GeV 1.5 GeV 2.0 GeV 2.4 GeV 3.0 GeV 3.5 GeV 𝒪cs 8.96 ×10−51.44 ×10−52.43 ×10−41.06 ×10−46.23 ×10−4NOPHSP 𝒪cd 2.45 ×10−43.88 ×10−48.02 ×10−42.91 ×10−42.47 ×10−38.25 ×10−5 Table 7.3: Calculated values of ℬsignal for each mass and decay mode extrapolated to total luminosity. 7.2 Long lived particles results In this line of work it has been proven that for some Higgs portal model a lot of different signatures may be probed with the CODEX-b experiment, wheather it be in conjunction with the LHCb experiment or as a completely standalone experiment. Production 0.1 m 1 m 10 m 100 m 1000 m Inclusive 371 12953 3978 506 35 Inclusive & LHCb 92 9 0 0 0 Weak-boson 2 31 8 1 0 Higgs-strahlung 0 34 18 2 0 Table 7.4: Number of events expected for all detection modes described for every studied production mode. Lifetimes are given in terms of 𝑐𝜏 and in meters. 7.3. Discussion 91 10−1100101102103 cτ[m] 100 101 102 103 104 Events @ 14TeV and 300fb−1 A0in codex A0in codex and LHCb A0in codex and jet in LHCb A0in codex and muon in LHCb 10−1100101102103 cτ[m] 10−6 10−5 10−4 Efficiency @ 14TeV A0in codex A0in codex and LHCb A0in codex and jet in LHCb A0in codex and muon in LHCb Figure 7.1: Efficiencies plot (right) and expected events (left) to be detected at the CODEX-b experiment for a ℒ=300 fb−1. 7.3 Discussion The obtained results suppose two novel approaches to the discovery of beyond Standard Model physics have been shown, on the one hand obtaining a new world best and first measurement of two operators of a B-mesogenesis and Dark Matter model with two decay modes hardly accessible by any other experiment while using a seldomly used tagging methodology that shows a very good performance in the signal to background discrimination. On the other hand, new studies that will have a longer run as soon as the CODEX-b demonstrator, CODEX𝛽 experiment starts taking data have been performed. These studies show that potential modes pointing to new physics could be studied at this experiment, obtaining a good performance that could compete with some of the other already consolidated experiments. 93 Chapter 8 Conclusions In this thesis the first analysis studying the 𝒪𝑐𝑠 and 𝒪𝑐𝑑 proposed in [18] was performed, obtaining the first measurement of potential expected branching ratios for two decay modes, Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾)) and Σ±(∗) 𝑏→𝜋±(Λ𝑏→ 𝜓DM𝐾(𝐷→𝜋𝜋𝐾)) . Also, a generator level efficiency to three Higgs production modes assuming Higgs portal decays has been computed. A detailed analysis of the 2018 Run II data has been performed in order to accomplish the first of the two mentioned tasks. In this work it has been showcased a rarely used tagging mechanism that could very much be used for many other missing energy analyses at LHCb, since due to the forward geometry of the detector, different approaches may be followed and traditional missing energy analyses are out of reach. Other traditional methodologies used in high energy physics such as the training of BDTs to obtain a better signal to background discrimination or the computation of expected limits through a hypothesis testing methodology. The CODEX-b experiment, soon to be installed near the LHCb is expected to start taking data soon at the moment of this writing, so computing and person power will be required. The job done in this thesis is expected to be a helpful tool to other scientists involved in this project. The code developed for this is very modular and easy to edit and works right out of the box, with very few python libraries, and it will be circulated to the whole collaboration. These two tightly related topics show that many beyond Standard Model physics are yet to be probed and studied, and that novel approaches may be followed in order to obtain new results while improving some of the already obtained ones. 95 Appendices 97 Appendix A Appendix Analysis A.1 Mass distributions for every dark matter mass This appendix shows every mass distribution as discussed in Section 6.4.3. −3−2−1 0 1 2 3 m2 miss −m2 teo 0.0 0.1 0.2 0.3 0.4 arbitrary units non star star data −3−2−1 0 1 2 3 m2 miss −m2 teo 0.0 0.1 0.2 0.3 0.4 arbitrary units non star star data −3−2−1 0 1 2 3 m2 miss −m2 teo 0.0 0.1 0.2 0.3 0.4 arbitrary units non star star data −3−2−1 0 1 2 3 m2 miss −m2 teo 0.0 0.1 0.2 0.3 0.4 arbitrary units non star star data Figure A.1: Mass distribution for the Σ±(∗) 𝑏→𝜋±(Λ𝑏→𝜓DM𝐾(𝐷→ 𝜋𝜋𝐾)) for mass hypothesis of 𝑚(𝜓DM)=0.94,1.5, 2.4 and 3.0 GeV. A.2 Signal fits for every dark matter mass This appendix shows every fit performed as discussed in Sections 6.4.4 and 6.4.5. 104 Appendix B. Resumo non se coñece, chamada materia escura (DM) [8,9]. Este feito non está contemplado dentro do Modelo Estándar, supoñendo outra das súas limitacións [10 – 12]. O SM tampouco é capaz de explicar toda a asimetría observada entre materia e antimateria, necesitando de mecanismos alternativos para dar conta desta discrepancia, como por exemplo a barioxénese. B.1.1 Matriz CKM As interacións do sector de sabor no Modelo Estándar están mediadas maioritariamente por bosóns 𝑊± en desintegracións tipo Λ→𝑝𝜇−¯ 𝜈𝜇 onde a nivel quarks o que está a suceder é 𝑠→𝑢𝜇−¯ 𝜈𝜇. Estas desintegracións estan caracterizadas pola matriz de Cabibbo-KobayashiMaskawa (matriz CKM) [13 – 15]. A súa construción consiste en, a partir da densidade lagranxiana do Modelo Estándar: ℒ𝐺=−Õ 𝑎 1 4𝑔2 𝑎+𝑖Õ Ψ 3 Õ 𝑖=1¯ Ψ𝑖/ 𝐷Ψ𝑖,(B.1) onde 𝑎 é cada unha das interacións do Modelo Estándar e Ψ = 𝑄𝐿, 𝑢𝑅, 𝑑𝑅, 𝐿𝐿, 𝑒𝑅. Observando as simetrías gauge globales desta lagranxiana obsérvase que está dexenerada en sabor, e estas simetrías poden romperse cunha interación Yukawa do tipo: ℒ𝑌=−𝑌𝑑 𝑖,𝑗 ¯ Ψ𝐿,𝑖 𝜙𝑑𝑅,𝑗 −𝑌𝑢 𝑖,𝑗 ¯ Ψ𝐿,𝑖 𝜀𝜙∗𝑢𝑅,𝑗 +ℎ.𝑐. (B.2) con 𝑌𝑞 matrices complexas, 𝜙 o campo do Higgs e 𝑖, 𝑗 índices que indican a que doblete/singlete pertencen as partículas. 𝜀 é o tensor antisimétrico en 2D [16] e ℎ.𝑐. indica o hermítico conxugado de toda a lagranxiana. A matriz que diagonaliza 𝑌𝑑 ou 𝑌𝑢 (non son matrices compatibles) é a coñecida como matriz CKM a cal pode escribirse como:  𝑑′ 𝑠′ 𝑏′ =©« 𝑉𝑢𝑑 𝑉𝑢𝑠 𝑉𝑢𝑏 𝑉𝑐𝑑 𝑉𝑐𝑠 𝑉𝑐𝑏 𝑉𝑡𝑑 𝑉𝑡𝑠 𝑉𝑡𝑏 ª®¬ 𝑑 𝑠 𝑏.(B.3) Esta matriz describe a física de sabor dentro do Modelo estándar, a cal pode expresarse de dous xeitos, como xiros no espazo de sabor [17] ou coma unha matriz que indica a xerarquía desta interación [15], onde os saltos de dúas xeracións están fortemente suprimidos fronte aos dunha soa xeración. Un comportamento similar no sector da materia escura estudarase nesta tese. B.1. Introdución 105 B.1.2 Materia escura e B-mesoxénese Un modelo fenomenolóxico [18,19] que explicaría a barioxénese e a materia escura será estudado neste traballo. As tres características que definen este modelo son as seguintes: • Non son necesarias altas temperaturas no Universo temperán, e funcionaría con temperaturas máis baixas 5MeV ≲𝑇≲30 MeV. • O número bariónico universal sería unha cantidade conservada, asumindo que a materia escura contén número bariónico. • A asimetría materia/antimateria estaría estreitamente ligada a diferentes observables dos mesóns 𝐵. Este modelo permite fraccións de desintegración relativamente altas de barións a materia escura e un número arbitrario de mesóns do SM así como de mesóns a materia escura e barións. Bases da B-mesoxénese Este tipo de modelos requiren de cumplir as chamadas condicións de Sakharov [25]: • Violación de C e CP: a materia e a antimateria son diferentes de base, o cal estaría garantido pola oscilación de mesóns B. • Alonxamento do equilibrio térmico: o equilibrio térmico non pode ser constante xa que entón a mesma materia e antimateria que se produce desaparece. Isto estaría garantido por un suposto campo presente no Universo temperán que decae a quarks 𝑏. • Violación do número bariónico: neste modeloa violaciónsería unicamenteaparente no sector do Modelo Estándar, pero no global sería unha cantidade conservada. Un diagrama destas condicións é o da Figure B.1. Descripción formal e restricións cinemáticas Debido a que unha soa partícula non pode describir toda a materia escura do Universo, a partícula descrita ata o de agora, 𝜓DM , podería decaer a outras dúas diferentes do sector escuro as cales xa serían estables baixo unha simetría Z2 que estabilizaría os novos singletes de materia escura 𝜙 e 𝜉 . A lagranxiana da interación sería da forma: ℒ ⊃ −𝑦𝑑¯ 𝜓DM𝜙𝜉 +h.c. (B.4) As condicións cinemáticas para a existencia deste modelo son as seguintes: 106 Appendix B. Resumo Figure B.1: Diagrama do modelo a estudar e como satisfai as condicións de Sakharov. A figura adaptouse de [18]. 𝑚𝐵>𝑚𝜓DM +𝑚𝑝⇒𝑚𝜓DM <𝑚𝐵−𝑚𝑝≃4.34 GeV/c2,(B.5) o cal garante que polo menos unha desintegración é posible. Por outra banda, para non comprometer a estabilidade do protón: 𝑚𝑝<𝑚𝜓DM +𝑚𝑒⇒𝑚𝜓DM >𝑚𝑝−𝑚𝑒≃937.8MeV/c2.(B.6) Con todo isto, o posible rango de masa da materia escura sería: 0.94 GeV/c2<𝑚𝜓DM <4.34 GeV/c2.(B.7) Operadores de materia escura e desintegracións permitidas Unha lagranxiana efectiva que permitiría as desintegracións a meteria escura viría dada pola seguinte densidade: ℒeff =𝒪𝑢𝑖𝑑𝑗 𝑦𝑖𝑦𝑗 𝑀2 𝑌 ,(B.8) onde 𝑦𝑖𝑦𝑗 é o produto do acoplamento referido aos quarks 𝑖 e 𝑗 . De acordo a esta lagranxiana, os operadores permitidos serían: 𝒪𝑢𝑑 =𝜓DM 𝑏 𝑢 𝑑, (B.9a) 𝒪𝑢𝑠 =𝜓DM 𝑏 𝑢 𝑠, (B.9b) 𝒪𝑐𝑑 =𝜓DM 𝑏 𝑐 𝑑, (B.9c) 𝒪𝑐𝑠 =𝜓DM 𝑏 𝑐 𝑠. (B.9d) B.1. Introdución 107 Operator and Decay Initial State Final State ∆M (MeV) 𝐵𝑑𝜓DM +𝑛(𝑢𝑑𝑑)4340.1 𝒪𝑢𝑑 =𝜓DM 𝑏 𝑢 𝑑 𝐵𝑠𝜓DM +Λ(𝑢𝑑𝑠)4251.2 ¯ 𝑏→𝜓DM 𝑢 𝑑 𝐵+𝜓DM +𝑝(𝑑𝑢𝑢)4341.0 Λ𝑏¯ 𝜓DM +𝜋05484.5 𝐵𝑑𝜓DM +Λ(𝑢𝑠𝑑)4164.0 𝒪𝑢𝑠 =𝜓DM 𝑏 𝑢 𝑠 𝐵𝑠𝜓DM +Σ0(𝑢𝑠𝑠)4025.0 ¯ 𝑏→𝜓DM 𝑢 𝑠 𝐵+𝜓DM +Σ+(𝑢𝑢𝑠)4090.0 Λ𝑏¯ 𝜓DM +𝐾05121.9 𝐵𝑑𝜓DM +Λ𝑐+𝜋−(𝑐𝑑𝑑)2853.6 𝒪𝑐𝑑 =𝜓DM 𝑏 𝑐 𝑑 𝐵𝑠𝜓DM +Σ0 𝑐(𝑐𝑑𝑠)2895.0 ¯ 𝑏→𝜓DM 𝑐 𝑑 𝐵+𝜓DM +Λ+ 𝑐(𝑑𝑐𝑢)2992.9 Λ𝑏¯ 𝜓DM +𝐷03754.7 𝐵𝑑𝜓DM +Σ0 𝑐(𝑐𝑠𝑑)2807.8 𝒪𝑐𝑠 =𝜓DM 𝑏 𝑐 𝑠 𝐵𝑠𝜓DM +Ω𝑐(𝑐𝑠𝑠)2671.7 ¯ 𝑏→𝜓DM 𝑐 𝑠 𝐵+𝜓DM +Σ+ 𝑐(𝑐𝑠𝑢)2810.4 Λ𝑏¯ 𝜓DM +𝐷−+𝐾+3256.2 Table B.1: Desintegracións máis lixeiras e diferencias de masas obtidas no modelo. Para cada operador particular as fraccións de desintegración que esperamos atopar son similares, xa que o espazo fásico é similar. Máis mesóns lixeiros poderían aparecer nos estados finais, unicamente cambiando a diferencia de masa e cunha supresión na fracción de desintegración. Adaptado de [18]. Este formalismo arroxa diferentes desintegracións posibles, entre elas as da Table B.1. As desintegracións a estudar nesta tese corresponden aos operadores 𝒪𝑐𝑠 e 𝒪𝑐𝑑 . En particular ás seguintes desintegracións: Λ𝑏→𝜓DM𝐾(𝐷→𝜋𝜋𝐾) e Λ𝑏→𝜓DM𝜋(𝐷→𝜋𝜋𝐾), respectivamente. Estado experimental actual Este modelo está pouco explorado na actualidade en colisores e en fábricas de mesóns 𝐵 . Unha búsqueda directa de 𝐵→Λ𝜓DM foi realizada en BaBar sen obter sinal significativa e obtendo un límite á fracción de desintegración de 0.13 −5.2×10−5 para 1.0<𝑚𝜓DM <4.2GeV/c2 [26]. BaBar tamén realizou a busca de 𝐵+→𝜓DM +𝑝 108 Appendix B. Resumo Figure B.2: Límites actuais en buscas inclusivas de Br( 𝐵→ ℬ𝜓DMℳ ) en función da masa da materia escura restrinxido polas busquedas de ALPEH, CMS e as re-análises de ALPEH. Figura obtida de [18] baixo licencia creative commons. sen atopar sinal significativa e establecendo un límite superior de 10−7−10−5 para 1.0<𝑚𝜓DM <4.3GeV/c2[27]. Buscas indirectas en CMS [28] e ATLAS [29], así como re-análises de ALEPH [30] permiten establecer límites ás fraccións de desintegracion dos outros operadores de 10−3. Un resumo destes traballos pode ser atopado en Figure B.2 B.1.3 Partículas de vida media longa Outros xeitos de expandir o Modelo Estándar implican a existencia de partículas de vida media longa [31,32], para as cales os detectores actuais non son óptimos. Os modelos estudados nesta tese son aqueles coñecidos como portais do Higgs, os cales propoñen que hai un sector rico de desintegracións que comezan co bosón de Higgs, entre as cales hai partículas de vida media longa. B.2. Obxectivos 109 Figure B.3: Diagrama dunha potencial desintegración permitida polo modelo de portal de Higgs a estudar. Modelos de vida media longa Un operador que permita estas desintegracións sería, por exemplo, da forma 𝑆𝐻𝐻† , 𝑆2𝐻𝐻† onde H é o SM Higgs e S unha nova partícula escalar. Estes operadores permitirían desintegracións como as da Figure B.3. Para caracterizar estas desintegracións tres modos de produción diferentes do Higgs serán estudados [39 – 41]: produción inclusiva de Higgs, onde ningunha restrición sobre o modo produción é imposta; Higgs-strahlung, onde o Higgs e producido xunto a un bosón feble e fusión de bosón feble, onde o Higgs e producido xunto a un jet. Estado experimental actual Algún experimentos do CERN estudaron ás partículas de vida media longa [42,43]. Ao non seren estes experimentos dedicados ao estudo de partículas de vida media longa outros dedicados á búsqueda desta física van aparecendo [44 – 46], como por exemplo CODEX, o cal é o marco desta sección da tese. Un diagrama resumo pode atoparse en Figure B.4. B.2 Obxectivos Búscase establecer por primeira vez límites a desintegracións relacionadas cos operadores 𝒪𝑐𝑠 e 𝒪𝑐𝑑 , así como obter unha eficiencia a nivel xerador para ás desintegracións do Higgs a partículas de vida media longa descritas. 110 Appendix B. Resumo Figure B.4: Diagrama de estado actual e previsto deste campo de estudo. Reproducido de [33] baixo licenza creative commons. B.3 Montaxe experimental B.3.1 Experimento CODEX-b CODEX-b trátase dun futuro detector que será instalado preto do punto de impacto do LHCb. Este detector consistirá nun volume de 10 m × 10 m × 10 m formado por cámaras de placas resistivas (RPCs) [56]. Estes paneis de 2 m × 1 m conformarán todo o volume do detector. A parametrización deste tomando o punto de impacto coma o (0,0,0)ven dado por •25,75 m < 𝑥< 35,75 m •-5m < 𝑦<5m •5m<𝑧< 15 m. Debido á súa localización detrás de diferentes blindaxes e moi transversal aos feixes de protóns permite unha representación moi fiel de todos os posibles fondos derivados do Modelo Estándar e un mantemento máis constante que outros experimentos. B.3.2 Experimento LHCb O LHCb é un dos catro grandes (ALICE, ATLAS, CMS e LHCb) experimentos no gran colisor de hadróns (LHC) do CERN. Este experimento caracterízase por ser un espectrómetro deseñado [62] para reconstruir e estudar a física relacionada cos quarks 𝑏 . Trátase dun detector cara adiante que pode reconstruir partículas cunha pseudorapidez 1.6≤𝜂≤4.9. Este experimento esta conformado por unha serie de subdetectores: B.4. Metodoloxía 111 • VELO [66 – 68]: o VELO (polo seu nome en inglés Vertex Locator) encárgase de medir con gran precisión o punto no que se producen e decaen hadróns pesados, os cales tipicamente conteñen un quark 𝑏. • RICH [70, 71]: detectores Cerenkov encargados de facer unha asignación probabilística á natureza das partículas en función da súa velocidade e con diferentes hipóteses de masa. • Sistema de trazas [72,73]: sistema encargado de reconstruir a traxectoria das partículas que atravesan o detector. • Imán [75]: dipolo magnético que se utiliza para curvar a traxectoria das partículas e así medir o seu momento. • Calorímetros [76,77]: miden a enerxía depositada por diferentes partículas o cal permite establecer unha selección en termos da enerxía transversa e axudan na caracterización da natureza das mesmas. • Estacións de muóns [78,79]: sistema deseñado para reconstruir a traxectoria seguida polos muóns no detector. B.4 Metodoloxía Para a búsqueda en LHCb xérase Monte Carlo para todos os modos de sinal de interese, e logo procedemos a realizar unha análise multivariante utilizando unha pequena porcentaxe dos datos coma fondo. Tras a análise multivariante realizamos un proceso de etiquetado enter Λ𝑏 e 𝜋 para reconstruir candidatos a Σ𝑏 xa que isto mellora significativamente a eficiencia no proceso de discriminar sinal de fondo. Tras realizar o mesmo proceso sobre unha desintegración coñecida contra a cal comparar e normalizar os resultados obtidos neste traballo, procederase ao cálculo do límite da fracción de desintegración. Por outra banda, xérase tamén Monte Carlo para os diferentes modos de produción do Higgs e aplícanse unha serie de cortes para obter as eficiencias desexadas. B.5 Partículas de vida media longa Xeráronse eventos de LHC en PYTHIA8 [89] cunha enerxía no centro de masas de 14 TeV para os tres modos de produción mencionados do Higgs. Aplicáronse os cortes para que as partículas de interese estean contidas nos detectores, así coma uns cortes en pseudorapidez e en momento transverso para os casos nos cales consideramos a detección simultánea en LHCb e en CODEX. Os resultados obtidos poden atoparse en Table B.2 e en Figure B.5. 112 Appendix B. Resumo Production 0.1 m 1 m 10 m 100 m 1000 m Inclusive 371 12953 3978 506 35 Inclusive & LHCb 92 9 0 0 0 Weak-boson 2 31 8 1 0 Higgs-strahlung 0 34 18 2 0 Table B.2: Eventos esperados para todos os modos de produción e detección descritos. As vidas medias 𝑐𝜏están en metros. 10−1100101102103 cτ[m] 100 101 102 103 104 Events @ 14TeV and 300fb−1 A0in codex A0in codex and LHCb A0in codex and jet in LHCb A0in codex and muon in LHCb 10−1100101102103 cτ[m] 10−6 10−5 10−4 Efficiency @ 14TeV A0in codex A0in codex and LHCb A0in codex and jet in LHCb A0in codex and muon in LHCb Figure B.5: Eficiencias (dereita) e eventos esperados (esquerda) en CODEX-b para unha luminosidade integrada de ℒ=300 fb−1. B.6 Materia escura e B-mesoxénese B.6.1 Datos e Monte Carlo Xerouse Monte Carlo para todos os modos de sinal así como para fondo e modo de normalización. Por outra banda, utilizouse unicamente unha pequena parte dos datos dispoñibles de todo o Run II, concretamente 0.44fb−1 para o operador 𝒪cs e 0.22fb−1 para o operador 𝒪cd . No caso do Monte Carlo, uns pequenos cortes sobre diferentes variables cinemáticas foron impostos para axilizar a xeración de eventos que superen a posterior selección. Unha eficiencia debida a estes cortes así como outra debido á eficiencia intrínseca de reconstrucción do detector é calculada. Todas as eficiencias serán presentados nunha soa táboa. B.6. Materia escura e B-mesoxénese 113 B.6.2 Selección Selección de Stripping Úsanse tres liñas, duas das cales foron deseñadas para esta análise: LambdaDecaysDMLambdaToDPiLine e LambdaDecaysDMLambdaToDKLine sendo a terceira Lb2LcPiNoIPLc2PKPiBeauty2CharmLine [109,110] a de normalización. As liñas de sinal teñen uns cortes cinemáticos e topolóxicos que buscan maximizar a discriminación de sinal contra fondo baseados en buscar vértices moi alonxados do punto de impacto. Deste selección obtemos unha nova eficiencia. Selección do disparador O experimento LHCb ten unha serie de disparadores (L0, HLT1 e HLT2) encargados de seleccionar eventos para a súa escritura en disco de acordo cunha serie de variables (número de trazas, momento transverso das partículas, topoloxía do evento...) para poder traballar cunhas taxas de datas manexables para as diferentes compoñentes de hardware e software. Nesta análise, as liñas do disparador para cada un dos seus niveles seleccionadas son as seguintes: L0HadronDecision para o L0; Hlt1TrackMVADecision e Hlt1TwoTrackMVADecision para o HLT1; Hlt2Topo2BodyDecision , Hlt2Topo3BodyDecision e Hlt2Topo4BodyDecision para o HLT. En base a esta selección obtesne unha nova eficiencia. Clasificador multivariante Resultan útiles para mellorar a discriminación de sinal contra fondo os algoritmos de aprendizaxe automático. Neste caso utilizamos unha árbore de decisión impulsada, concretamente un clasificador de aumento de gradiente [115,116]. 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