More light on Higgs flavor at the LHC: Higgs boson couplings to light quarks through h+γ production

More light on Higgs flavor at the LHC: Higgs boson couplings to light quarks through h+γproduction J. A. Aguilar-Saavedra,1,2,* J. M. Cano ,2,3,†and J. M. No 2,3,‡ 1Departamento de Física Teórica y del Cosmos, Universidad de Granada, E-18071 Granada, Spain 2Instituto de Física Teórica, IFT-UAM/CSIC, Cantoblanco, 28049 Madrid, Spain 3Departamento de Física Teórica, Universidad Autonoma de Madrid, Cantoblanco, 28049 Madrid, Spain (Received 9 September 2020; revised 4 February 2021; accepted 27 April 2021; published 24 May 2021) Higgs production in association with a photon at hadron colliders is a rare process, not yet observed at the LHC. We show that this process is sensitive to significant deviations of Higgs couplings to firstand second-generation SM quarks (particularly the up type) from their SM values, and we use a multivariate neural network analysis to derive the prospects of the High Luminosity LHC to probe deviations in the up and charm Higgs Yukawa couplings through hþγproduction. DOI: 10.1103/PhysRevD.103.095023 I. INTRODUCTION Whereas the Yukawa couplings of the 125 GeV Higgs boson to third-generation Standard Model (SM) fermions have been measured rather precisely at the Large Hadron Collider (LHC), the values of the corresponding Higgs boson couplings to light SM fermions are still weakly (or very weakly, for first-generation fermions) constrained. In the last few years, there has been an important theoretical [1–15] and experimental [16–22] effort to probe the charm-quark Yukawa coupling, as well as the rest of the light SM quarks (see, e.g., Refs. [2,3,8]). Some of the proposed methods to probe the Yukawa couplings of the light SM quarks at the LHC are quark-flavor specific (they rely on tagging/identifying a specific flavor in the final state—e.g., a charm-quark jet produced in association with a Higgs boson [7], or a strange-flavored meson from a rare Higgs decay process [2]), yet others could be sensitive to deviations in any of the Higgs couplings to firstand second-generation SM quarks. Altogether, there exists a strong interplay among all these different probes, which are key to unraveling the details of the mass-generation mechanism for the first two generations of matter: while the LHC will not be sensitive enough to probe the SM values of the corresponding Higgs Yukawa couplings, it will explore beyond-the-SM scenarios with significant enhancements in these Yukawa couplings (see Refs. [23–29] for some examples).1Our current lack of understanding of the pattern of Higgs Yukawa couplings motivates probing such enhancements to gain insight on the entire Higgs flavor structure, as well as to provide the strongest possible experimental constraints on these couplings (even if they are still far from the SM-predicted values). In this paper, we explore a complementary probe of the Higgs couplings to light SM quarks through the production of a Higgs boson in association with a photon at hadron colliders, pp →hγ(see Refs. [31–37] for other Higgs þ photon LHC studies). This is a rare process in the SM, with the leading-order (LO) gluon-initiated contribution gg →hγ [see Fig. 1(left)] vanishing due to Furry’s theorem [38,39]. The largest contributions to the inclusive hγproduction at the LHC include extra objects with high transverse momentum in the final state [34]. In the absence of such extra finalstate particles besides the Higgs boson and photon, the contribution to Higgs þphoton production at the LHC from bottom-antibottom (b¯ b) and charm-anticharm (c¯ c) initial states [see Fig. 1(right)] becomes important, making this process sensitive to the respective Higgs Yukawa couplings yband yc. In addition, the presence of a large deviation from its SM value in the Yukawa couplings of the quarks q¼s,u, d(strange, up, and down) would greatly enhance the corresponding q¯ q-initiated contribution from Fig. 1(right). These contributions are at the same time proportional to the square of the quark electric charge Qq, which suppresses the cross section for down-type quark-initiated q¯ q→hγprocesses relative to up-type quark-initiated processes by a factor ðQu=QdÞ2¼4. We thereby study the sensitivity of this *[email protected] †[email protected] ‡[email protected] Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3. 1Large enhancements of Higgs Yukawa couplings to light quarks can also impact other physical observables—see, e.g., Ref. [30]. PHYSICAL REVIEW D 103, 095023 (2021) 2470-0010=2021=103(9)=095023(6) 095023-1 Published by the American Physical Society process to the value of the Yukawa coupling yqfor q¼u,c at the High Luminosity (HL) LHC, focusing on (in our view) the most promising Higgs decay channel for this purpose, h→WW→lνlν(with lbeing electrons/muons). II. h+γPRODUCTION AT THE LHC As outlined in the Introduction, the dominant q¯ qinitiated contributions to the exclusive production of a 125 GeV Higgs boson in association with a photon at hadron colliders [see Fig. 1(right)] are proportional to the square of the corresponding light quark Yukawa coupling y2 q, evaluated at the scale of the Higgs mass mh. The running masses for the bottom, charm, and up quarks, evaluated at the scale mh¼125 GeV, are given in the tadpole-free pure MS scheme by mbðmhÞ¼2.777 GeV, mcðmhÞ¼0.605 GeV, and muðmhÞ¼0.0013 GeV [40], with the SM values of the Yukawa couplings at this scale given by ySM qðmhÞ¼ ffiffiffi 2 pmqðmhÞ=v, and vbeing the electroweak (EW) scale. We then parametrize the departure of the Higgs Yukawa couplings to light quarks from their SM values as κq¼yqðmhÞ=ySM qðmhÞ. The respective ffiffiffi s p¼14 TeV center-of-mass (c.m.) LHC cross sections at LO for b¯ b→hγ,c¯ c→hγ, and u¯ u→ hγevaluated with M ad G raph 5 [41], for a photon with transverse momentum pγ T>20 GeV and pseudorapidity jηγj<2.5, using the NNPDF31_ NNLO _ AS _0118_ LUXQED [42] parton distribution function (PDF) set, are σb¯ b¼κ2 b×0.397 fb;σc¯ c¼κ2 c×0.160 fb; σu¯ u¼κ2 u×5.16 ×10−3ab:ð1Þ For the SM, the c¯ ccontribution is found to be smaller but comparable to σb¯ b(despite the large hierarchy between Yukawa couplings), owing to the relative ðQc=QbÞ2¼4 factor and larger PDF of the charm quark with respect to the bottom quark. At the same time, while σu¯ uin the SM is negligible, an enhancement of the up-quark Yukawa making it comparable to the SM charm Yukawa yuðmhÞ∼ ySM cðmhÞ(corresponding to κu∼500) would raise the u¯ uinitiated hγcross section to ∼1.3fb.2This might allow for a test of firstvs second-generation Yukawa universality in the up-quark sector at the HL-LHC with 3ab−1of integrated luminosity via this process. We also note that subdominant contributions to the q¯ q→hγexclusive production, such as q¯ q→γ=Z→hγ, quickly become negligible for sizable light Yukawa enhancements—e.g., for κc∼3, their size is ∼5% of the σb¯ bþσc¯ ccross section sum. Before presenting our analysis in the next section, let us discuss briefly the production of a Higgs boson and a photon at the LHC in an inclusive manner, allowing for extra high-pTobjects to be produced in the process. The dominant contributions to the inclusive hþγproduction are [34,35] vector boson fusion (VBF, hγjj) and associated production with a Wor Zboson (AP, hγV). Slightly smaller than the latter but also important are the production together with a high-pTjet (hγj) and production in association with a top-quark pair (t¯ thγ). Cross sections for these processes are in the Oð1–10Þfb ballpark, and they do not depend on κq(except for small contributions to hγjand hγjj, only important for large κcvalues). Thus, to gain sensitivity to the Higgs Yukawa couplings to light quarks, these processes need to be efficiently suppressed in favor of the b¯ band c¯ c-initiated ones. Fortunately, this may be easily achieved by vetoing extra hard activity in the hγevent selection and exploiting the different kinematics of the Higgs boson and photon among these processes, as we will discuss below. III. SENSITIVITY VIA h→WW→lνlν In the remainder of this work, we focus on the h→ WW→lþνl−¯ νdecay of the Higgs boson as the most sensitive channel for our purposes. Other Higgs decay choices like h→b¯ band h→τþτ−face very large SM backgrounds, or suffer from very small decay branching fractions, as is the case of h→γγ and h→ZZ→4l. To search for the hγsignature via the decay h→ WW→lþνl−¯ νat the LHC with ffiffiffi s p¼14 TeV c.m. energy, we select events with exactly two oppositely charged leptons (electrons or muons) and a photon with pseudorapidities jηl;γj<4. The transverse momentum of the photon is required to satisfy pγ T>25 GeV, and the transverse momenta of the leading (l1) and subleading (l2) leptons need to satisfy pl1 T>18 GeV, pl2 T>15 GeV or pl1 T>23 GeV, pl2 T>9GeV, following Run 2 ATLAS dilepton triggers [43]. Dilepton trigger thresholds are in fact expected to lower for HL-LHC [44], and a dilepton þ photon trigger with lower thresholds could also be implemented. We also require the missing transverse energy in the event to be ET>35 GeV. In order to suppress events with extra high-pTactivity, we veto events having a jet with pT>50 GeV or having two jets with pT>20 GeV and a pseudorapidity gap Δηj1j2>3. The dominant SM backgrounds are the irreducible processes pp →lþνl−¯ νγ and pp →Zγ,Z→τþτ−with FIG. 1. Left: Feynman diagram for gg →hγ, whose amplitude vanishes due to Furry’s theorem. Right: example tree-level Feynman diagram for q¯ q→hγ(with q¼u,d,s,c,b) in the SM. 2This is a factor ∼10 larger than the SM value for σc¯ cfrom Eq. (1) due to the much larger PDF for the up quark inside the proton. AGUILAR-SAAVEDRA, CANO, and NO PHYS. REV. D 103, 095023 (2021) 095023-2 both τleptons decaying leptonically, together with the reducible background pp→t¯ tγ(with t→blþν,¯ t→¯ bl−¯ ν). The latter can be further suppressed by imposing a b-tagged jet veto on the selected events. We note that the Zþjets and Zð→llÞγSM backgrounds have a very large cross section (see, e.g., Refs. [45–47]). However, the above selection—in particular, the ETcut—combined with a Z-mass window veto on the invariant mass of the two leptons jmZ−mllj> 30 GeV greatly suppresses these processes. Selecting the two leptons in the event to be of opposite flavor (OF) would provide an additional suppression for these backgrounds. In any case, we retain both OF and SF (same-flavor) lepton events,3and we disregard Zþjets and Zð→llÞγbackgrounds altogether. We generate our signal and SM background event samples (both at LO) in M ad G raph 5 [41] with subsequent parton showering and hadronization with PYTHIA 8[48] and detector simulation via DELPHES v3.4.2 [49], using the antikTalgorithm [50] with R¼0.4for jet reconstruction with F ast J et [51] and the DELPHES detector card designed for HL-LHC studies. We do not include pileup in our simulation for simplicity: in the experimental measurements, it has been shown that the pileup contamination can be very efficiently removed by using pileup subtraction algorithms such as PUPPI [52], SOFTKILLER [53], or constituent level subtraction [54]. After event selection, the SM background cross sections are 5.08 fb for pp →lþνl−¯ νγ, 3.86 fb for Zγ,Z→τþτ− and 1.07 fb for t¯ tγ, where the latter includes the effect of the various vetoes in the selection. Assuming SM branching fractions for the Higgs boson (we discuss variants of this assumption in the next section), the signal cross section after event selection is 27.6 ab for κb¼κu¼1,κc¼10, and 41.2 ab for κb¼κc¼1,κu¼2000. In the following, we consider independently the possible enhancement of the charm and up-quark Yukawa couplings with respect to their SM values, performing two separate sensitivity studies. The rich event kinematics allows for an efficient signal discrimination following the initial event selection discussed above. An important role is played by the transverse mass MTreconstructed out of the dilepton system þ missing energy: M2 T¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi M2 ll þj pll Tj2 qþET2 −j pll Tþ ETj2;ð2Þ with  pll Tbeing the vector sum of the lepton transverse momenta, Mll the invariant mass of the dilepton system, and  ETthe missing transverse momentum of the event. Other key variables are the dilepton invariant mass Mll itself, the transverse angular separation Δϕðll;ETÞbetween the dilepton momentum  pll Tand missing momentum ET,or the distance ΔR≡ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Δϕ2þΔη2 pbetween each lepton and the photon ΔRl1γ,ΔRl2γ. In Fig. 2, we show the MT(top) and Mll (middle) distributions for the signal (with κb¼κu¼1,κc¼30) and the dominant SM backgrounds at the HL-LHC. We also show in Fig. 2(bottom) the normalized Δϕðll;ETÞand ΔRl2γdistributions for the signal and SM backgrounds. Performing a cut-and-count signal selection, MT∈½80;150GeV, Mll ∈½5;55GeV, ΔRl1γ>1,ΔRl2γ>0.8, and Δϕðll;ETÞ>2allows us to extract a HL-LHC projected sensitivity jκcj<13.9at a FIG. 2. Top: MTdistribution of events for the dominant SM backgrounds lþνl−¯ νγ (red), t¯ tγ(green), and Zð→τþτ−Þγ (yellow), all stacked, at the HL-LHC ( ffiffiffi s p¼14 TeV;3ab−1). In blue, the corresponding MTdistribution for the hγsignal with κb¼κu¼1,κc¼30 is displayed. Middle: same as above, but for Mll variable. Bottom: normalized Δϕðll;ETÞand ΔRl2γ distributions for signal and SM backgrounds. 3Considering only OF events results in a ∼ffiffiffi 2 preduction in our signal sensitivity. Yet, an experimental analysis splitting the events into OF and SF categories would recover part of this sensitivity. We also note that the SF signal events contain a minor contribution from h→ZZ→ν¯ νlþl−. MORE LIGHT ON HIGGS FLAVOR AT THE LHC: HIGGS …PHYS. REV. D 103, 095023 (2021) 095023-3 95% confidence level (C.L.), using a simple S= ffiffiffiffi B p≃2 estimate (with Sand Bbeing the number of signal and background events) and assuming Higgs boson SM branching fractions. Given the variety of relevant event kinematic variables and the significant correlations among several of them, it is possible to enhance the signal sensitivity with respect to the above “squared”cut-and-count analysis by accessing the full kinematic information of the events. To this end, we adopt here a multivariate approach and use the following set of kinematic variables (which contains all the relevant kinematic information of each event): MT;M ll;Mllγ;p l1 T;p l2 T;p γ T; ET; Δϕll;Δϕl1γ;Δϕl2γ;Δϕðll;ETÞ;ηl1;ηl2;ηγð3Þ to train a neural network (NN) to discriminate the hγsignal from the various SM backgrounds. The NN architecture uses two hidden layers of 128 and 64 nodes, with rectified linear unit (ReLU) activation for the hidden layers and a sigmoid function for the output layer. The NN is optimized, using as its loss function the binary cross-entropy, using the Adam optimizer [55] (other generalized loss functions such as the one proposed in Ref. [56] do not give an appreciable improvement). Since the experimental dataset is unbalanced—that is, the SM background overwhelms the signal—it is useful to train the NN using more SM background than signal events, so that the NN learns optimally to identify (and reject) the former. Specifically, we use 1.5×104events for the lþνl−¯ νγ background, 104 events for the t¯ tγbackground, and 5000 events for the Zγ (Z→τþτ−) background (a total of 3×104SM background events) in the NN training, together with 1.5×104events of the hγsignal. The validation set contains the same number of events from each class. The signal discrimination power achieved by our multivariate analysis is very high, with areas under the “receiver operating characteristic”(ROC) curve of 0.941 and 0.938, respectively, for charm-quark and up-quark Yukawa sensitivity studies. The multivariate NN score variable θNN [which may be regarded as a highly nonlinear function of the kinematic variables in Eq. (3)] for the signal and dominant SM backgrounds in the charm-quark Yukawa study is shown in Fig. 3. In this case, a cut in the NN score variable θNN >0.78 yields a signal efficiency ∼0.57 together with SM background efficiencies 0.057, 0.034, and 0.003, respectively, for lþνl−¯ νγ,t¯ tγ, and Zð→τþτ−Þγ. For the up-quark Yukawa study, the optimal cut is also found to be θNN >0.78, yielding a signal efficiency ∼0.56 and respective SM background efficiencies of 0.056, 0.031, and 0.003. In addition to the dominant SM backgrounds, we also consider the VBF and AP hþγproduction processes as potential, yet minor backgrounds for our charm and up-quark Yukawa sensitivity analysis, as discussed in Sec. II. The extra high-pTactivity vetoes imposed in our initial event selection suppress these processes down to a hð→lþνl−¯ νÞγcross section (assuming SM branching fractions for the Higgs boson) of 32.6 ab for VBF, 2.24 ab for hγW(with W→jj or W→lν), and 1.84 ab for hγZ(with Z→jj or Z→ν¯ ν), with other backgrounds like hγjand tthγnegligible after the event selection. Due to such small cross sections, these backgrounds are not included in the NN training. The NN selection efficiencies for them are the following: in the charm-quark Yukawa study, the cut θNN >0.78 yields the efficiencies 0.42, 0.25, and 0.27 for the VBF, hγW, and hγZbackgrounds, respectively; for the up-quark Yukawa case, the cut θNN >0.78 yields the corresponding efficiencies 0.42, 0.26, and 0.28. Altogether, these backgrounds do not appreciably reduce the sensitivity to κcand κufrom our multivariate analysis, which is driven by the NN ability to reject the main irreducible SM background, pp →lþνl−¯ νγ. IV. CONSTRAINTS ON κcAND κu For SM branching fractions of the Higgs boson, the sensitivity to κcand κuat the HL-LHC from the NN analysis of the previous section is jκcj<11.8and jκuj< 1930 at a 95% C.L. (improving on the cut-and-count analysis from Sec. III, as expected). This assumes that the statistical uncertainty of the SM background will largely dominate over its systematic uncertainty at the HL-LHC, which is justified in the present scenario, particularly since the main backgrounds are electroweak processes. The above projected bounds also assume that only one Yukawa coupling of the Higgs boson departs from its SM value. Enhancing ycor yuby an amount that makes them comparable to the SM bottom-quark Yukawa coupling FIG. 3. Multivariate NN score variable θNN for the hγsignal (blue) and dominant SM backgrounds lþνl−¯ νγ (red), t¯ tγ(green), and Zð→τþτ−Þγ(yellow) in the charm-quark Yukawa sensitivity study. AGUILAR-SAAVEDRA, CANO, and NO PHYS. REV. D 103, 095023 (2021) 095023-4 would modify significantly the total width of the Higgs boson and therefore its branching fractions. Nevertheless, it has long been realized that light quark Yukawa couplings remain essentially unconstrained by global fits to Higgs production and decay rates at the LHC [57–59] (see also Ref. [14]), unless further assumptions are made. The effect of an enhanced Higgs Yukawa coupling yqto a light quark q¼u,d,c,son the Higgs branching fractions may be compensated by a related increase of the Higgs couplings to gauge bosons and third-generation fermions, leading to a “flat direction”in the fit along which the Higgs signal strengths remain unchanged. From the present good agreement between SM predictions and LHC Higgs measurements [22,60,61], this flat direction may be approximately described by a single generic κhenhancement factor for all Higgs couplings other than the light quark Yukawa yqof interest [14]: κ2 h≃ 1−BrSM q¯ q 2þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1−BrSM q¯qÞ2þ4BrSM q¯qκ2 q q 2;ð4Þ with BrSM q¯ qbeing the branching fraction for h→q¯ qin the SM. While the combination of Higgs signal strengths with other measurements—e.g., with electroweak precision observables or an indirect measurement of the Higgs total width (model-dependent, see Ref. [62])—can help in lifting the flat direction [Eq. (4)], this discussion highlights the importance of complementary probes of Higgs couplings to light quarks. Considering κcand κualong the flat direction defined by Eq. (4) weakens our analysis’s sensitivity with respect to the assumption of SM branching fractions, since κq>κh for q¼c,u, and the effect of this becomes particularly important once yq=ySM b≳1. The projected 95% C.L. sensitivities to κcand κualong the flat direction are jκcj< 26.3and jκuj<2300. The projected bounds on κcwhich we obtain are complementary to other existing probes in the literature. Yet, they may not be competitive with the most sensitive proposed direct probes of the charm Yukawa coupling [7,9], which yield a current 95% C.L. experimental limit on κc(assuming SM Higgs branching fractions) of κc≲13 [22]. In contrast, the achievable hγsensitivity to κudoes lie in the same ballpark of other currently proposed probes. V. CONCLUSIONS In this paper, we have studied hγproduction at the HLLHC. While interesting in its own right, as this process is yet to be observed at the LHC, we demonstrate its role as a sensitive probe of the Higgs boson couplings to the light quarks of the first two generations of matter, still largely unconstrained by present measurements. The associated production with a photon enhances the contribution of the up-type quarks with respect to their down-type counterparts, yielding a way to disentangle Yukawa coupling enhancements from both quark types. This makes hþγ highly complementary to other existing light quark Yukawa probes. Concentrating on the h→lþνl−¯ νdecay channel of the Higgs boson, we have performed a multivariate neural network analysis to fully exploit the rich kinematics of this final state, and derived HL-LHC projected sensitivities to the Higgs Yukawa couplings to charm and up quarks. Particularly in the latter case, hþγmay help us to gain further insight on Higgs flavor at the LHC. 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