Enhancing $thj$ Production from Top-Higgs FCNC Couplings

In this paper, we study the single top and Higgs associated production $pp \to thj$ in the presence of top-Higgs FCNC couplings($\kappa_{tqh}, q=u,c$) at the LHC. Under the current constraints, we find that the cross section of $pp \to thj$ can be sizably enhanced in comparison with the SM predictions at 8 and 14 TeV LHC. We also find that the full cross section of $pp \to thj$ with $\kappa_{tch}$ is larger than the resonant cross section of $pp \to t\bar{t} \to thj$ by a factor 1.16 at 8 TeV LHC and 1.12 at 14 TeV LHC, respectively. We further explore the observability of top-Higgs FCNC couplings through $pp \to t(\to b\ell^{+} \nu_{\ell}) h( \to \gamma\gamma) j$ and find that the branching ratios $Br(t\to qh)$, $Br(t \to uh)$ and $Br(t \to ch)$ can be respectively probed to $0.12\%,~0.23\%$ and $~0.26\%$ at $3\sigma$ sensitivity at 14 TeV LHC with ${\cal L} =3000$ fb$^{-1}$.


I. INTRODUCTION
The discovery of the Higgs boson at the LHC is a great triumph of the Standard Model(SM) and marks a new era in the particle physics [1,2]. Given the large uncertainties of the current Higgs data, there remains a plenty of room for new physics in Higgs sector [3]. So the precise measurement of the Higgs boson's properties will be a dominant task at the LHC in the next decades.
Concerning the probe of new physics through the Higgs boson, the Yukawa couplings can play the important role since they are sensitive to new flavor dynamics beyond the SM. In particular, top quark, as the heaviest SM fermion, owns the strongest Yukawa coupling and has the preference to reveal the new interactions at the electroweak scale [4]. One of the interesting things is that the top quark is just heavier than the observed Higgs boson, which makes the top quark flavor changing neutral current(FCNC) processes t → hq (q = u, c) be accessible in kinematics. In the SM, these top quark FCNC transitions are extremely suppressed by the G.I.M. mechanism [5]. But they can be greatly enhanced by the extended flavor structures in many new physics models, for example the minimal supersymmetric model (MSSM) with/without R-parity [6,7], two-Higgs-doublet model(2HDM) type-III [8,9], and the other miscellaneous models [10][11][12]. So the study of top-Higgs FCNC interactions is a common interest of the theory and experiment communities [13,14]. However, up to now, the null results of the searches for t → qh at the LHC give the strong limits on the top-Higgs FCNC couplings. Among them, the most stringent constraint Br(t → hc) < 0.56% at 95% C.L. was reported by the CMS collaboration from a combination of the multilepton channel and the diphoton plus lepton channel [15]. Except for the widely studied t → qh decays, the importance of the single top+Higgs production pp → th in probing the top-Higgs FCNC couplings has been also emphasized in the recent theoretical studies [16][17][18][19][20][21].
In this paper, we investigate the top-Higgs FCNC interactions through pp → thj with the sequent decays t → bℓ + ν and h → γγ at the LHC. In the SM, the process pp → thj can only be induced by the weak charged current interaction and has a relative small cross section, which is about 18 (88) fb at 8 (14) TeV LHC. However, such a process is found to be very sensitive to modifications of the Higgs couplings [22][23][24][25][26][27][28]. Among them, the top-Higgs FCNC couplings can sizably enhance thj cross section due to the new contributions induced by the strong interaction. Besides, unlike tt production, the process pp → thj also includes the contributions of the non-resonant FCNC productions and is affected by the initial parton distributions, which can be used to disentangle the FCNC couplings of the top quark with light quarks. So it is worthwhile to perform a complete calculation of pp → thj in the presence of the top-Higgs FCNC couplings by including the contributions of hj resonant production from tt and other non-resonant productions, and explore its sensitivity to probe the top-Higgs FCNC couplings at the LHC. This paper is arranged as follows. In Sec. II, we set up the notations and briefly describe the top-Higgs FCNC interactions. In Sec. III, we discuss the observability of the top-Higgs FCNC couplings through the process pp → thj at 14 TeV LHC. Finally, a summary is given in Sec. IV.

II. TOP-HIGGS FCNC INTERACTIONS
A general effective Lagrangian describing the top-Higgs FCNC interaction can be written where h is the SM Higgs boson, and the real parameter κ L,R tqh denote the left-handed and right-handed FCNC couplings of the Higgs boson to the light up-type quarks q = u, c. By neglecting the light quark masses and assuming the dominant top decay width t → bW , the Leading Order(LO) branching ratio of t → qh can be approximately given by, where G F is the Fermi constant, to Br(t → qh) is estimated as 10% according to the results of high order corrections to t → bW [29] and t → ch [30]. In some specific models, the left-handed coupling κ L tqh is not expected to be large because its relation with the CKM mixing parameter. Also, can be constrained by the low energy observables, such as B 0 − B 0 mixing [9,31]. However, we do not consider these indirect constraints in our study since they are model-dependent and their relevance strongly depends on the assumptions made for the generation of the quark flavor structures [32]. On the other hand, the CMS collaboration reported a model-independent bound κ L tqh 2 + κ R tqh 2 < 0.14 at 95% C.L. from the combined result of multilepton and diphoton in tt production [15], which indicates |κ L,R tqh | should be less than 0.14. In our work, we assume κ L tqh = κ R tqh = κ tqh and require κ tqh ≤ 0.1 to satisfy the direct constraint from the CMS result.

III. NUMERICAL CALCULATIONS AND DISCUSSIONS
We implement the top-Higgs FCNC interactions by using the package FeynRules [33] and calcualte the LO cross section of pp → thj with MadGraph5 [34]. We use CTEQ6L as the parton distribution function(PDF) [35] and set the renormalization scale µ R and factorization scale µ F to be µ R = µ F = (m t + m h )/2. The SM input parameters are taken as follows [36]: In Fig.1, we show the dependence of the cross sections σ thj on the top-Higgs FCNC couplings κ tqh at 8 and 14 TeV LHC respectively for three different cases: (I) κ tqh = κ tuh = κ tch , (II) κ tqh = κ tuh , κ tch = 0 and (III) κ tqh = κ tch , κ tuh = 0. From Fig.1, we can have the following observations: • Case-(I): When κ tqh = 0.1, the total cross section of pp → thj at 8 and 14 TeV LHC can be respectively enhanced up to nearly 215 and 173 times the SM predictions. For the smaller values of κ tqh , the cross section will decrease and become comparable with the SM prediction when κ tqh ∼ 0.01. Here it should be mentioned that although the CMS collaboration has performed a search for thj event at √ s = 8 TeV and given a 95% upper limit on the thj cross section σ thj < 2.24 pb, this bound is not suitable for our case because a forward jet with |η| > 1.0 is required in the experimental analysis.
We can also see that the full cross section of pp → thj is 1.23 (1.18) times larger than the one of pp → tt → thj at 8 (14) TeV LHC due to the contributions of the nonresonant productions of hj. By assuming the high order correction factor of pp → thj same as pp → tt, we can improve the current upper limit of κ tqh from 0.1 to 0.08 at 8 TeV LHC [15]. So we can expect that the full result of pp → thj production will be better to extract the constraints on top-Higgs FCNC couplings in the future experimental analysis.
• Case-(II) and (III): For the same values of κ tuh and κ tch , the cross section of pp → thj in case-(II) is much larger than that in case-(III), since the up-quarks have the larger PDF than the charm-quarks. This feature allows us to separately probe the couplings between κ tuh and κ tch at the LHC. So, in general, for a given collider energy and luminosity, we can expect the sensitivity to the coupling κ tuh will be better than κ tch .
In the following calculations, we perform the Monte Carlo simulation and explore the sensitivity of 14 TeV LHC to the top-Higgs FCNC couplings through the channel, which is characterized by two photons appearing as a narrow resonance centered around the Higgs boson mass. So the SM backgrounds to the Eq. We generate signal and backgrounds events with MadGraph5 and perform the parton shower and the fast detector simulations with PYTHIA [37] and Delphes [38]. When generating the parton level events, we assume µ R = µ F to be the default event-by-event value. We cluster the jets by setting the anti-k t algorithm with a cone radius ∆R = 0.7 [39]. The b-jet tagging efficiency(ǫ b ) is formulated as a function of the transverse momentum and rapidity of the jets [40]. The misidentification 10% and 1% for c-jets and light jets are also included and the mis-tag of QCD jets is assumed to be the default value as in Delphes. In our simulation, we generate 100k events for the signals and backgrounds respectively. In Fig.3, we present the normalized invariant mass distribution of two photons at 14 TeV LHC. Although the γγ decay channel has a small branching ratio, it has the advantage of the good resolution on the γγ resonance and is also free from the large QCD backgrounds.
From Fig.3, we can see that the spreading of the γγ invariant-mass peak at m h for the signal and the resonant backgrounds is relatively small. We will use a narrow invariant mass window |M γγ − M h | < 5 GeV to further reduce the non-resonant backgrounds. In Fig.4, we plot the normalized invariant mass distribution of the b jet and lepton at 14 TeV LHC, which is another effective cut to remove the backgrounds. From Fig.4, we can see that the invariant mass M b 1 ℓ 1 of the signal is always less than the top quark mass since the leading b jet and lepton in our signal come from the same top quark decay. The Similar distribution also occurs in the non-resonant background tjγγ. But other backgrounds can have higher invariant mass M b 1 ℓ 1 than the signal.
According to the above analysis, events are selected to satisfy the following criteria: • exact one isolated lepton with p T (ℓ 1 ) > 20 GeV and |η ℓ 1 | < 2.
• a hard jet with p T (j 1 ) > 25 GeV and |η j 1 | < 2.5 and one b-jet with p T (b 1 ) > 25 GeV and |η b 1 | < 2.5; • two photons with p γ 1 T > 50 GeV and p γ 2 T > 25 GeV and their invariant mass M γ 1 γ 2 in the range of M h ± 5 GeV; • the invariant mass of b-jet and lepton M bℓ < 200 GeV.   Table I, we give the cross sections of the signals in the case (I)−(III) and backgrounds after the cut flow at 14 TeV LHC, where κ tqh , κ tuh and κ tch are assumed to be 0.1 respectively.
From Table I, we can see that all the non-resonant backgrounds after the cuts of the two photons are reduced by half while the signals and the resonant backgrounds are hurt slightly.
Then, the invariant mass of b-jet and lepton will greatly remove the backgrounds that do not involve the top quark. Finally, the diphoton invariant mass cut will further suppress the non-resonant backgrounds by half. So at the end of the cut flow, the largest background is tjγγ, which is followed by ttγγ. In

IV. CONCLUSION
In the work, we investigated the process pp → thj induced by the top-Higgs FCNC couplings at the LHC. We found that the full cross section of pp → thj can be sizably enhanced in comparison with the SM predictions at 8 and 14 TeV LHC under the current constraints. We studied the observability of top-Higgs FCNC couplings through pp → t(→ bℓ + ν ℓ )h(→ γγ)j and found that the branching ratios Br(t → qh), Br(t → uh) and Br(t → ch) can be respectively probed to 0.19%, 0.26%, 0.29% at 3σ sensitivity at 14 TeV LHC with L = 3000 fb −1 .