Evaluation of Higgs Mass in the MSSM

Evaluación de la Masa del Higgs en el MSSM (Evaluation of Higgs Mass in the MSSM) Trabajo de Fin de Máster para acceder al MÁSTER EN FÍSICA DE PARTÍCULAS Y COSMOS Autor: Roberto Guerrero Romero Director\es: Dr. Sven Heinemeyer Julio - 2021 ii UIMP-UC Abstract Cantabria and Menéndez Pelayo University College Physics MSc UIMP-UC Evaluation of the Higgs mass in the MSSM by Roberto C. GUERRERO ROMERO This works used the state-of-art calculation implement in FeynHiggs for the calculation of mass of light CP −even Higgs boson h. We explore the benchmark scenarios propose by author in Ref.[13,14] with the last version of FeynHiggs which implements new methods as the calculation of uncertainties for the mass mhof light Higgs boson h. iii Acknowledgements I would like to thank to my classmate Jerry, Rufa and Jimmy, and proffessor Alberto Ruiz for the discussion of any doubt I ever had. I am especially grateful with my supervisor Sven Heinemeyer, for all the support and all the patience he had pointing out my mistakes. iv Index Abstract ii Acknowledgements iii 1 Introduction 1 2 Standard Model 2 2.1 Gauge Theory ......................................... 2 2.2 Standard Model with Higgs ................................. 3 2.3 Experimental Status of Standard Model Higgs Boson .................. 5 3 Supersymmetry 7 3.1 Dark Matter .......................................... 7 3.2 Gauge Coupling Unification ................................. 7 3.3 Hierchary Higgs Mass Problem ............................... 8 4 Minimal Supersymmetric Standard Model:MSSM 10 4.1 Supersymmetric particle spectrum ............................. 12 4.2 The Higgs sector in MSSM .................................. 13 4.3 Higher order corrections ................................... 17 4.4 Calculation in MSSM. FeynHiggs .............................. 19 5 Benchmarks Scenarios in MSSM 20 5.1 M125 hScenario ......................................... 21 5.2 M125 h(˜ τ)Scenario ....................................... 23 5.3 M125 h(˜ χ)Scenario ....................................... 25 6 Benchmark Scenarios at low tanβRegion. 27 6.1 Scenario M125 h,EFT ........................................ 28 6.2 Scenario M125 h,EFT(˜ χ)...................................... 31 7 State of SUSY searches 35 8 Summary 38 Bibliography 39 1 Chapter 1 Introduction Standard Model(SM) theory is based on gauge the gauge SU(3)c×SU(2)L×U(1)Y, where C,L and Ymeans respectively Colour, Left Handed and Hypercharge. SM describes every interaction except gravitation and its predictions started with the discovery of neutral currents in 1973 at CERN, followed by boson vector Z and W in 1983. Thirty years after, the ATLAS and CMS detector announced that they found a particle in agreement with the last particle predicted by SM, the Higgs Boson. But SM has problems, for instance the Higgs mass hierarchy problem , the gravitation force, dark matter and energy. As solutions, there are many theoretical models called Beyond Standard Models and one of them is the Minimal Supersymmetry Standad Model(MSSM). MSSM predicts an extension of particles, SUSY particles, and in simply words, every fermion in SM there is a bosonic SUSY particle and every bosonic SM particle has a SUSY fermion particle. Since we did not see any of these particle, they must be in other range of energy, the SUSY scale, heavier that the electroweak scale. Due to the addition of SUSY particles, that differs in spin half a unit in comparison with the SM partners, MSSM increase the number of free parameters to 100 but is possible reduce until 10 in order to predict scenarios where LHC is able to reach. The chapter 2 and 3 is an introduction to Standard Model and why we need physics beyond SM. In chapter 4, we described a bit the MSSM, focusing on the main parameters that we are going to use in the following chapters. Chapter 5 and 6 describe with in detail, the benchmark scenarios according to the searches by LHC. Finally, the last chapter collects the results of CMS and ATLAS collaboration according to the MSSM predictions. 2 Chapter 2 Standard Model The Standard Model(SM) is the best framework we have so far to describe mathematically the particle physics. Its construction began in the fifties in order to explain the new interactions between particle that had been appeared in the experiments. During this time, it was a short confusion period but it raised three good ideas which helped the development of SM. The first was the quark model, where protons and neutrons are made by elementary particles with fractional charge. Thus encouraged to study the mesons, which are particle composed of one quark and one antiquark. The second was the construction of Gauge Theory by Yang and Mills in 1954. They developed a theory based on three dimensional group(SU(2)) of isotopic spin conservation with the aim of explain the strong interaction. And the third idea was to apply a concept from the successful theory of superconductivity, the Spontaneous Broken Symmetry, crucial for the Higgs mechanics. With these ideas Weinberg[1], Glashow and Salam developed the Electroweak model. As we said, the motivation of Gauge theory was to explain the strong interaction but they could not apply these ideas to explain it. Instead of applying these concepts on strong force, Weinberg decided to apply them in weak interaction without considering the quarks 1and got a successful model based on gauge symmetry SU(2)×U(1). 2.1 Gauge Theory Gauge symmetry are local transformation in space-time. For instance, for the most simple scalar lagrangian L0=∂µφ∗∂µφ−V(φ∗φ), φ(x)→´ φ(x) = eiα(x)φ(x), (2.1) where α(x)is an arbitrary phase. For being an invariance gauge we must define: Dµ=∂µ−igAµ(x)(2.2) Aµ(x)→´ Aµ(x) = Aµ(x) + 1 g∂µα(x), (2.3) where Dµis the definition of Covariant Derivative and ´ Aµis the gauge transformation of the vector field. Notice that we introduce by definition Aµ. Thus allows us to have additional terms into the lagrangian, Lnew =L0−gJµAµ−g2AµAµφ∗φ, (2.4) where Jµ=i[φ(Dµφ)∗−φ∗(Dµφ)] is the current. This example shows how is the interaction between a scalar field and a vector field with a U(1)symmetry, i.e., there is only an phase, α. 1quarks will add later 2.2. Standard Model with Higgs 3 In a general case SU(N): φ(x)→´ φ(x) = eiαaTaφ(x), (2.5) Dµ=∂µ−igTaAa µ(x), (2.6) Aa µ(x)→´ Aa µ(x) = Aa µ(x) + 1 g∂µαa(x)−fabcαbAc µ(x), (2.7) where facb is the structure constant of the group SU(n)with n2−1Tagenerators. This gauge transformation is called Nom-Abelian gauge in contrast with the first case, Abelian gauge. The difference come from the structure constant and is specially relevant the case SU(2)in the electroweak theory. 2.2 Standard Model with Higgs Weimberg, Salam got contruct the SM based on the gauge symmetry SU(2)L×U(1)Y, generating four massless gauge boson, Wi µwith i=1, 2, 3 and Bµ. To account the (V−A)pattern only left fermions interact with Wi µand form SU(2)Ldoublets: [2]: L=νl l−L ,Q=qu qdL ,qu=u,c,t;qd=d,s,b;l=e,µ,τ. (2.8) Since generator of SU(2)are Pauli matrices, σi 2, we can find in analogous with the (2.2) and (2.5), the covariant derivative in the case of doublets. ∂µ→Dµ=∂µ+igWT.Wµ+i´ gY 2Bµ, (2.9) DL µ=  ∂µ−i 2(gW3 µ+´ gYf LBµ)−ig √2W− µ −ig √2W− µ∂µ+i 2(gW3 µ−´ gYf LBµ) . (2.10) And right handed singlet DR µ=∂µ−i´ gYf R 2Bµ, (2.11) with W±=1 √2(W1 µ∓iW2 µ)and g,´ gare the couplings with the vector field Wµand Bµrespectively and Ythe hypercharge. The minimal Higgs model consists of one complex scalar field[2] φ=φ+ φ0=1 √2φ1+iφ2 φ3+iφ4. (2.12) The correspond lagrangian is L= (∂µφ)†(∂µφ)−V(φ), (2.13) with a potential V(φ) = µφ†φ+λ(φ†φ)2, (2.14) where µand λare free parameters of the model. For µ2<0, the potential has an infinite set of minimums. ∂V ∂φ†|φ=φ0=0→ −µ2 2λ=ν2 2. 4Chapter 2. Standard Model As we impose the symmetry SU(2)L×U(1)Y, then we can find a parameterization for the double scalar Higgs by φ=1 √2exp iξiσi ν 0 ν+h, (2.15) where ξiare scalar fields relate with φ1,φ2and φ4and ν+h(x) = φ3(x). Then, going to unitary gauge, we are able to remove the phase with the intention of obtaining a real field h(x) φ(x) = 1 √20 ν+h(x). (2.16) The vacuum state or vacuum expectation value(vev) is φ0=h0|φ(x)|0i=v √2. (2.17) Then, applying the gauge transformation in our lagrangian (2.12) (Dµφ)†(Dµφ) = 1 2(∂µh)(∂µh) + 1 8g2 W(W1 µ+iW2 µ)(W1,µ−iW2,µ)(ν+h)2 +1 8(gWW3 µ−´ gBµ)(gWW3,µ−´ gBµ)(ν+h)2. (2.18) As W3 µand Bµare neutral, they must mix so as to obtain the Zµand Aµboson fields. From the last equation, the mass term is following by the quadratic term ν2, hence ν2 8(gWW3 µ−´ gBµ)(gWW3,µ−´ gBµ) = ν2 8W3 µBµg2 W−gW´ g −gW´ g´ g2W3,ν Bµ. (2.19) We see that both fields are relate by a non-diagonal matrix. Weinberg found that, Aµand Zµ, are the eigenvalues, hence Aµ=cosθWBµ+sinθWW3 µ, (2.20) Zµ=−sinθWBµ+cosθWW3 µ, (2.21) where θWis the weak angle. Moreover, as Higgs couples with bosons, it couples with fermionic fields as the following gaugeinvariant Yukawa Lagrangian LY=−ye(¯ Lφ)eR−yd(¯ Qφ)dR−yµ¯ QφCuR+h.c.. (2.22) which involves the Yukawa coupling, yfand it describes the interaction between Higgs and the left doublet with the right singlets fermions. The term φC=iσ2φ∗, hence −LY=∑ f yfν √21+h ν¯ f f =∑ f mf1+h ν¯ f f,f=u,d,e. (2.23) We can see that in the case of neutrinos, the Higgs mechanism does not generate a mass term. To sum up, the Lagrangian of SM is LSM =Lgauge(gs,g,´ g) + LYukawa(yl,yu,yd) + LHiggs(λ,µ2). (2.24) 2.3. Experimental Status of Standard Model Higgs Boson 5 2.3 Experimental Status of Standard Model Higgs Boson The most recent data of Higgs Boson results come from LHC, ATLAS and CMS particularly. There are four big channel where Higgs boson is produced: (A) Gluon-Gluon Fusion (B) Vector Boson Fusion channel (C) VH channel (D) ttH channel FIGURE 2.1: Higgs channels production The symbol V refers to the boson W/Zand qfor quarks in the SM. For each diagrams, the respective cross sections at √s13 TeV are[3]: 1. σ(ggF): 48.6 ±2.8 pb 2. σ(VBF): 3.78 ±0.08 pb 3. σ(VH): 1.37±0.03,0.88 ±0.03 pb 4. σ(ttH): 0.50 ±0.04 pb These cross sections give an idea of which decay is the predominant, and looking the value, it seems that the dominance is the ggF. On the other hand, quarks hadronize 2very fast and its detection are based on the detection of mesons or hadron after the hadronization in jets. This process lasts until the jets reach a stable energy , but in the process involve many quarks interaction among themlselves and gluons, therefore, it produce a large background, hampering the data analysis. The respective branching ratios are: Decay Branching ratio Rel. uncertainty H→γγ 2.27 ×10−32.1% H→ZZ 2.62 ×10−2±1.5% H→W+W−2.14 ×10−1±1.5% H→τ+τ−6.27 ×10−2±1.6% H→b¯ b5.82 ×10−1 1.2% −1.3% H→c¯ c2.89 ×10−2+5.5% −2.0% H→Zγ1.53 ×10−3±5.8% H→µ+µ−2.18 ×10−4±1.7% TABLE 2.1: Higgs Branching ratio and the relative uncertainty for SM Higgs boson with mH=125 GeV. Table from Status of Higgs Boson Physics, [3] Although the most significant decay is the H→b¯ b, the channel H→γγ is the most clean. The problem with it is not the background, but photons is produced easily, hence, the identification is more difficult. 2Top quak does not hadronize, it decay due to the large mass 12 Chapter 4. Minimal Supersymmetric Standard Model:MSSM A summary at the moment is that we have all our particle in a superfield denoted byˆ. The total lagrangian is the sum of superfield lagrangian plus a kinetic lagrangian obtained with the contributions and combination between gauge bosons, plus a superpotential. In order to separate SUSY and SM particles, we need to add a new term,the soft SUSY-breaking lagrangian. It preserves the cancellation in hierarchy problem and generates finite quantum corrections. 4.1 Supersymmetric particle spectrum Above, we just mention the SUSY particle for each SM particle. Here, we are going to detail a bit more those particle that will be present in our analysis. There are a combination of neutral higgsinos H0 1,H0 2and the neutral gauginos ˜ B,˜ W0called Neutralino. From this combinations, we can obtain the following mass matrix:[4] Mχ=    M10−cβswMZsβswMZ 0M2cβcwMZ−sβcwMZ −cβswMZcβcwMZ0−µ sβswMZ−sβcwMZ−µ0     . (4.7) The terms sβ=sinβ,cβ=cosβ,sw=sinθW. Diagonalizing the matrix, we can find the eigenvalues mχ0 1,mχ0 2,mχ0 3and mχ0 4. The parameter µmust be real to avoid CP violations effects. In the limit of large |µ|, the masses of neutralinos can be expressed as: mχ0 1≃M1−M2 Z µ2(M1+µsin2β)sin2θW, (4.8) mχ0 2≃M2−M2 Z µ(M2+µsin2β)cos2θW, (4.9) mχ0 3≃ |µ|+1 2 M2 Z µ2eµ(1−sin2β)(µ+M2sin2θW+M1cos2θW), (4.10) mχ0 4≃ |µ|+1 2 M2 Z µ2eµ(1+sin2β)(µ−M2sin2θW−M1cos2θW). (4.11) The parameter eµrefers to the sign of µ. Analogous to neutralinos, the combination of ˜ W±,˜ H− 1and ˜ H+ 2give us two particles, the Charginos. In the limit |µ|  M1,M2, we can express the mass as mχ± 1≃M2−M2 W µ2(M2+µsin2β), (4.12) mχ± 2≃ |µ|+M2 W µ2eµ(M2sin2β+µ). (4.13) We are interested in particles that couple with the Higgs boson sector. Therefore, in the case of sfermions, the highest contributions come from the stop, sbottom and stau. For these particles, we can write the mass matrix as m2 ˜ f= m2 LL +m2 fmfX∗ f mfXfm2 RR +m2 f!, (4.14) 4.2. The Higgs sector in MSSM 13 where the parameter Xtis defined as Xi=Ai−µcotβ,i=u,c,t; (4.15) Xj=Aj−µtanβ,j=e,µ,τ,d,s,b. (4.16) In addition, the parameter m2 LL and m2 RR are m2 LL =m2 ˜ fL+ (T3,f−Qfsin2θW)M2 Zcos2β, (4.17) m2 RR =m2 ˜ fR+Qfsin2θWM2 Zcos2β. (4.18) Here, Qfis the electric charge, and T3,fthe third component of isospin. Notice that for each sfermions, we have two scalar SUSY partner, one left and one right. One can diagonalize the mass matrix taking account that ˜ f1 ˜ f2= cosθ˜ fsinθ˜ f −sinθ˜ fcosθ˜ f!˜ fL ˜ fR. (4.19) The mixing angle and sfermion masses are sin2θf=2mfXf m2 ˜ f1−m2 ˜ f2 ; (4.20) cos2θf=m2 LL −m2 RR m2 ˜ f1−m2 ˜ f2 ; (4.21) m2 ˜ f1,2 =m2 f+1 2hm2 LL +m2 RR ∓q(m2 LL −m2 RR)2+4m2 fX2 fi. (4.22) 4.2 The Higgs sector in MSSM MSSM has two Higgs complex scalar field H1=H0 1 H− 1with YH1= +1, H2=H+ 2 H0 2with YH2= -1 (4.23) The respective Higgs potential V is V=VD+VF+Vso f t. (4.24) VDis called Dterms and it contains the quartic Higgs interactions VD=1 2∑ a ∑ i gaφ∗ iTaφi!2 , (4.25) where φiis a scalar field, Taand gaare the generators and coupling of SU(2)L×U(1)Y. VFis called Fterms and come from the Superpotential W. (4.1) VF=∑ i ∂W(φj) ∂φi 2 . (4.26) 14 Chapter 4. Minimal Supersymmetric Standard Model:MSSM And the last contribution Vso f t comes from the soft-SUSY breaking scalar Higgs mass terms and the bilinear term. Sum all contributions, one obtains that VH=(|µ|2+m2 1)|H1|2+ (|µ|2+m2 2)|H2|2−µBeij(Hi 1Hj 2+h.c.) g2 2+g2 1 8(|H1|2−|H2|2)2+1 2g2 2|H∗ 1H2|2. (4.27) Defining ¯ m2 1=|µ|2+m2 1,¯ m22=|µ|2+m2 2,¯ m2 3=Bµ. (4.28) And finding the potential minimum, one can find that hH+ 1i=0 and hH− 2i=0. In this way, we can reduce the eq. (4.27) and write only the neutral potential terms as VH=¯ m2 1|H0 1|+¯ m2 2|H0 2|2+¯ m2 3(H0 1H0 2+h.c.) + g2 2+g2 1 8(|H0 1|2−|H0 2|2)2. (4.29) There are two vacuum for each complex Higgs field hH0 1i=ν1,hH0 2i=ν2. (4.30) They must follow the relation (ν1+ν2)2=ν2=2m2 Z g2 2+g2 1 = (246 GeV)2, (4.31) where νis the SM vev. We define the quotient of vacuums as tan(β) = ν2 ν1 . (4.32) From the minimum condition in Eq. (4.29), ∂VH ∂H0 1min =0, ∂VH ∂H0 2min =0. (4.33) We obtain the following relation ¯ m2 1=−¯ m2 3tanβ−1 2M2 Zcos(2β),¯ m2 2=−¯ m32cotβ+1 2M2 Zcos(2β)(4.34) As we have two double complex Higgs, we have 8 degrees of freedom and 3 of them are Goldstone boson G0,G±which give mass to the boson Z0and W±[see section 2.2]. The remainder are Higgs scalar; h,Hare CP-even neutral scalar, Ais CP-odd neutral scalar and H±is charged. The lightest higgs are h,H, and we are going to work with the hierarchy h<H. Hence, the Higgs SM boson is identified by hin the MSSM. We can change the states H0 1and H0 2to mass eigenstates. H0 2 H0 1=ν2 ν1+1 √2Rαh0 H0+i √2Rβ0G0 A0. (4.35) H+ 2 H−∗ 1=Rβ±G+ H+. (4.36) 4.2. The Higgs sector in MSSM 15 The rotational matrices are: Rα=cosαsinα −sinαcosα, (4.37) Rβ0=sinβ0cosβ0 −cosβ0sinβ0, (4.38) Rβ±=sinβ±cosβ± −cosβ±sinβ±. (4.39) We can write the potential in function of the eigevalues of Eq. (4.35) (4.36) VH=1 2m2 h0(h0)2+1 2m2 H0(H0)2+1 2m2 G0(G0)2+1 2m2 A0(A0)2 +m2 G±|G+|2+m2 H±|H+|2 (4.40) In the tree-level β0=β±=β, and m2 G0=m2 G±=0.[see Fig. 4.2] m2 A0=2Bµ sin2β=2¯ m2 3 sin2β(4.41) m2 h0,H0=1 2m2 A0+m2 Z∓q(m2 A0−m2 Z)2+4m2 Zm2 A0sin2(2β)(4.42) m2 H±=m2 A0+m2 W(4.43) The mixing angles, at tree-level, are related by: sin2α sin2β=− m2 H0+m2 h0 m2 H0−m2 h0!,tan2α tan2β= m2 A0+m2 Z m2 A0−m2 Z!. (4.44) We comment that the number of free parameters is 111 in MSSM, plus 19 from SM. We need to reduce this huge number. Hence, we can do the following hypothesis: 1. All the soft SUSY-breaking parameters are real, i.e., there is not a CP violation as occurs in the CKM matrix. 2. The matrices for the sfermions masses and for the trilinear couplings are all diagonal, implying the absence of FCNCs(Flavour Changing Neutral Currents) at the tree-level. 3. The masses and trilinear coupling of the first and second generations are the same at low energy Thus, we deal with 22 input parameters: • tanβ:the ratio of the two vacuum of the two Higgs doublet scalar field. •µ,MA: the Higgs mass parameters squared. •M1,M2,M3: Gauginos mass parameters •m˜ q,m˜ uR,m˜ dR,m˜ l,m˜ eR: the first and second sfermions mass. •m˜ Q,m˜ tR,m˜ bR,m˜ L,m˜ τR: the third sfermion mass. •Au,Ad,Ae: the first and second generations trilinear couplings. •At,Ab,Aτ: the third generation trilinear coupling. 16 Chapter 4. Minimal Supersymmetric Standard Model:MSSM We change the parameters m2 H1,m2 H2in function of physical parameters µand MA. Also, we can reduce the number of parameters if we impose that the mass of all generation sfermions are equals. This is called MSUSY, and it indicates the mass SUSY scale of SUSY partners fermions. The parameters Au,Ad,Aeare not relevant for phenomenology. Doing the previous hypothesis, we have <10 parameters. (A) Higgs-like hmass vs the parameter MAat tree level for different values of tanβ (B) Heavy Higgs neutral mass Hvs the parameter MAat tree level for different values of tanβ. FIGURE 4.1: Masses of lightest Higgs hand Hat tree level with the inputs: MSUSY=1000 GeV, Xt=1000 GeV, M2=200 GeV, M3=1000 GeV, µ=1000 GeV. Obtained with FeynHiggs 2.18 Furthermore, it is interesting see how is the relation of neutral higgsinos among gauge bosons and themselves looking the coupling: ghVV =sin(β−α)gSM HVV (4.45) gHVV =cos(β−α)gHVV (4.46) gh,AZ =cos(β−α)g1 2cosθW (4.47) ghb¯ b,ghτ+τ−=−sinα cosβgSM Hb¯ b,Hτ+τ−(4.48) ght¯ t=cosα sinβgSM Ht¯ t(4.49) In this case, the super-index SM indicated the Standard Model gauge bosons and βand αare the mixing angle defined in Eqs.(4.32),(4.37). These equations show how is coupling of MSSM at tree level, but there are small corrections to keep in mind. In Fig.4.2, we see how is the behaviour of Eq.(4.45). We see that both coupling are the same for MA> 100 GeV. This is crucial for Supersymmetry because it allows the cancellation in Eq. (3.5) (Hierarchy Higgs mass problem). 4.3. Higher order corrections 17 FIGURE 4.2: Parameter sin(β−α) = ghVV gSM HVV vs MAat tree level. The inputs parameters are the same as Fig. 4.1 4.3 Higher order corrections The mass of Higgs-like mhis, according to the Eq. 4.47 mh<MZ. (4.50) We can observe this behaviour in Fig. 4.1 at tree level. The higher corrections ∆mhcontributes as m2 h=m2 h,tree +∆m2 h(4.51) The radiative correction are crucial for the mass of Higgs boson hto reach to 125 GeV. In particular, the coupling of Higgs hwith the stop,sbottom and top quarks are strong, therefore the highest correction come from the coupling with these particles. Here, we show some Feynman diagrams which involves quark top,stop, gluons(gluinos is also included at 2-loop but is not drawn). (A) 1-loop Higgs coupling with quark stop (B) 1-loop. Higgs coupling with quark top (C) 1-loop. Higgs coupling with quark stop (D) 2-loop. Higgs coupling with quark top and top with gluon (E) 2-loop. Higgs coupling with quark top and scalar φ0 (F) 2-loop. Higgs coupling with quark stop and scalar field φ0 FIGURE 4.3: Some Diagrams contributions to Higgs Boson with top quark tand stop quark ˜ t. Parameter yrefers to Yukawa coupling. Above, we see some interactions of Higgs with quark top and stop. We can substitute the terms yt,sby αt,s=y2 t,s/(4π). For instance, in Fig. 4.3a and 4.3b we see that the diagram is proportional to ∼y2 t∼αt. Thus, for Fig. 4.3c , we have that ∼y2 sy2 t∼αtαs[8] and for Fig. 4.3d,∼y2 ty2 t∼α2 t. [9] 18 Chapter 4. Minimal Supersymmetric Standard Model:MSSM In general, the contribution goes with O(αtm2 tαn t,s[lnn(m˜ t/mt)]) and O(αtm2 tαn t,s[lnn+1(m˜ t/mt)]) [7]. Here, we need to distinguish two parts, one with fix-order contributions that involves terms as α that can be calculated with perturbation theory, and other with logarithms. Exist two ways of calculate these contributions, which we briefly describe [10]. • Fixed-order(FO) approach: Precise for low SUSY scales, but for high scales large lograrithms appears and we lose the convergence. In the FO approach, the diagrmas of a certain order (e.g. 1 or 2 loop) are evaluated and added to obtain the Higgs-boson mass. • Efective Field Theory(EFT) approach: Concerning logarithms mentioned above. It yields contributions of type ∑∞ n=0cnαtm2 tαn slnn+2(m˜ t/mt). It is integrated out all heavy particles and SM is treated as an efective field theory. Hence, EFT method is a resummation of logarithms which become large if the relevant scales are widely separated. Precise for high SUSY scales. The best approach is a mix of both, a Hybrid approach, where it is included both approximation avoiding the double counting. We call SUSY scale MSfor the scale where sfermions live, Mχfor EW-ino bosons scale, MAfor the scale of neutral boson Aand the Standard Model Scale. Below, we show two examples of SUSY scale. FIGURE 4.4: SUSY scales hierarchy. THDM refers to two Higgs double model THDM, Two Higgs Double Model refers to the double Higgs sector described in section 4.2. At 1-Loop correction, the leading radiative correction of Higgs bosons comes from quark top and stop [6] ∆m2 h∼Gµm4 tlog m˜ t1m˜ t2 m2 t(4.52) Of course, there are much more contributions, but this is the dominant. This equation shows us how is the relevance of top mass, and the mixing stop quarks as well. Usually, as we just take into account stop quarks, we introduce a new definition of SUSY scale MS=m˜ t1+m˜ t2 2. (4.53) 4.4. Calculation in MSSM. FeynHiggs 19 4.4 Calculation in MSSM. FeynHiggs FeynHiggs is a Fortran code that we use for the calculation in MSSM predictions. It can be obtain from http://www.feynhiggs.de/ and it uses a very complex numerical calculation and approximation that can be summary in simple commands or flags [11]. • The following flags are used by default. These commands represents some aspect of the complex calculation and computation in FeynHiggs. 1. mssmpart = 4. Specifies the scope of the 1-loop part in full MSSM. 2. higgsmix = 2. Determinates the mixing in the Higgs sector. All CP-violating nondiagonal self energies = 0. 3. p2approx = 4. The momemtum in the one-loop part of the calculation is fully taken into account. 4. runningMT = 1. Determinates which top mass shall be used in the 1-loop corrections. 5. botResum = 1. Determinates whether the O(tannβ)corrections shall be resummed. 6. tlCplApprox = 0. Determinates how the two-loop corrections are treated in the presence of complex parameters(cMSSM). • In section 4.3, we discuss how it is calculated the radiative corrections. In few words, we have two contributions. Fix-order contributions, treated by Feynman diagrams, where loops are calculated; and EFT calculations, that focus on the calculation of resummation of logarithm , especially when become large. The first is controlled in FeynHiggs by the flag looplevel, and the second by the flag loglevel. In Fig. 4.4 the loglevel=3 uses the hierarchy on the right and loglevel=4 on the left. Thus affects the way in which is calculated the radiative corrections. For instance, loglevel=3 has terms as ∆m2 h∼log M2 S/M2 tand loglevel=4 ∆m2 h∼log M2 S/M2 A. In this work, we compare both ways for the MSSM predictions and see what is the difference. A very important feature in FeynHiggs is the computation of the theory uncertainty of the calculation of the light Higgs boson mass due to non-calculated higher-order corrections. We use it for the Higgs mass prediction and is calculated using an approximation at three quantum corrections order. Lets call the logarithm term as Ln=logn(M2 S/m2 t), then we have • 1 order: ∆m2 h∼O(αt)(L0+L1). • 2 order: ∆m2 h∼(O(αtαs) + O(α2 t))(L2+L1+L0) • 3 order: ∆m2 h∼(O(αtα2 s) + O(α2 tαs) + O(α3 t)(L3+L2+L1) FeynHiggs estimates the missing term at 3-loop order calculations as the uncertainty by the approximation δm2 h∼αs∆m2 h(αt,αs,L0). To clarify, we use as mass prediction m2 h= tree level + 1 order(+ 2 order 1) and the uncertainty δm2 has an approximation of 3 order. Also, there is a calculation for the EFT approach that is included in the uncertainty. The sum of both is the total uncertainty given by FeynHiggs. This technique is only implemented in loglevel=3 at the moment in FeynHiggs. 1This depend on the flag chosen. 20 Chapter 5 Benchmarks Scenarios in MSSM Supersymmetry introduces a large numbers of free parameters that need to be reduce in order to simplify the model.These parameters are called input parameters, i.e., we need to define them. Above, we see how to reduce more than 100 parameters into 10 approximately, and working with them it is possible to create some scenarios according to the LHC searches, that we are going to see in Chapter 6. The idea of all of them is that the neutral Higgs hmust be agreement with the LHC measurement. Hence, the mass of this Higgs should be around 125 GeV. Moreover, the fermions and bosons superpartner can be heavy or light depending on the input parameters and this generates different features and patterns in the model, for instance, some forbidden decays or regions where we cannot find that mh=125 GeV. In this chapter, we reproduce three benchmarks scenarios from [12,13,14], looking that the Higgs mass mhis close to 125 GeV in the plane (MA,tanβ). The scenarios are denoted by M125 h,M125 h(˜ τ) and M125 h(˜ χ), respectively. For all scenarios, the flag are fixed as, 1)mssmpart =4, 2)higgsmix =2, 3)p2approx =4, 4)looplevel =2, 5)loglevel =3, 6)runningMT =1, 7)botResum =1, 8)tlCplxAprox =0. Notice that the calculation uses loglevel=3. From the discussion in section 4.3 and 4.4, loglevel=3 has a quantum correction contribution different of loglevel=4. This chapter analyses both ways. Apart of that, the higher contribution come from the third generation of sfermion. Thus, we extend the notation w.r.t. Chapter 4. In comparison with table 4.2 M˜ Q=MQii=1, 2, 3 (i generation) M˜ Uc=MUii=1, 2, 3 (i generation) M˜ Dc=MDii=1, 2, 3 (i generation) M˜ Ec=MEii=1, 2, 3 (i generation) M˜ Lc=MLii=1, 2, 3 (i generation) And last, but no least, we need to define SM free parameters defined in [12](less mpole t) that involve our calculations mpole t=172.9 GeV, αs(MZ) = 0.118, GF=1.16647 10−5GeV−2, mb=4.18 GeV, MZ=91.1876 GeV, MW=80.385 GeV. 5.1. M125 hScenario 21 The value defined in [12] for mpole tis 172.5 GeV, however, we choose the value from PDG(Particle Data Group) of 172.9 GeV 5.1 M125 hScenario The inputs parameters are fixed[14] : MQ3=MU3=MD3=1.5 TeV, ME3=ML3=2 TeV, µ=1 TeV, M1=1 TeV, M2=1 TeV, M3=2.5 TeV, Xt=2.8 TeV, Ab=Aτ=At. This choice generate heavy SUSY particles, around 1-2 TeV. Thus, the decay of heavy Higgs to sfermions are suppressed. Therefore, Higgs particles are force to decay into SM particles. From the input parameters, we see that the parameter Xtfrom Eq. (4.14) is high, therefore, the mix stop are strong and the masses of m˜ t1and m˜ t2are not degenerate, i.e. one stop is heavier than the other. In addition, as the radiative corrections come from the coupling with stops, the parameter Xtis chosen to increase the Higgs mass to 125 GeV w.r.t the tree level. The µparameter is related with the higginos mass, and in this scenario is chosen large, in comparison with the EW scale. We compare the results obtained in [14] with ours using the last versions of FeynHiggs-2.18. In the previous work, authors use the version FeynHiggs 2.14, therefore, we expect bit changes in the calculation of radiative corrections. The Fig. 5.1a is taken from [14] and it shows the region in the plane (MA,tanβ) compatible with the Higgs mass mharound 125 GeV. In the figure on the left, the green lines mark the value of Higgs mass for the light CP-even Higgs boson h. Also, it is plotted a blue region which is the exclusion region by LHC searches, predominantly by decays H/A→τ+τ−. In addition, the hatched region are excluded by incompatible measurement with the properties of Higgs husing FeynHiggs and HiggsSignals. On the right(Fig. 5.1b), we show the result obtained by last version of FeynHiggs. The grey region are predicted masses lower than 122 GeV and green lines correspond to the value of Higgs mass mh. In comparison, we notice that the green line, corresponding to 125 GeV, is localised in a higher position in our case than the previous result. Taking into account the blue area, this region is neglected and the available region correspond to masses around 124 GeV. Thus, the new calculation for radiative corrections available in the latest version of FeynHiggs reduces the plane (MA,tanβ) for predicted mass higher than 125 GeV. Also, notice that in Fig.5.1a, for MA∼150 GeV, all green lines converges for tanβ> 40, and this should be occur in our results. Indeed, we appreciate this convergence in our results though is not clearly as the graph on the right. The calculation at loglevel=3 allows us to obtain the uncertainty for each mass prediction. We know that the Higgs mass status is MSM H=125.10 ±0.14 GeV. We can see what is the region compatible with this mass according with the uncertainty (δmh). For instance, if we have a mass mh=123.5, and δmhis 1.5 GeV, this mhdoes not reach 125.1 and then is excluded. As we have theoretical and experimental uncertainties, and because of uncertainty close to 125 usually is small, we define the region: •σ1:δmh=δmtheo h+2δmexp h[GeV] •σ2:δmh=2(δmtheo h+δmexp h)[GeV] The results is drawn in Fig 5.2a. The red zone is the region according to σ1and the red plus lightblue is the region according to σ2. If we want to be very precise, we can excluded the σ2, though it is a small region. In this way, FeynHiggs produce a very powerful prediction, however there is still a big work for reducing the uncertainty in order to exclude regions by mass predicted. In addition, 28 Chapter 6. Benchmark Scenarios at low tanβRegion. Notice that loglevel=4 is chosen instead of loglevel=3. The reason is that we are treating with large hierarchy of MSUSY w.r.t the MA(Fig. 4.4), where it is appreciated that the scale THDM is localised higher. Thus, for loglevel=4, the THDM is above the SM scale, then this hierarchy enables the THDM as low-energy theory. The SUSY scale increases faster for low tanβand MA, where we can reach values higher than 1010 GeV until maximum as 1016 GeV, the GUT scale. The SUSY scale in the plane (MA,tanβ)is calculated in [14] and can be found in [15] and /example/LHCHXSWG in FeynHiggs. The input SM parameter are fixed according to [12] mpole t=172.5 GeV, αs(MZ) = 0.118, GF=1.16647 10−5GeV−2, mb=4.18 GeV, MZ=91.1876 GeV, MW=80.385 GeV. Moreover, the SUSY parameters equals for both scenarios are M3=2.5 TeV, At=Ab=Aτ=0. (A) Mass spectrum for the CP-even light Higgs mass hin the scenario M125 h,EFT. The grey region is for masses predicted below 122 GeV (B) Mass spectrum for the CP-even heavy Higgs Hin the scenario M125 h,EFT in the plane (MA,tanβ) FIGURE 6.1: Mass spectrum for the CP-even Higgs h,Hin the scenario M125 h,EFT. For the scenario M125 h,EFT(˜ χ)the plots are very similar. This is due to the SUSY scale chosen. 6.1 Scenario M125 h,EFT The input parameters are fixed µ=1 TeV, M1=1 TeV, M2=1 TeV The main difference between M125 h,EFT[13] and M125 h([14] and section 7.1) is the election of SUSY scale, defining the parameters MQ3=MU3=MD3=ME3=ML3=MSUSY. Also, the parameter Xtand Atwhose relation is Eq. (4.15). Due to theoretical fine-tuning arguments, low Atvalues are preferred in case of a Tev-scale M3and TeV-scale electroweakinos. Usually, Xtis fixed in the TeV scale in order to increase the radiative correction to 125 Gev, but this function is done by large values of MSusy. According to the input parameters, the EW-ino sector is mixed, and with masses around the TeV scale, however, the most interesting part is the SUSY Higgs sector. In Fig. 6.2 is represented the SUSY scale used for the calculation. On the left(picture taken from [13]), it is plotted the SUSY 6.1. Scenario M125 h,EFT 29 scale in [13] in the range of MA[1002000] GeV. The blue region is the exclusion area due to LHC searches and the hatched is the region disfavoured at the 2σlevel by the SM-like Higgs-boson rate. In addition, the grey area is rejected due to predicted masses below 122 GeV. On the right, it is plotted the SUSY scale used in our work obtained by interpolation of data[see above] in the range of MA[100-1000] GeV. The dots black region is the exclusion for mhbelow 122 GeV. The hatched region is forbidden for decays H→hh because mHdoes not reach the minimum mass ∼250 GeV. In both plots, the green lines are the SUSY scale needed to obtain 125 GeV. Notice the increasing of SUSY scale whereas tan βand MAgo lower. Looking the peak of grey and black region, the last version of FeynHiggs produces a peak a bit higher than the peak in [13]. With our result, the peak is for MA∼230 GeV, and the peak in the previous result is for MA∼200 GeV. The remainder lines are exactly the same, less in the region where green lines converge(MA∼180 GeV), but this region is inside of the exclusion area. The problem with convergence zone is that we need a huge statistic in order to distinguish the contribution for each line. This behaviour is repeated in some plots; nevertheless, the tendency to convergence of the lines are appreciated and we can extrapolate this convergence to our plots. In this work, we reduce the range of MAto facilitate the calculation time and to focus on the statistic. The region for Heavy bosons decays(H,A) are localised in this range of MA. In figure 6.3 is plotted the plane (MA,tanβ)for decays of CP −even Higgs H, BR(H→hh)(blue) and BR(H→t¯ t)(green). The mass allowed for decay into hh is ≥250 GeV localised and predominant in the window mass [250-400] GeV, where it can reach to 50 %. From that range, MA≥400 GeV, the decay H→t¯ tis predominant(at low tanβ). From Eq. (4.46), we know that, at tree level, exits a coupling of Hwith VV, and that is proportional to cos(β−α). In addition, the coupling gH,tt goes with cotβ, thus, the branching ration increases its values at low tanβ. In the decoupling limit (MAMZ), the mixing angle tends to α≈π/2 −β, then the coupling cos(β−α)→0 , thus, there is a small contribution from H→VV. Therefore, for (MA,tanβ)∼(700 GeV,2.5), the branching ratio sum, BR(H→hh) + BR(H,→t¯ t)≈95% plus a small contribution from BR(H→VV). Moreover, we compare the results in [13] with our data with the same inputs variables. Both pictures are very similar. Nevertheless, the branching ratio into two Higgs has been decreased w.r.t the previous result, especially, for BR(H→hh)∼0.4 −0.5. For the decay BR(H→t¯ t), both are very similar for tanβ> 3, but for lower tanβ, the initial lines for BR(H→t¯ t)= 0.5,0.75 and 0.9, are shifted w.r.t the previous result. For example, for BR(H→t¯ t)=0.75, the line starts approximately, at MA∼350 GeV for the picture on the left, however, in our result, it starts at MA∼520 GeV. Furthermore, in the panel on the right,it appears a dotted line that marks the exclusion region at the 2 σlevel by the measured Higgs boson signal rate and the dashed line, that indicates the exclusion by LHC. If we assume that these exclusion areas are the same in both plots, the decay into two Higgs is almost suppress and substituted by decay into top-antitop. For Fig. 6.4 is plotted the decay for neutral CP −odd boson A into higgs and Z boson, and topantitop. Here, as is plotted the value of MA, the decays are more clearer. For MA>200 GeV, it is allowed the decay A→Z,huntil MA= 350 GeV, which is the mass threshold for the decay A into top-antitop. It seems that are very related, because, the decay into h,Zdrops quickly when it is open the decay into t¯ t. The symmetry CPodd constricts the decay into SM particle, letting the decays only for top-antitop and bottom-antibottom. The coupling for A→Zh is the same as H→VV, however, the approximation taken before(MAMZ) is not too much accuracy because this decay is predominant in the range of MA[230,350]. The coupling for the decay A→t¯ tgoes with cotβ, therefore, as lower tanβ, higher branching ratio. The exclusion region is the same as the area presented in Fig. 6.2. Again, we compare the results in [13] on the left panel with our result, on the right. In this case, we point out the values for BR(A→Zh)in ranges of percentages of branching ratio due to lines are not clearer as the previous result. The egde of blue region in Fig.6.4b correspond to blue line 30 Chapter 6. Benchmark Scenarios at low tanβRegion. 0.05 in Fig. 6.4a, the frontier between blue and orange region correspond to blue line 0.1 and so on. Both results show the same region for BR(A→Zh). The difference come from only close to the convergence zone (MA∼200 GeV), where our result is less sensitive. This is because there are a mix of points ,as we see in the range (MA,tanβ)∼(200-250 GeV,2). For the other decay, BR(A→t¯ t), the result seem equals and, again, the convergence region for green lines drawn in Fig.6.4a is not presented in our calculation but is similar. (A) The M125 h,EFT benchmark scenario shown in the plane (MA,tanβ). The green lines indicate the SUSY scale and the black dotted line, besides the hatched area, mark the parameter space which is disfavoured at the 2 σlevel by the measured Higgs boson signal rates. Gray region is excluded for masses below 122 GeV and and blue region is excluded by LHC searches. [13] (B) Reproduction of MSvalues in the benchmark scenario M125 h,EFT. The green lines show the SUSY scale and the hatched region indicates the region where Higgs boson H is forbidden for decay H→hh. The black dots area is the exclusion region for masses below 122 GeV. The exclusion region by LHC searches is not indicate, but is similar as the plot on the left. FIGURE 6.2: Constraints on the M125 h,EFT scenario in the plane (MA,tanβ) for SUSY scales. On the left is shown the SUSY scale used by [13] and on the right, the SUSY scale used in this work. 6.2. Scenario M125 h,EFT(˜ χ)31 (A) Branching ratio of the heavy CP-even Higgs boson Hinto a pair of the light CP-even Higgs bosons h(blue) and into pair of tops(green). It is plotted the same exclusion region described in Fig.6.2. [13] (B) Branching ratio of the heavy CP-even Higgs boson Hinto a pair of the light CP-even Higgs bosons h(blue) and into pair of tops(green). The black region belong for masses below 122 GeV and the exclusion region by LHC searches is not indicate, but is similar as the panel on the left. FIGURE 6.3: Comparison of results according to the branching ratio of Heavy Higgs Hinto a pair of ligh hand a pair of top quarks obtained in [13] with our result obtained with the last version of FeynHiggs 2.18. (A) Branching ratio of the heavy CP-odd Higgs boson Ainto a pair of the light CP-even Higgs boson hbesides Z boson(blue) and into pair of tops(green). It is plotted the same exclusion region described in Fig.6.2. [13] (B) Branching ratio of the heavy CP-odd Higgs boson A into a pair of the light CP-even Higgs boson hbesides Z boson(colour region) and into pair of tops(blue). The black region belong to masses below 122 GeV. The exclusion region is not indicated but is similar as the left plot FIGURE 6.4: Comparison of results according to the branching ratio of Heavy Higgs Ainto a pair of ligh hbeside Z boson and a pair of top quarks obtained in [13] with our result obtained with the last version of FeynHiggs 2.18. 6.2 Scenario M125 h,EFT(˜ χ) The input parameters are fixed µ=180 GeV, M1=160 GeV, M2=180 GeV 32 Chapter 6. Benchmark Scenarios at low tanβRegion. This scenario focus on the predictions of light neutralinos and charginos. At the tree level, the mass of electrowikinos spectrum are determined by input parameters µ,M1and M2. This election generates a mass for the lightest neutralinos from ∼85 GeV to ∼112 GeV between tanβ=1 and tanβ=10. Therefore, it is opened a new channel decay for heavy Higgs boson H,Ainto neutralinos and charginos, reducing branching ratio for the rest of decays. Another consequence, is the growth of radiative corrections due to the contribution of light neutralinos, therefore, it is not necessary to have a SUSY scale as high as in the scenario M125 h,EFT to reach 125 GeV for the light CP-even boson h. Nevertheless, whereas tanβand MAgo for low values, the SUSY scale, inevitably, needs to increase until GUT scale ∼1016 GeV. As the case as M125 h,EFT, the only change between M125 h,EFT(˜ χ)[13] and M125 h(˜ χ)(section 5.3 and [14]) is the election of SUSY scale and the defined parameters in the way as the last scenario. Also, Xt and Athave other values and the discussion for this change is exactly the same as the previous scenario. In Fig.6.5, the SUSY scale is marked by green lines. We can observe how the SUSY scale drops in comparison with the scenario M125 h,EFT, especially, for SUSY scale 104GeV, which drops from tanβ∼ 9 to tanβ∼6.5 for MA=450 GeV. Also, in Fig.6.5a([13]) appears the exclusion region by LHC searches(blue), besides the exclusion at 2σfor Higgs boson signal rate measurements(hatched region). The grey region represents the area for predicted masses below 122 GeV. In the panel on the right, it is plotted the same scale, used in our work. Here, the black region correspond to grey region, however, the peak is a bit higher in our result. The hatched region indicates the forbidden area for decay H→hh because mHdoes not reach the threshold mass. We use the range for MA between 100 and 1000 GeV, intead of the range [1002000] used in the panel on the left. The reason is to facilitate the statistic and to focus on the decays of heavy Higgs boson H,A. In Fig. 6.6, we explore the branching ratio for the decay of CP-even heavy Higgs boson Hinto a pair of CP-even Higgs hand into a pair of top quarks. The green lines belongs to the decay H→hh and shows the branching ratio from 5 % until a maximum of 30%. The hatched region marks the forbidden area for this decay, because, the Heavy boson Hdoes not reach the threshold mass >250 GeV. The window mass where it is predominant this decay is the range for MA∼[250-400] GeV and tanβ∼[2-5]. In comparison with the scenario M125 h,EFT, the introduction of light neutralinos reduces considerately, the branching ratio for the di-higgs channel. For values of MA> 400 GeV, it is opened the threshold for a pair of top quarks(blue), and , in the same way as the channel H→hh, the decay seems suppressed by the introduction of light neutralinos and charginos. The top pair channel drops, in the same region of plane, from values higher than 90 % to 50 %. Extrapolating the exclusion region drawn in Fig. 6.5a,MA≥700 GeV and tanβ≥2, the decay for H→hh is forbidden and the region for BR(H→t¯ t)≤25 % is only available for top channel decay. From the discussion in [13] , in that region, the branching ratio into neutralinos/charginos reach value higher than 50 %. This means that, in this scenarios, the decay of heavy Higgs boson Hhave two predominant channels, the neutralinos and the pair of top quarks. In the next figure, 6.7, it is plotted the branching ration of CP-odd heavy Higgs boson Ainto a pair of CP-even Higgs boson hbesides the Z boson and into a pair of top quarks. The threshold for the channel h,Zis allowed for MA≥215 GeV. Here the maximum branching ratio is localised in the range for MA∼[220,270] GeV, with a maximum of 3%. This result is so much lower than the case of M125 h,EFT, where, for the same range, the branching ratio reaches values close 50 %. Going further than 350 GeV, the decay into pair top quarks is available, but, as the same case for heavy boson H, the decay is suppressed by the neutralinos and charginos. The maximum value is obtained for tanβ<2, but, this region is rejected if the exclusion region is extrapolate. Hence, the decay into h and Z boson is dismissed and it is only available the BR(A,t¯ t)<50 %. This suppression region is compensate for the introduction of new decay, A→˜ χ˜ χ, where, the branching ratio goes higher than 50 % for tanβ≥2. 6.2. Scenario M125 h,EFT(˜ χ)33 (A) The M125 h,EFT(˜ χ)benchmark scenario shown in the plane (MA,tanβ). The green lines indicate the SUSY scale and the black dotted line, besides the hatched area, mark the parameter space which is disfavoured at the 2 σlevel by the measured Higgs boson signal rates. Gray region is excluded for masses below 122 GeV and and blue region is excluded by LHC searches. [13] (B) Reproduction of MSvalues in the benchmark scenario M125 h,EFT(˜ χ). The green lines show the SUSY scale and the hatched region indicates the region where Higgs boson H is forbidden for decay H→hh. The black dots area is the exclusion region for masses below 122 GeV. The exclusion region by LHC searches is not indicate, but is similar as the plot on the left. FIGURE 6.5: Constraints on the M125 h,EFT scenario in the plane (MA,tanβ) for SUSY scales. On the left is shown the SUSY scale used by [13] and on the right, the SUSY scale used in this work. FIGURE 6.6: Branching ratio of the heavy CP-even Higgs boson Hinto a pair of the light CP-even Higgs bosons h(blue) and into pair of tops(green). The black region belong for masses below 122 GeV and the hatched region is the area forbidden for mHbecause does not reach the threshold ∼250 GeV. The exclusion region by LHC searches is not indicate, but is similar as the panel on Fig. 6.5a. 34 Chapter 6. Benchmark Scenarios at low tanβRegion. FIGURE 6.7: Branching ratio of the heavy CP-odd Higgs boson Ainto a pair of the light CP-even Higgs boson hbesides Z boson and into pair of tops(green). The black region belong to masses below 122 GeV. The exclusion region is not indicated but is similar as Fig. 6.5a 35 Chapter 7 State of SUSY searches The last chapter is a review of searches for new physics leading by LHC. The searches Beyond Standard Model involves many types of theories, and analysis as well. One of this theories is the Supersymmetry, which, as it has a huge number of free parameters, it has many scenarios which many SUSY particle to take into account. In this work, we focus on scenarios where heavy Higgs bosons can decay into SM particles, or light SUSY particles like neutralinos or light stau. The LHC searches for new SUSY particles was considerate in Run I and II, rejecting scenarios which predicts decays in that range of energy accessible for the LHC. Searches for invariant Heavy Higgs mass in large range of energies ∼(0.1-1 TeV) was done[16] and another with a shorter range(70-110)[17] GeV as well. This difference in range is because the two Higgs double model produces five Higgs, and three of them are neutral. This work establish that the lightest Higgs boson hcorrespond with Higgs boson measured by LHC, but this is a hypothesis. Another problem to take into account is gap of energy produced by particle which does not interact with our detector. Distinguish this ghost particle among other ghost particle and neutrinos, is also a challenge. This is the case of M125 h,EFT(˜ χ), which produce light neutralinos and charginos. This scenario, besides M125 h,EFT have a mass degeneration for heavy boson Hand A, therefore, it shows us a a shorter range of energy for searching the invariant mass and which decay is predominant. Both scenarios have a large value for the sfermion mass, hampering the decay of heavy Higgs into pair of these sfermions. In addition, we analyse a scenarios with a sfermion mass in the order of TeV scale in Chapter 5. Furthemore, the scenario M125 h(˜ τ)produced light stau particles, allowing the channel H/A→˜ τ˜ τ. The the main exclusion region in Fig.7.1 is produced by decays H/A→ττ. There, the plot includes many exclusion region decay for heavy Higgs H/A→γγ,¯ bb,ττ;H→hh ;A→Zh. The data come from Run I and II at √s=13 TeV in the ATLAS experiment and focus in the hMSSM scenario. This approach consider that, in the Higgs basis, the only important radiative corrections are those affecting the Higgs boson mass. In the next figure, 7.2, shows a comparison between M125 hscenario(left) with the hMSSM approach(right). In the panel on the left, it is appreciated the region of masses below 122 GeV, similar to our result. From the discussion in section 5.1, the heavy sfermion mass cause that the heavy Higgs decay only into SM particles. On the left, the panel shows the exclusion region for the hMSSM. In Fig. 7.3 it is shown the exclusion region for the M125 h(˜ χ)and includes the decay of Heavy Higgs boson H/Ainto top, bottom quark and tau lepton. The experiments belong to CMS and ATLAS, whose analysis is collection in [18,19,20,21]. 36 Chapter 7. State of SUSY searches FIGURE 7.1: Plane (tanβ,MA0) excluded in the hMSSM via direct searches in ATLAS for heavy Higgs bosons and fits to the measured rates of observed Higgs bosons production and decays. The color region exclusion for each decay is presented at √s=13 TeV. [20] FIGURE 7.2: Plane (tanβ,MA0) excluded in the hMSSM and M125 h,EFT via direct searches in CMS for heavy Higgs bosons and fits to the measured rates of observed Higgs bosons production and decays. The color region exclusion for each decay is presented at √s=13 TeV. [21] Chapter 7. State of SUSY searches 37 FIGURE 7.3: Plane (tanβ,MA0) excluded in the M125 h,EFT(˜ χ)via direct searches in ATLAS for heavy Higgs bosons to τ+τ−and tb. The colour region exclusion for each decay is presented at √s=13 TeV. The scenarios are chosen close to TeV scale, where SUSY particles can decay into SM particles. From our calculation, we see the same behaviour in comparison with these results from LHC. We expect that after the Run III, the exclusion region increases the area, therefore the range of energies for searches of invariant mass keeps small as possible.