h->mu^+ mu^- via tth Production at the LHC

In this work, we examine the process at the LHC in which a Higgs boson is produced in association with a t t-bar pair and subsequently decays to a pair of muons. We show that the statistical significance for the discovery of a light, Standard-Model Higgs boson with a mass around 120 GeV in this channel is comparable to those for other processes (gluon fusion, weak-boson fusion) in which the Higgs decays to a muon pair. Combining all three of these channels, we show that evidence for a Higgs boson with a mass in the range 115 GeV<m_h<130 GeV could be obtained at the 3 sigma significance level with an integrated luminosity of 300 fb^{-1}. We also calculate the enhancement factor to the cross-section that would be needed to discover a non-standard Higgs boson in this channel.


I. INTRODUCTION
The CERN Large Hadron Collider (LHC) -a pp collider with center-of-mass energy √ s = 14 TeV -will begin taking data in the very near future. One of the primary missions of the LHC is to investigate the physics behind electroweak symmetry-breaking. Since many of the most attractive candidate theories involve a Higgs sector containing one or more light, scalar degrees of freedom, a great deal of effort has been invested into determining how best to search for these scalars (and in particular the lightest CP-even scalar) at the LHC (see [1,2,3,4]). For a relatively light Higgs boson in the Standard Model (SM), with 114 GeV < ∼ m h < ∼ 125 GeV, the most favored channels are gg → h → γγ, tth(h → bb). For a Higgs with intermediate mass 125 GeV < ∼ m h < ∼ 140 GeV, the most promising channel is the weak-boson fusion (WBF) [5] process qq ′ → qq ′ h(h → τ τ ) [6]. For a heavier Higgs, with m h > ∼ 140 GeV, the channels of interest are h → W W * and h → ZZ * , with the Higgs produced through either gluon fusion or WBF [3,4].
Clearly, additional channels which might provide evidence for a light, CP-even Higgs scalar in these mass ranges can also play a crucial role in Higgs phenomenology. This is especially true if the Higgs sector realized in nature turns out to be more complicated than the single SU(2) doublet of the SM. In such cases, the most promising discovery channels could turn out to be quite different from those pertinent to a SM Higgs boson [7]. For this reason, it has become increasingly clear that channels for which the significance of discovery for a Standard Model Higgs is low may be of crucial importance for detecting whatever variety of Higgs boson is actually out there -provided of course that nature employs a scalar Higgs sector to break the electroweak symmetry. Furthermore, if a light, CP-even Higgs boson is discovered early at the LHC, within the first 10 − 30 fb −1 of data, processes which can put the most stringent bounds on parameters such as its mass, its couplings to the Standard Model fermions, etc. will become increasingly important for precision analyses of the Higgs sector that could point the way toward new physics.
One Higgs-decay channel that is of particular interest is h → µ + µ − . The primary advantage of this channel is that a signal involving a pair of high-p T muons will be easy to identify at the LHC. Indeed, the muon-identification efficiency at the LHC detectors is more that 90%[1, 2]. Once a Higgs boson is discovered in this channel, its mass could be readily reconstructed with high precision. Additionally, such a channel could be used in determining the muon Yukawa coupling. This is of particular interest because most of the existing literature on the measurement of Higgs-boson Yukawa couplings focuses on the third generation Yukawa couplings, y b , y τ and y t . Consequently, h → µ + µ − processes could be important for determining whether or not the effective Higgs Yukawa couplings are indeed generation-universal.
The difficulty with h → µ + µ − processes is the small Higgs branching fraction into muon pairs, both in the Standard Model -in which it is of O(10 −4 ) -and in most simple extensions of the Higgs sector. Indeed, under the assumption of universal Yukawa couplings among the lepton generations, the small size of the muon mass m µ compared to m τ results in BR(h → µµ) being roughly two orders of magnitude smaller than BR(h → τ τ ). Consequently, while a great deal of attention has been focussed on processes in which the Higgs boson decays to a tau pair (for example, weak-boson fusion with h → τ + τ − is now regarded as one of the promising discovery channel for the SM Higgs in the intermediate mass region [1,2,5]), h → µ + µ − processes have not been extensively considered. Nevertheless, some parton-level studies have been carried out: investigations of gg → h → µµ and the weak-boson fusion process qq ′ → qq ′ h(h → µµ) at the LHC were performed in Ref. [8] and Ref. [9], respectively. It was found that by combining the results from both of these channels, an observation of h → µ + µ − at the 3σ level could be obtained with 300 fb −1 of integrated luminosity for low Higgs masses. Higgs decays to muon pairs in the Minimal Supersymmetric Standard Model have also been studied (see, for example, Ref. [10]).
In this letter, we examine the associated Higgs production process tth with h → µ + µ − at the LHC. While the rate for this process is far smaller than that for the tth(h → τ τ ) channel discussed in [11], a muonic final state has a number of advantages. Perhaps the most significant of these is that the final-state muon pair affords an exceptionally good Higgsmass resolution -of similar order (around 1%) to that afforded by gg → h → γγ [2,12]. In addition, the absence of any additional sources of missing energy for semileptonic top decays (beyond the single neutrino from t → bℓν) reduces the uncertainty in top-quark reconstruction. We show that, for a SM Higgs boson with a mass around 120 GeV, the statistical significance of discovery in the tth(h → µµ) channel is on the same order as that obtained from the gluon fusion and WBF channels. We also investigate the prospects for detecting a SM Higgs boson via its decays to muon pairs using the combined gluon fusion, WBF, and tth channels, and discuss the potential implications for Higgs discovery using the tth(h → µµ) channel in beyond-the-Standard-Model scenarios.

II. SIGNAL AND BACKGROUNDS
For a SM Higgs sector, the tth(h → µµ) channel will be useful primarily in the case where the Higgs boson is light: 114 GeV < ∼ m h < ∼ 140 GeV. (The production cross-sections drop quickly for heavier Higgs masses.) Here, we present results for the specific choices m h = 115 GeV, 120 GeV, 130 GeV, and 140 GeV. The leading-order (LO) tth production cross-section and Higgs branching fraction to muons for each of these choices are listed in Table I. The former were calculated using the MadGraph package [13], with factorization and renormalization scales both set to (2m t + m h )/2; the latter were calculated using HDECAY [14]. It is apparent from Table I that the leading-order (LO) tth production cross-section for a Higgs boson in this mass range at the LHC ranges from around 350 to 600 fb, while the Higgs branching fraction to muons is of O(10 −4 ), as discussed above.
Since this implies a rather small overall rate for tth(h → µµ) events, we would like to include in our analysis all final states which permit an unambiguous reconstruction of both t andt from their decay products. These include processes in which both W bosons decay hadronically (45.7% of the time) and semileptonic decays in which the charged lepton is either an electron or a muon (28.8% of the time). Therefore, we study two types of signals: (I) hadronic signatures: 6 jets + µ + µ − , (II) semileptonic signatures: 4 jets + µ + µ − ℓ ± + missing E T , ℓ = e, µ.
For fully-leptonic tt decay, the masses of the top quarks cannot be completely reconstructed, due to the presence of multiple neutrinos in the final state. We therefore do not consider this final state in our results, but note that a more detailed analysis based on kinematical distributions as in the top-mass reconstruction methods of [1, 15] could perhaps render this channel useful.
It may be noted that no distinction between b-jets and other jets was made in the definition of signals (I) and (II). Indeed, b-tagging is not used in this analysis and that the cuts outlined below are applied to all jets, irrespective of their b-character. The reason for this is that the b-tagging efficiency at ATLAS is around 50% [1] (the efficiency at CMS is comparable), which would lead to a substantial loss in signal events. However, we shall justify this procedure below and show that the relevant reducible backgrounds can be effectively eliminated merely by demanding that t,t, h and both W -bosons, can all be appropriately reconstructed from the momenta of the final-state particles.  The effect of next-to-leading order (NLO) QCD corrections is incorporated in our analysis in the standard manner, via the introduction of a K-factor for each relevant signal or background process. NLO corrections to the tth production cross-section were calculated in Ref. [16] for m h = 120 GeV. For this choice of Higgs mass, the K-factor was found to be about 1.2 at the scale µ = (2m t + m h )/2, and was found not to vary substantially with m h over the mass range considered here. We therefore take K S , the K-factor for the signal process, to be equal to 1.2 for all 115 GeV ≤ m h ≤ 140 GeV.
The primary irreducible Standard Model background for all final states resulting from tth(h → µµ) comes from similar processes in which the Higgs boson is replaced by an offshell photon γ * or a Z boson. The background was also calculated using MadGraph [13], with both the factorization and renormalization scales set to (2m t + m Z )/2. We found the tree-level cross section for ttZ/γ * (Z/γ * → µµ) to be 32.27 fb, where we require p T > 10 GeV for final-state muons to keep the results well-behaved when soft photons are taken into account. This result is also modified at next-to-leading order by a K-factor, which was calculated in Ref. [17] and found to be K BG = 1.35 at the scale µ = (2m t + m Z )/2. Reducible backgrounds such as bbW W Z, also exist, but they can be eliminated by a sensible choice of cuts. In particular, mandating the successful reconstruction of the top quarks in both the hadronic channel and the semileptonic channel will render such backgrounds negligible. Therefore, in our analysis below, we only consider the irreducible background coming from ttZ/γ * .
We impose two sets of cuts on the signal and background data for each type of signature (hadronic or semileptonic) under consideration. The first of these sets (which we will refer to as the Level I cuts) is applied universally to all processes, and is designed to reproduce a realistic detector acceptance: • p ℓ T > 20 GeV for all leptons, |η µ | < 2.4, |η e | < 2.5, • p j T > 15 GeV, |η j | < 3.0 for all jets (including b jets), Here, ∆R ab = (∆φ ab ) 2 + (∆η ab ) 2 denotes the "lego-plot" separation distance between final-state particles a and b, and p a T denotes the transverse momentum of a. Reconstruction requirements underlie the second set of cuts, the specifics of which depend on the particular final states under consideration. Since the invariant mass resolution for the muon pair will be quite good at both ATLAS [1] and CMS [2], we retain only events in which the invariant mass of some pair of muons lies within the range |M µµ − m h | < 2.5 GeV for the particular value of m h under consideration. In addition to this requirement, for the fully hadronic final state (I), which involves 6 jets + µ + µ − , we demand that some combination of jet momenta exists for which the invariant masses M 2 jaj b jc = (p ja + p jc + p jc ) 2 of two different sets of jets (j a , j b , j c ) both reconstruct a top quark. Furthermore, we require that within each such set, one combination of jet momenta M 2 jaj b = (p ja + p j b ) 2 reconstructs a W boson. Thus the full roster of Level II cuts in the fully hadronic channel comprises: • 6 jets and 2 muons passing the Level I cuts, • two groups of three jets each for which |M ja j b jc − m t | < 50 GeV, • one jet pair within each such group for which |M ja j b − M W | < 40 GeV, For the semileptonic signature (II), which involves 4 jets + µ + µ − ℓ ± + missing E T , the situation is complicated both by the presence of missing transverse momentum from the neutrino and by combinatorial issues that arise when ℓ ± is a muon. To address the former, we follow the standard procedure [1], which is to assume that a single neutrino produced by the leptonically-decaying top is responsible for the entirety of the missing momentum in the transverse plane and that M 2 W = (p ν + p ℓ ) 2 . Under this assumption, one can solve for the longitudinal component p ν z of the neutrino momentum up to a sign ambiguity. Of the two resulting solutions for p ν z , we select the one with the larger absolute value and use it to reconstruct a mass for the leptonically-decaying top. For final states involving at least one electron, we then require that there exist one jet and one electron which, in this manner, reconstruct m t to within 50 GeV. For final states that contain at least three muons, we accept any event for which there exists some combination of muons which reconstructs both m h and m t successfully according to the method outlined above, provided that the muons used to reconstruct the Higgs mass have opposite sign. However since combinatorial issues of this sort can have a pronounced effect when the primary background is associated with the tail of a kinematical distribution, far away from the Zpole, we apply a more stringent constraint in this case and require that m t be reconstructed within 10 GeV. To reconstruct the remaining top quark, we use the same method employed in the fully-hadronic case: we require that there exist one combination of three other jets whose invariant mass reconstructs m t within 50 GeV, two of which reconstruct M W within 40 GeV.
To recapitulate, then, the Level II cuts for the semileptonic case are: • 4 jets and 3 charged leptons (at least two of which are muons) passing the Level I cuts, • a groups of three jets each for which |M ja j b jc − m t | < 50 GeV, • one jet pair within this group for which |M ja j b − M W | < 40 GeV, • 2 opposite-sign muons for which |M µµ − m h | < 2.5 GeV, • one additional electron and one additional jet for which |M jeν − m t | < 50 GeV, or one additional muon and one additional jet for which |M j µν − m t | < 10 GeV, where the neutrino four-momentum is reconstructed in the manner discussed above. Note that the process in which the charged lepton from the leptonically-decaying top is a muon and the process in which it is an electron represent two distinct channels with different backgrounds, detection efficiencies, etc. These results pertaining to these channels will thus be reported separately.

III. RESULTS
The results of our analysis of tth(h → µµ) in the hadronic and semileptonic channels are displayed in Tables II and III, respectively. The respective efficiencies ǫ S and ǫ B of the cuts discussed above in reducing the number of signal and background events in each case are shown, along with cross-sections for the corresponding processes which include the effect of these efficiencies. Note that here we have defined ǫ S and ǫ B for each channel to include the branching fraction of tt to the corresponding final state. In addition, signal-to-background ratios S/B and statistical significances (S/ √ S + B) are also displayed. Signal and background events for each process were generated using the MadEvent package [13] and processed using PYTHIA [18]. The generated events were then passed through PGS4 [19] for detector simulation. A total of 40, 000 events were simulated for the signal process; for the background process, on which the effect of the cuts is more severe, ten times that number were simulated in order to limit the effect of statistical fluctuations.     Table II. The combined statistical significance S/ √ S + B in the semileptonic channel from both contributions for L = 300 fb −1 is also supplied.
The hadronic channel gives the best statistical significance for tth(h → µµ). We find that evidence for a light (m h = 115 GeV) SM Higgs boson may be obtained at the 2.23σ significance level with 300 fb −1 of integrated luminosity at both ATLAS and CMS. The statistical significance of this channel decreases with increasing Higgs mass, primarily due to the decrease both in the tth production cross-section and in the branching ratio of Higgs decay to muons. This notwithstanding, for all 115 GeV < m h < 140 GeV, the signal crosssection for this process is large enough that a reasonable number of signal events can be expected at such luminosities.
By contrast, the semileptonic channels are slightly less promising, primarily because the efficiency factor ǫ S is significantly smaller than in the fully-hadronic channel. Furthermore, a much larger fraction of background events survive the cuts in the channel in which the charged lepton produced by the leptonically-decaying top is a muon than in the channel   [8] and weak-boson fusion [9] processes in which the Higgs boson decays to µ + µ − . The significance values quoted here correspond to L = 300 fb −1 for both ATLAS and CMS.
where it is an electron. Taking into account the contributions from both of these final states, we find that with 300 fb −1 of integrated luminosity at both ATLAS and CMS, semileptonic tth events can provide evidence at the 1.13σ significance level for a light (m h = 115 GeV) Higgs boson. Since the signal cross-sections are relatively small for both contributing channels, however, with σ S of O(ab) after all cuts have been applied, only a small number of surviving events will be produced at such luminosities -at least for a standard model Higgs boson. Table IV presented the tth results combining all three channels. We also list the results for gg → h → µµ [8] and qq ′ → qq ′ h(h → µµ) [9] for comparison. For a SM Higgs mass around 120 GeV, the statistical significance in the tth(h → µµ) channel is similar to or even higher than that in the other two channels. With L = 300 fb −1 , we observe that a statistical significance of 4.19σ may be obtained via the combined channels. This represents a substantial increase over the 3.37σ obtained from considering the gluon-fusion and WBF processes alone. In Table V, we presented the integrated luminosity at the LHC that is needed for a 3σ and 5σ discovery with tth(h → µµ) alone (combining both the hadronic channel and the semileptonic channels), and with all three production processes (tth, gluon fusion, WBF) included. For a Higgs boson just slightly heavier than the LEP bound of 114 GeV [20], a 3σ discovery can be obtained with around 150 fb −1 of integrated luminosity.
We have shown that the tth(h → µµ) channel can provide 2.5σ evidence for a light, SM Higgs boson around 115 GeV. In non-Standard Model Higgs scenarios, however, the branching ratio for h → µ + µ − and/or tth production cross section might potentially be enhanced, rendering this channel even more significant for Higgs-boson detection. Depending on the enhancement factor, a 5σ discovery might even possible -and at a reasonably low integrated luminosity. In order to quantify these effects, we define an overall enhancement factor κ, which represents the net effect of all modifications to BR(h → µµ) and the tth production cross-section in a given extension of the SM Higgs sector: (1) Figure. 1 shows the enhancement factor κ as a function of Higgs mass for a 3σ or 5σ 1 )  115  432  1200  154  427  120  511  1419  157  436  130  859  2386  204  566  140 2014 5594 420 1166  (1) -necessary to obtain evidence for a light, non-standard CP-even Higgs boson at the 3σ or 5σ level at LHC with L = 100 fb −1 , given as a function of the Higgs boson mass m h . The dotted line corresponds to a 3σ effect, whereas the solid line corresponds to a 5σ effect. discovery at the LHC with 100 fb −1 of integrated luminosity. For values of m h in the range 115 ≤ m h < ∼ 130 GeV, an enhancement factor of κ > ∼ 3 − 5 (depending on m h ) is sufficient to result in a 3σ excess, while κ > ∼ 7 − 12 will result in a 5σ excess in the combined tth(h → µµ) channels and the clear discovery of a beyond-the-Standard-Model Higgs boson. IV.

CONCLUSIONS
In this letter, we have investigated the observability of a light, CP-even Higgs boson at the LHC in the channel tth(h → µµ). We have shown that for a light SM Higgs boson with a mass around 120 GeV, evidence for a Standard Model Higgs can be obtained in this channel at roughly the same significance level as in the gg → h → µµ and qq ′ → qq ′ h(h → µµ) channels, and with comparable Higgs-mass resolution. The best statistical significance is obtained in the fully hadronic mode. Moreover, we have shown that for m h between 115 GeV and 130 GeV, the combined results from the gluon-fusion, weak-boson fusion, and tth channels, with h decaying to µ + µ − , can provide evidence for a SM Higgs boson at about 3σ or better with 300 fb −1 of integrated luminosity. In beyond-the-Standard-Model scenarios in which the tth production cross-section and/or the branching fraction BR(h → µµ) are enhanced relative to their SM values, this channel could become extremely important for the detection and analysis of a light Higgs boson, providing an accurate measurement of the Higgs mass, and a precise determination of the muon Yukawa coupling.

V. ACKNOWLEDGMENTS
We wish to thank A. Belyaev, T. Han, B. McElrath, and M. Schmitt for correspondence and discussion. We also wish to thank the Institute for Nuclear Theory at the University of Washington for its hospitality and the Department of Energy for partial support during the completion of this work. This work was supported in part by the Department of Energy under Grant DE-FG02-04ER-41298.