Lifting degeneracies in Higgs couplings using single top production in association with a Higgs boson

Journal of High Energy Physics, May 2013

Current Higgs data show an ambiguity in the value of the Yukawa couplings to quarks and leptons. Not so much because of still large uncertainties in the measurements but as the result of several almost degenerate minima in the coupling profile likelihood function. To break these degeneracies, it is important to identify and measure processes where the Higgs coupling to fermions interferes with other coupling(s). The most prominent example, the decay of h → γγ, is not sufficient to give a definitive answer. In this paper, we argue that t-channel single top production in association with a Higgs boson, with h → bb, can provide the necessary information to lift the remaining degeneracy in the top Yukawa. Within the Standard Model, the total rate is highly reduced due to an almost perfect destructive interference in the hard process, W b → th. We first show that for non-standard couplings the cross section can be reliably computed without worrying about corrections from physics beyond the cutoff scale Λ ≳ 10 TeV, and that it can be enhanced by more than one order of magnitude compared to the SM. We then study the signal pp → thj(b) with 3 and 4 b’s in the final state, and its main backgrounds at the LHC. We find the 8 TeV run dataset to be sensitive to the sign of the anomalous top Yukawa coupling, while already a moderate integrated luminosity at 14 TeV should lift the degeneracy completely.

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Lifting degeneracies in Higgs couplings using single top production in association with a Higgs boson

Marco Farina 5 Christophe Grojean 3 4 Fabio Maltoni 1 Ennio Salvioni 2 4 Andrea Thamm 0 4 0 Institut de Tehorie des Pehnomenes Physiques , EPFL, CH-1015 Lausanne, Switzerland 1 Centre for Cosmology, Particle Physics and Phenomenology (CP3) , Universiet Catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve, Belgium 2 Dipartimento di Fisica e Astronomia, Universiat di Padova and INFN, Via Marzolo 8, I-35131 Padova, Italy 3 ICREA at IFAE, Universitat Auotnoma de Barcelona , E-08193 Bellaterra, Spain 4 Theory Division, Physics Department , CERN, CH-1211 Geneva 23, Switzerland 5 Department of Physics , LEPP, Cornell University , Ithaca, NY 14853, U.S.A Current Higgs data show an ambiguity in the value of the Yukawa couplings to quarks and leptons. Not so much because of still large uncertainties in the measurements but as the result of several almost degenerate minima in the coupling prole likelihood function. To break these degeneracies, it is important to identify and measure processes where the Higgs coupling to fermions interferes with other coupling(s). The most prominent example, the decay of h ! , is not sucient to give a denitive answer. In this paper, we argue that t-channel single top production in association with a Higgs boson, with h ! bb, can provide the necessary information to lift the remaining degeneracy in the top Yukawa. Within the Standard Model, the total rate is highly reduced due to an almost perfect destructive interference in the hard process, W b ! th. We rst show that for non-standard couplings the cross section can be reliably computed without worrying about corrections from physics beyond the cuto scale & 10 TeV, and that it can be enhanced by more than one order of magnitude compared to the SM. We then study the signal pp ! thj(b) with 3 and 4 b's in the nal state, and its main backgrounds at the LHC. We nd the 8 TeV run dataset to be sensitive to the sign of the anomalous top Yukawa coupling, while already a moderate integrated luminosity at 14 TeV should lift the degeneracy completely. Contents 1 Introduction Single top and Higgs associated production Signal and background study 3.1 Parton-level simulation 3.2 Final state with 3 b-tags 3.3 Final state with 4 b-tags 4 Implications on Higgs couplings 5 Conclusions A Forward W b ! th scattering Introduction After 48 years of desperate searches, the most wanted elementary particle, the Higgs boson, or something that wickedly looks like it, has nally been caught by the ATLAS and CMS experiments [1, 2]. Uncertainties concerning its spin and CP properties remain and will be subject to intense experimental scrutiny in the present and forthcoming run of the LHC. Concurrently, an important program has been launched to measure its couplings to other known elementary particles of the Standard Model (SM). The goal is not so much to determine a few further unknown parameters of the SM but to understand the underlying structures of the laws of physics at high energy: if the SM were to be valid up to the scale of quantum gravity, the couplings of the Higgs boson would be uniquely xed in terms of other already known and well-measured quantities. On the contrary, any deviation in these couplings, for instance of the order of 20%, would unambiguously signal new physics at a scale below 5 TeV. The study of the LHC sensitivity to the Higgs couplings has been initiated in refs. [3{ 6]. Upon the rst and still incomplete measurements reported by both ATLAS and CMS as well as by the Tevatron experiments, a simple methodology inspired by a chiral eective Lagrangian approach has been developed in refs. [7{9] in order to quantify to which extent the Higgs boson is really fullling the role it has been devoted to in the SM, namely the screening of scattering amplitudes involving massive bosons and fermions at high energy. At the LHC, the main production channel of the Higgs boson as well as its cleanest decay mode proceed through purely quantum mechanical processes and rely on couplings to massless gluons and photons that are vanishing in the Born approximation. This results in an ambiguity in the value of the tree-level Higgs couplings since the coupling likelihood function exhibits several and almost degenerate minima (see e.g. refs. [6, 8, 9]). It has been emphasized [9, 10] that these degeneracies are likely to remain even after the on-going analyses will be extended to the whole 8 TeV dataset. Measuring processes involving real top quarks in the nal state will bring invaluable information. With the largest rate, the Higgs production in association with a top pair is a golden channel and has received great attention by the experimental [11, 12] as well as theoretical [13{17] communities. In this paper we argue that, even though subleading, Higgs boson production in association with a single top quark can also bring valuable information, in particular regarding the sign of the top Yukawa coupling.1 This is because an almost totally destructive interference between two large contributions, one where the Higgs couples to a space-like W boson and the other where it couples to the top quark, takes place in the SM. This fact can be exploited to probe deviations in the Higgs coupling structure, which will inevitably jeopardize perturbative unitarity at high energy and lead to a striking enhancement of the cross section compared to the SM. We discuss how this enhancement can be used to extract information on the sign of the top Yukawa coupling and we show that th production can be used to lift the degeneracy plaguing the Higgs coupling t of the LHC data. While a moderate integrated luminosity at 14 TeV should allow us to make a conclusive statement, we point out that already with the full 2012 luminosity, corresponding to 25 fb 1 per experiment, an interesting sensitivity on the sign of the top Yukawa could be reached. In our study we focus on the decay of the Higgs into bb, updating the early analysis of ref. [18] (see also refs. [19, 20]). This choice leads to an experimental signature (lepton + missing energy + multijets, among which 3 are b-jets) which is very similar to the one ATLAS and CMS have already analyzed in their searches for tth production [11, 12]. In this respect we believe that the experimental collaborations could easily perform the analysis we propose here in the very near future, thus adding new important information to the challenge of identifying the true nature of the recently discovered particle. The large enhancement of the th cross section for nonstandard Higgs couplings is associated to the growth of the scattering amplitude at high energy, which in turn implies that perturbative unitarity is lost at some UV scale . We estimate , which acts as the cuto of our eective theory, to be at least of O(10) TeV and thus above the energy scales that the LHC will be able to probe. In fact, the th invariant mass distribution in LHC collisions essentially vanishes above 1 TeV, therefore we can safely conclude that our analysis remains insensitive to UV physics above the cuto scale. Our paper is structured as follows: we start by introducing the general features of the th process and discussing its implications, including an estimate of the scale where perturbative unitarity is lost, in section 2. We proceed in section 3 to the analysis of the signal and of the main backgrounds at the LHC, performing a parton-level simulation. In section 4, we discuss the implications on the determination of the Higgs parameters. Finally, we conclude in section 5. Unless otherwise specied, the Higgs mass is assumed to 1The sign of the top Yukawa coupling is not physical by itself, but the relative sign compared to the Higgs coupling to gauge bosons (we take the latter to be positive) is physical. Figure 1. Feynman diagrams contributing to the partonic process W b ! th. be mh = 125 GeV throughout this work. For the top mass we take mt = 173 GeV. Finally, the shorthand th is always understood to include also the charge-conjugated case where t is replaced by t. Therefore all our cross sections include both t and t production. Single top and Higgs associated production The Feynman diagrams contributing to the core process W b ! th are shown in gure 1. The diagram where the Higgs is emitted from a b leg is suppressed by the bottom Yukawa, and will be consistently neglected in our study. In the th production process at the LHC the initial W is radiated from a quark in the proton, and is thus spacelike. However, at high energy the eective W approximation [21, 22] holds, which allows us to factorize the process into the emission of an approximately on-shell W from the quark times its hard scattering with a bottom. Thus it makes sense to discuss the amplitude for W b ! th at high energies assuming the initial W to be on-shell, in order to gain an approximate understanding of the full picture. In the high-energy, hard-scattering regime, where s; t; u mt2; m2W ; m2h, the amplitude for WLb ! th (the longitudinal polarization dominates at large s) reads2 (2.1) where we have omitted terms that vanish in the high-energy limit and, for simplicity, also neglected the Higgs mass in addition to setting mb = 0. The generalized couplings of the Higgs are dened as cV ghW W =ghSWMW and cF ghtt=ghStMt . The functions A; B are given by B (t=s; ; t; b) = ty @eiq 1 + t=s eip1 + t=s 0! 2We take nal momenta outgoing, and dene s = (pW + pb)2, t = (pW ph)2. is the azimuthal angle around the z axis, which is taken parallel to the direction of motion of the incoming W . HcV = 1L where in the rightmost term of each line we have chosen a specic basis for the spinors, namely bL = bR = tL = tR = which correspond to the chiral states fFL; FRg (F = b; t) in the mF ! 0 limit.3 The amplitudes involving the helicity state bR, which is identied with a right-handed bottom since we are assuming mb = 0, exactly vanish due to the V A structure of the couplings of the W to fermions. From eq. (2.1) we see that when cV 6= cF the amplitude grows with energy like ps and is enhanced compared to the case cV = cF (which includes the SM), where the amplitude is constant in the large s limit. The non-cancellation of the terms in the amplitude growing with energy is at the origin of the striking enhancement of the cross section when cV 6= cF . The cross section for W b ! th is shown as a function of the center of mass energy in gure 2. The large enhancement of the hard scattering cross section (dened by a centrality cut j j < 2) for cF = cV is evident.4 At large energies, the amplitude is constant for cV = cF and thus the cross section vanishes as 1=s. On the other hand, when cF 6= cV the amplitude grows with energy like ps and as a consequence the cross section tends to a constant for large s. It is easy to compute this asymptotic value of the cross section: squaring the leading term of the amplitude in eq. (2.1), summing and averaging 3However, note that the limit mt ! 0 does not interest us here. 4Incidentally, we note that the cross section shows another feature, a Coulomb enhancement at small jtj due to the diagram with a W exchange in the t-channel. As can be read o gure 2 the forward cross section tends to a constant limit for large s, which can be computed in a simple way in terms of the parameter cV alone and is insensitive to the value of cF . A short discussion of the forward cross section is contained in appendix A. Figure 3. Feynman diagrams for the processes pp ! thj and pp ! thjb. over polarizations and integrating over t we nd This simple formula gives accurate results: for example for ps = 5 TeV, cV = cF = 1 and a centrality cut5 j j < 2 we nd that the cross section computed without any approximations is full(j j < 2) = 41:3 pb, whereas (j j < 2; s ! 1) = 40:7 pb . Since for cV 6= cF the hard scattering amplitude grows with energy, perturbative unitarity will be lost at some cuto scale , which we now estimate. In the spinor basis of eq. (2.4), only one s-wave amplitude is non-vanishing a0 = A(t=s; ; tR; bL) = from which, imposing the condition ja0j < 1, we nd that perturbative unitarity is violated at a scale ps with = 12 p2 v2 mt jcF cV j For example, for cV = cF = 1 the cuto is 9:3 TeV. One may worry about other processes involving top quarks, in which perturbative unitarity could be lost at a scale lower than the one in eq. (2.7) for cF < 0. A relevant and often mentioned process is WL+WL ! tt, for which we nd = 16 v 2=(mt j1 cV cF j) : For cV = cF = 1 this formula yields 8:8 TeV, essentially the same cuto scale we found for WLb ! th. For previous discussions of perturbative unitarity breakdown in processes with external fermions, see refs. [23, 24]. Having analyzed the behavior of the partonic cross section, we can now turn our attention to single top and Higgs associated production in hadron collisions. At the LHC, t-channel single top production goes through an initial-state gluon splitting into a bb pair. Such a process can be eciently described by a 5-avor scheme where bs are in the initial state and described by a perturbative b PDF, gure 3(a). In this scheme, the non-collinearly enhanced contribution, where the spectator b (i.e. the one not struck by the W boson) is central and at high pT (see gure 3(b)), is moved to the next-to-leading order term. This contribution, which we indicate with pp ! thjb, is nite and can be easily calculated at treelevel, contributing to a nal state signature with an extra b-jet, a useful handle to suppress 5Note that for the expression in eq. (2.5) to be reliable, ~ cannot be too large. In fact, as already mentioned, in the forward region the cross section has a Coulomb enhancement which is not captured by the approximations we made here. See also appendix A. cF = 1 cF = cF = 1 cF = 8 TeV 14 TeV 17:4 80:4 Table 1. Leading-order cross sections for the processes pp ! thj and pp ! thjb (with pbT > 25 GeV and j bj < 2:5) at the LHC. The parameter cV has been set to 1. cF = 1 cF = 8 TeV the background. In table 1 we present the rates for th production in the 5-avor scheme, fully inclusive as well as with the requirement of the extra b to be in the tagging region, for 8 and 14 TeV, in the cV = 1; cF 1 cases. Our analysis in section 3 will consider both processes, which lead to nal states containing 3 and 4 b-jets respectively, once the decay of the Higgs to bb is taken into account. The cross sections in table 1 were computed using MadGraph 5 [25] with CTEQ6L1 PDFs [26], setting the factorization and renormalization scales to the default event-by-event MadGraph 5 value. As an estimate of the theoretical uncertainty on the signal, we have computed the fully inclusive cross sections at NLO in QCD, in the 5-avor scheme, using aMC@NLO [27{29] and CTEQ6M PDFs [26]. The results are reported in table 2, where the uncertainties correspond to variations of the factorization and renormalization scales with F = R around = (mt + mh)=2 from = 2 to 2 . The NLO cross sections appear to be extremely stable under radiative corrections and therefore we deem the theory uncertainty of the signal rates in our analysis negligible. The striking enhancement of the hadronic cross section for cF 6= cV is shown in gure 4, where (pp ! thj) for an LHC energy of 14 TeV, normalized to its SM value, is displayed as a function of cF for three dierent choices of cV (very similar plots are obtained considering 8 TeV and/or the pp ! thjb process). For example, for a standard hW W coupling, i.e. cV = 1, a top Yukawa with equal magnitude and opposite sign with respect to the standard one (cF = 1) yields an enhancement of the cross section of more than a factor 10. As noted above, perturbative unitarity in W b ! th scattering is lost at a scale & 10 TeV for cV ; cF O (1). Figure 5 clearly shows that after convolution with the p p t h j HLHC 14 TeVL 10.0 M5.0 S p p t h j HLHC 8 TeVL 0.12 0.10 `s0.08 d0.06 d0.04 0.02 p p t h j HLHC 14 TeVL cF=1 HSML cF=-1 PDFs the contribution of the region ps^ & 1 TeV, where ps^ is the center of mass energy of the th system, to the hadronic cross section is negligible. This implies that our perturbative computations can be fully trusted. Indeed gure 5 demonstrates that the relative contribution to the cross section from large values of ps^ is more sizable in the SM than for cF 6= cV . This is compatible with the dierent behaviors of the partonic cross section in the two cases, shown in gure 2. Signal and background study Parton-level simulation Signal and background events have been generated at the parton level using MadGraph 5 with CTEQ6L1 PDFs, setting the factorization and renormalization scales to the default event-by-event MadGraph 5 value. Jets are dened at the parton level. In order to take showering, hadronization, detector and reconstruction eects minimally into account, we Table 3. Acceptance cuts applied to the signal and backgrounds at the reconstructed level. The R requirement applies to all objects. smear the pT of the jets uniformly in using a jet energy resolution dened by (ppTT ) = paT pbpT c ; where the parameters are taken to be a = 2, b = 0:7 and c = 0:06. With these choices, eq. (3.1) is compatible with the results of the ATLAS jet energy resolution study of ref. [30] (see gure 9 there). The jet 4-momentum is then rescaled by a factor psTmeared=pT . The acceptance cuts reported in table 3, chosen following the ATLAS tth analysis [11], are applied on the physical objects. We do not require any acceptance cut on the missing transverse energy. An object is considered to be missed if it does not pass one of the acceptance cuts. If, in particular, two jets are collinear with R < 0:4 we merge them by summing their 4-momenta and we consider them as a single jet when applying further cuts.6 Additionally we require the lepton to be isolated from any jet in the event, including those that do not pass acceptance cuts and therefore are missed. In all the signal and background processes we consider in this paper, a semileptonically decaying top is present. We assume a 100% eciency for the reconstruction of this top, which implies an unambiguous identication of the b originating from its decay. This assumption is of course idealized, however the use of a more realistic semileptonic top reconstruction eciency will only aect the overall normalization of both signal and background, and not their relative values. Concerning b-tagging, we assume the following performance: eciency b = 0:7, charm mistag probability c = 0:2 and light jet mistag probability j 0:008 [11]. Finally we assume a lepton reconstruction eciency = 0:9. Final state with 3 b-tags We start by discussing the 3 b-jet nal state, which arises from pp ! thj after selecting the Higgs decay into bb. Requiring the top to decay semileptonically (t ! b+ ) gives the signature 3 b + 1 forward jet + + ETmiss: We can now turn our attention to the most relevant backgrounds:7 tZj, Z ! bb: an irreducible background where a Z boson mimics the Higgs in decaying to bb. tbbj: an irreducible QCD background. tt, t ! bcs: a reducible background where either the c or s are mistagged. ttj, t ! bcs: also in this case, either the c or s are mistagged while the other is missed. As can be seen in table 4 for 8 TeV and in table 5 for 14 TeV, after acceptance cuts and eciencies the last two backgrounds are extremely large. In particular, their values are larger than those quoted in ref. [18], mainly due to a larger charm mistag rate considered here (we use c = 0:2, whereas ref. [18] adopted c = 0:1) and to the fact that we increased the pT threshold for jets, which results in a larger probability of missing a jet from ttj. The dominance of backgrounds where a c is mistagged suggests that it may be sensible to prefer a b-tagging performance with smaller eciency but higher rejection against charm. However, for deniteness we stick to the numbers reported in section 3.1, taken from ref. [11]. After acceptance cuts and eciencies, the signal is overwhelmed by the tt background not only for the standard case cF = 1, but even considering the enhanced case cF = 1 (we set cV = 1). Thus, we require a set of additional cuts in order to isolate the signal. These cuts are listed in tables 4{5, together with the cross sections obtained after their application. The value of each cut is chosen by optimizing the Poisson exclusion limit in the cF = 1 case. We remark that since we are assuming ideal top reconstruction, the b coming from the semileptonic top is always assumed to be unambiguously identied, therefore no cut on it is applied beyond the acceptance ones, neither for the signal nor for the backgrounds. The rst cut we apply requires the bb pair to have an invariant mass around mh, which of course helps to eliminate the tZj background. The second cut selects large values for the bbj invariant mass and is eective against the reducible backgrounds, in particular it suppresses enormously tt, where the jet and 2 bs are decay products of a top and therefore we expect their invariant mass to be close to mt. The last cut singles out a forward jet, which is a distinctive feature of the signal. However, after all cuts the background cross section, completely dominated by ttj, is still one order of magnitude larger than the signal for cF = 1. In the last line of tables 4 and 5, we present the number of signal and total background events expected after 25 fb 1 of integrated luminosity. At 8 TeV, the Poisson exclusion is at 97:4% CL or 2:2 (by abuse of notation, we are expressing the probability in terms of number of s, e.g. 2 approximately corresponds to the 95% CL), while at 14 TeV it reaches 4 . Final state with 4 b-tags As suggested in ref. [18], a way to enhance the sensitivity on the th signal is to require an extra b, coming from the splitting of an initial gluon: the process of interest is thus pp ! thjb. Requiring a semileptonic top and the decay h ! bb leads to the signature 4 b + 1 forward jet + + ETmiss: Here the main backgrounds are: tZbj, Z ! bb: an irreducible background where the Z mimics the Higgs. tbbbj: similarly to the 3 b case, an irreducible QCD background. ttbb, t ! bjj: a reducible background where one of the two jets, originating from a hadronically decaying W , is missed. ttbb, t ! bcs (one mistag): here the c or the s is mistagged, while either the other one is missed (and one b is not tagged) or one of the bs is missed. ttj, t ! bcs (two mistags): in this case both c and s are mistagged. Looking at tables 6 and 7, we see that requiring 4 b-jets allows us to obtain a much larger signal to background ratio after acceptance cuts compared to the 3 b case. On the other hand, the overall rates are obviously smaller. Analogously to what was done in the 3 b case, a set of additional cuts are imposed to enhance the signal. The cuts are listed in tables 6{7, together with the cross sections obtained after their application. The value of each cut is again chosen by optimizing the Poisson exclusion limit in the cF = 1 case. Signal Backgrounds cF = 1 cF = 1 Total tZbj tbbbj ttbb 0:043 0:63 7:81 0:11 0:26 2:66 (0:48) 0:039 0:58 4:06 0:03 0:08 0:94 (0:40) 0:023 0:30 0:67 0:002 0:015 0:20 (0:18) 0:008 0:15 0:014 0: 0:007 0:002 (0:001) 0:2 3:8 0:4 Table 6. Cross sections in fb for the 4 b-tag case at 8 TeV. In the event line backgrounds are summed. For ttbb, the contribution of tth is shown in parentheses. Signal Backgrounds cF = 1 cF = 1 Total tZbj tbbbj ttbb 0:19 2:85 39:14 0:46 1:07 14:40 (1:94) 0:17 2:61 19:78 0:12 0:32 4:88 (1:63) 0:13 1:82 5:97 0:05 0:09 1:68 (1:04) 0:07 1:20 0:35 0:02 0:06 0:03 (0:03) 1:7 30:1 8:7 Table 7. Cross sections in fb for the 4 b-tag case at 14 TeV. In the event line backgrounds are summed. For ttbb, the contribution of tth is shown in parentheses. The rst cut requires the invariant mass of one of the 3 bb pairs (we recall that ideal reconstruction of the semileptonic top is assumed) to be inside a window around mh. This helps again to eliminate the tZbj background. The second cut demands all bb invariant masses to be higher than about 100 GeV, and is most eective on ttj, where the mistagged c and s, coming from a W decay, have an invariant mass around mW . The last cut requires all 3 bj pairs to have a large invariant mass. This eciently suppresses the ttbb backgrounds, for which in most cases at least one bj pair comes from a top decay and thus has an invariant mass mbj . qmt2 m2W 150 GeV. The exclusion limits obtained for cF = 1, assuming 25 fb 1 of data, are 2:4 and 6 at 8 and 14 TeV respectively. The sensitivity at 8 TeV is comparable to the one obtained in the 3 b case, while at 14 TeV requiring an extra b-jet improves the result signicantly. Before discussing the implications of our results, we wish to comment here on the sensitivity of the proposed analysis to the tth process. As can be read from tables 6 and 7, this process makes up a sizable fraction of the ttbb cross section after the cuts. Moreover, after the rst three cuts, the rate for tth is comparable to the th signal for cF = 1. Being insensitive to the sign of the top Yukawa, tth can be considered as a background process in our analysis. It is, however, quite useful to observe that the simple search strategy we propose in the 4b channel would be sensitive to both single and pair top production in association with a Higgs boson. In this respect, a key role is played by the cut on mbj that was designed to suppress processes with a tt pair in the nal state, as discussed above. The relative contribution of tth to the ttbb background with one mistag, on the other hand, is small, approximately 5%. Implications on Higgs couplings We are now able to study the implications of our results on the general parameter space of Higgs couplings. To do so we combine the two analyses that we discussed in section 3, i.e. 3 and 4 b-tags, to exploit the full LHC sensitivity in th ! tbb production. Note that in the combination we consider the 3b and 4b samples as independent. While this is an approximation (which can be easily lifted in a more realistic analysis by dening fully exclusive samples), in practice it has a small eect as the 4 b sample is signicantly smaller than the 3b one. We combine the (Poisson) p-values through Fishers method, dening X2 = 2 X log pi where k = 2 in our case, and p1;2 are the p-values of the two analyses. It can be shown that X2 has a 2 distribution with 2k degrees of freedom. Thus the combined p-value is the one associated to the value of X2 at each point in parameter space. This denition is conservative compared to the estimate based on the naive product of p-values. In gure 6 we present the results of our analysis in the (cV ; cF ) plane, where a universal rescaling of the Higgs couplings to fermions ct = cb = c = cc = cF is assumed. The regions that can be excluded (at 95% CL) by th production with an integrated luminosity of 25 and 50 fb 1 are presented, along with the regions currently favored by a t to Higgs data. As can be seen, already at 8 TeV parts of the preferred region with cF < 0 can be excluded. The current best t point with cF < 0 is excluded at 2:1 with 50 fb 1. On the other hand, a moderate luminosity at 14 TeV can conclusively remove the degeneracy between the two regions that are at the present time preferred by Higgs data, for example reaching a 5:8 exclusion of the best t point with cF < 0 after 50 fb 1. Notice that in addition to the th production cross section (recall gure 4), also the branching ratio of the Higgs into bb depends on the parameters (cV ; cF ). It is also possible to relax the assumption of universal couplings of the Higgs to fermions and consider the case where only the htt coupling ct has a rescaled value compared to the SM while cb = c = cc = 1, so in particular ( h ! bb) is equal to its SM value. In this case, the th ! tbb rate is essentially xed by the dependence on cV ; ct of the production cross section (a mild sensitivity to cV ; ct through the Higgs total width is also present). The results are shown in the (cV ; ct) plane in gure 7. Excluded regions at 95% C.L. are displayed for 25 fb 1 and 50 fb 1 integrated luminosity. Superimposed are the regions currently favored by Higgs data. The most striking feature is, that the best t region with ct < 0 can already be completely excluded at 8 TeV with 25 fb 1 (reaching a 4:0 exclusion of the best t point with negative ct). After the time of discovery comes the need for measuring. The couplings of the putative Higgs boson are of prime importance since they control the behavior of the whole theory at high energy. The dominant processes involving the Higgs boson that are currently investigated at the LHC do not allow us to determine all its couplings unambiguously. An important task now is therefore to systematically identify additional processes that could complement the rst LHC information and lift degeneracies appearing in Higgs coupling ts. In this paper, we have studied single top production in association with a Higgs boson, focusing on the Higgs decay into bb. We discussed the form of the amplitude of the hard scattering process W b ! th, showing that for nonstandard couplings of the Higgs to the W boson and/or to the top quark a striking enhancement of the cross section can be obtained. The enhancement is due to the non-cancellation of terms that grow with energy in the amplitude and lead to violation of perturbative unitarity at some UV scale. We estimate the cuto scale to be at least 10 TeV, concluding that corrections to our computation of the cross section from physics above the cuto are always negligible. We have performed a parton-level study of the LHC signal processes pp ! thj and pp ! thjb, and of the corresponding irreducible and some of the most relevant reducible backgrounds. The combination of the two nal states, containing 3 and 4 b-jets respectively, shows that if a universal rescaling cF of the fermion couplings is assumed, already at 8 TeV parts of the preferred region with cF < 0 can be excluded. On the other hand, a moderate luminosity of 50 fb 1 at 14 TeV can conclusively remove the degeneracy between the two regions that are at the present time preferred by Higgs data, reaching a 5:8 exclusion of the best t point with negative cF . In addition, we investigated the case where only the htt coupling diers from its SM value while the other Yukawa couplings are standard. Here, the best t region with negative top Yukawa coupling can be completely excluded at 8 TeV with 25 fb 1, reaching a 4:0 exclusion of the best t point with ct < 0. Our results therefore motivate the undertaking of a full-edged analysis by the ATLAS and CMS collaborations on one side, and the improvement on the accuracy of the theoretical predictions on the other. In the former case, in addition to having a complete simulation of th events, one could also study the possibility of improving the signal over background ratio by using further discriminating variables (such as for example the different rates for th and th with respect to the main backgrounds which are symmetric) or multivariate analyses. On the latter, it would be certainly interesting to evaluate the (possibly signicant) impact of NLO QCD corrections to irreducible backgrounds, i.e., thj and tZj, a task that can now be accomplished in a fully automatic way [15, 27, 28, 32]. Further information on the Higgs couplings to heavy quarks could also come from other processes at the LHC. One example is double Higgs production, gg ! hh. This process proceeds through a triangle and a box diagram, which, again, interfere destructively in the SM and therefore result in a sensitive probe of the Higgs-heavy quarks interactions, see, e.g., refs. [33{35]. Finally we remark that complementary information could a priori also come from the observation of Bs ! + very recently reported by LHCb [36]. The measured value of BR(Bs ! + ) agrees well with the SM prediction [37]. The SM contribution is actually dominated by the interactions associated to the top Yukawa coupling and therefore this measurement could be naively expected to provide a good probe of any deviation of the top Yukawa itself. However, only the Yukawa interactions between the Goldstone bosons and the quarks contribute to this process. What we have proposed to probe via th production is rather the interaction of the physical Higgs boson with the top quark, i.e. the one controlled by the parameter ct. Actually, if the deviations from ct = 1 originate from pure Higgs non-linearities as in composite Higgs models, for instance via a higher dimensional operator like jHj2QLHytR, then it is easy to see that the prediction for BR(Bs ! + ) remains unaected. 8 Note added. During the nal stages of this project another study discussing th production appeared [38] that focuses on the h ! decay channel. We are grateful to A. Coccaro, P. Francavilla, G. Isidori and V. Sanz for useful discussions. We also wish to thank V. Hirschi for help with aMC@NLO. M.F. thanks CERN for hospitality during the early stages of this work. This research has been partly supported by the European Commission under the ERC Advanced Grant 226371 MassTeV and the contract PITN-GA-2009-237920 UNILHC. C.G. is also supported by the Spanish Ministry MICNN under contract FPA2010-17747. The work of F.M. is partially supported by the IAP Program, BELSPO VII/37 and the IISN-FNRS conventions 4.4511.10 and 4.4517.08. E.S. has been supported in part by the European Commission under the ERC Advanced Grant 267985 DaMeSyFla. The work of M.F. has been supported in part by the NSF grant PHY-0757868 and by the Fondazione A. Della Riccia. A.T. has been partially supported by the Swiss National Science Foundation under contract 200020-138131. Forward W b ! th scattering The forward cross section for the partonic process W b ! th, dened for example by a cut on j j > , can be computed for large s in a very simple way. In fact, for this purpose the diagram with top exchange in the s-channel can be neglected, and we only need to look at the diagram with W exchange in the t-channel. In the regime we are interested in, i.e. large s, the longitudinal polarization of the W dominates. The leading term in the amplitude, which is enhanced at small jtj, goes as s=(t m2W ) and reads At large s and generic t, the fermion bilinears relevant to the amplitude read u(pt)p=W (1 5)u(pb) = 2s B (t=s; ; t; b) + : : : 8We thank G. Isidori for illuminating discussions on this point. where the functions A; B have been dened in eqs. ( 2.2){(2.3), and the dots stand for subleading terms. Thus squaring the amplitude in eq. (A.1), summing and averaging over polarizations (we neglect the contributions of the transverse components of the W ) and recalling that we are interested in the region s j tj we nd jAfwj2 = from which we derive the approximate expression of the forward cross section R(; s ) = valid for tanh 1 (i.e. for large ). We note that as expected, the forward cross section is controlled only by cV and is insensitive to the value of cF . As a consequence, the forward cross section is insensitive to the growth with energy of the \hard scattering" amplitude, which takes place for cV 6= cF and was discussed in section 2. As a numerical example, let us consider cV = 1, a cut j j > 3 and let us set the center of mass energy to ps = 5 TeV. Then computing the cross section without approximations gives full(j j > 3) = f16:3; 16:5; 16:8g pb; cF = f1; 0; 1g whereas using the approximate formula in (A.5) yields (j j > 3; ps = 5 TeV) = 16:4 pb, a very accurate result. The factor R has the value R( = 3; ps = 5 TeV) 0:91. Open Access. This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Marco Farina, Christophe Grojean, Fabio Maltoni. Lifting degeneracies in Higgs couplings using single top production in association with a Higgs boson, Journal of High Energy Physics, 2013, 22, DOI: 10.1007/JHEP05(2013)022