Probing the top-Higgs FCNC couplings via the h → γγ channel at the HE-LHC and FCC-hh

Abstract We investigate the sensitivity of future searches for the top-Higgs Flavour Changing Neutral Current (FCNC) couplings tqh (q = u, c) at the proposed High Energy Large Hadron Collider (HE-LHC) and Future Circular Collider in hadron-hadron mode (FCC-hh). We perform a full simulation for two processes in the h → γγ decay channel: single top quark FCNC production in association with the Higgs boson (plus a jet) and top quark pair production with FCNC decays t → qh. All the relevant backgrounds are considered in a cut based analysis to obtain the limits on the Branching Ratios (BRs) of t → uh and t → ch. It is shown that, at the HE-LHC with an integrated luminosity of 15 ab and at the FCC-hh with an integrated luminosity of 30 ab, the BR(t → uh) and BR(t → ch) can be probed down to the order of 10 at the 95% Confidence Level (CL), which is two orders of magnitude better than the current 13 TeV LHC experimental results and one order of magnitude better than the existing projections for the 14 TeV High Luminosity LHC (HL-LHC) with an integrated luminosity of 3 ab.


I. INTRODUCTION
The discovery of a 125 GeV Higgs boson [1,2] at the Large Hadron Collider (LHC) 1 was a landmark in the history of particle physics and it has opened up a new area of direct searches for Beyond the Standard Model (BSM) phenomena, since the h state may well be the portal into a New Physics (NP) world. Possible signals of NP are Flavour Changing Neutral Current (FCNC) interactions between the Higgs boson, the t-quark and a uor c-quark, i.e., the vertex tqh (q = u, c). In the SM, the FCNC top quark decays t → qh (q = u, c) are forbidden at the tree level and strongly suppressed at the loop level due to the Glashow-Iliopoulos-Maiani (GIM) mechanism [3]. For instance, the predicted BR(t → qh)'s with q = u, c are expected to be of O(10 −12 − 10 −17 ) [4][5][6] at one-loop level and are therefore out of range for current and near future experimental sensitivity. However, in some NP models the BRs for the t → qh decays are predicted to be in the range of O(10 −6 − 10 −3 ) [7][8][9][10][11][12][13][14][15][16][17][18]. Thus, any observation of such FCNC processes would be a clear signal of BSM dynamics.
A more promising result was put forward by the ATLAS Collaboration [44,45], which has predicted the sensitivities BR(t → uh) < 2.4 × 10 −4 and BR(t → ch) < 1.5 × 10 −4 at 95% CL at the High Luminosity LHC (HL-LHC). One can expect to improve further these limits at higher c.m. energies [46]. The future High Energy LHC (HE-LHC) with 27 TeV c.m. 1 Henceforth, it will be denoted by the symbol h.  [49][50][51][52]. So it is rather appropriate to assess their scope in accessing tqh vertices too, the main reason being the common prejudice in the particle physics community that BSM phenomena are likely to manifest themselves in the interactions between the two heaviest states of the SM, indeed t and h, which are in fact intimately related to the hierarchy problem of the SM, the main puzzle that Nature has forced upon us.
In our present paper, we perform an updated study of top-Higgs FCNC interactions at the HE-LHC and FCC-hh, by considering both single top quark production in association with the Higgs boson (plus a jet) and top quark pair production followed by a Higgs decay of one (anti)top state. A previous study done in Ref. [53] has investigated the top-Higgs FCNC interactions through pp → thj with the subsequent decays t → bℓ + ν and h → γγ at the HL-LHC.
Here, we intend to revisit that analysis in the context of the aforementioned higher energy and luminosity hadron machines.
Furthermore, past literature also included the study of single top and Higgs boson associated production via the process pp → th, affording one with an improved sensitivity to especially the tuh coupling (and somewhat less so to the tch one) [54]. Specifically, the authors of Ref. [55] investigated the top-Higgs FCNC interactions through the pp → t(→ bℓ + ν)h(→ γγ) process at the HL-LHC. However, one realises that the final numbers of events for these signals at the 14 TeV LHC are too small against the overwhelming SM background rate, even considering the high luminosity option of 3 ab −1 , also because the signals suffer from a small BR (0.23%) for the h → γγ channel. Yet, this is possibly the cleanest probe of the SM-like Higgs boson, so it ought to be nonetheless explored. In contrast, at both the HE-LHC and FCC-hh, the same production cross sections for signal (and SM background) can be enhanced significantly due to the higher energies available therein, so that one can find it a more favourable environment than the 13 and 14 TeV LHC to study the top-Higgs FCNC couplings via the h → γγ decay channel, at the same time benefiting a larger luminosity.
This paper is arranged as follows. In Sec. II, we give a brief introduction to the top-Higgs Although the anomalous FCNC couplings between the top quark and Higgs boson may arise from different sources, an effective field theory approach can describe the effects of NP beyond the SM in a model-independent way [5]. The most general Lagrangian for the top-Higgs FCNC interactions is written as where κ tuH and κ tcH represent the strength of top-Higgs FCNC interactions. In this study we take them as real and symmetric, i.e., κ tqH = κ † tqH = κ qtH = κ † qtH (q = u, c), since we here do not intend to consider CP-violating effects.
The decay width of the dominant top quark decay mode t → W b could be found in Ref. [56].
Neglecting the light quark masses and assuming the dominant top decay width t → W b, the Next-to-Leading Order (NLO) BR(t → qh) is given by [57,58] with the Fermi constant G F and Here the factor λ QCD is the NLO QCD correction to BR(t → qh) and equals about 1.1 [59][60][61]. In our work, we require κ tqh ≤ 0.04 to satisfy the direct constraint from the ATLAS result mentioned in the previous section.

B. Production processes
At the LHC, the cross section for pp → thj involving top-Higgs FCNC couplings would be coming from two subprocesses: (i) top pair production followed by one FCNC top decay, pp → tt → thj, shown in Fig. 1(a-b) (henceforth referred to as 'top FCNC decay'); (ii) single top-Higgs associated production in presence of a jet, pp → thj, as shown in Fig. 1(c-f), which includes a gg (henceforth referred to as 'tH associated production') and a qg (henceforth referred to as 'qg fusion') induced subchannels, respectively yielding a(n) (anti)quark or gluon in the final state. The contribution of other subprocesses, such as qq fusion channels, is smaller than the above ones due to the suppression from colour factors and Parton Distribution Functions (PDFs) and thus is not shown in the Feynman diagrams, but all the contributions are included in our calculations. Obviously, the conjugated processes can also occur at tree level and are accounted for.
For the simulations of the HE-LHC and FCC-hh dynamics, we first use the FeynRules package [62] to extract the Feynman rules from the effective Lagrangian and to generate the Universal FeynRules Output (UFO) files and calculate the LO cross sections of pp → thj by using MadGraph5-aMC@NLO [63] with NNPDF23L01 PDFs [64], considering the renormalisation and factorisation scales to be µ R = µ F = µ 0 /2 = (m t + m h )/2. In our numerical calculations, the SM input parameters are taken as [65]: In Fig. 2, we show the dependence of the cross sections for the three thj subprocesses on the top-Higgs FCNC coupling parameter at the HE-LHC and FCC-hh for two scenarios, as follows: Case I is for κ tqh = κ tuh , κ tch = 0 whereas Case II is for κ tqh = κ tch , κ tuh = 0. From Fig. 2 one can see that, for a given coupling parameter κ tqh , the production cross sections can be very significant at the higher c.m. energies of these two future machine. Besides, we also have the following observations. Thus, for a given collider energy and luminosity, we can expect the sensitivity to the coupling κ tuh to be better than that to the κ tch one.

III. DISCOVERY POTENTIAL
A. The signal-to-background analysis In this section, we present the numerical calculations at the HE-LHC and FCC-hh of the where ℓ = e, µ and j represents (a(n) (anti)quark or gluon) jet, interfaced to the subsequent parton shower by using the MLM matching scheme [66,67]. The final state of signal process is thus characterised by two photons appearing as a narrow resonance centered around the SMlike Higgs boson mass. The main SM backgrounds that include both a Higgs boson decaying into di-photons in association with other particles and non-resonant production of γγ pairs are accounted for here: • pp → tth, • pp → thj, • pp → W ± jjh, • pp → ttγγ, • pp → tjγγ, The parton level events for the signal and the SM backgrounds are interfaced to parton shower, fragmentation and hadronisation by using PYTHIA8.20 [68]. Then, we have passed all generated events through Delphes3.4.2 [69] for detector simulation. Finally, event analysis is performed by using MadAnalysis5 [70]. As far as jet reconstruction is concerned, the anti-k t algorithm [71] with a jet radius of 0.4 is used. For the HE-LHC and FCC-hh analysis, we have used the default HL-LHC and FCC-hh detector card configuration implemented into the aforementioned detector emulator.
The cross sections of the signal and dominant backgrounds at LO are adjusted to NLO QCD through K-factors, i.e., K = 1.4 for the pp → tt → thj process [72], K = 1.5 for the tH associated production process [37,38] and K = 1.3 for the pp → tth process [72][73][74]. For the sake of simplicity, we have rescaled the other SM background processes by a K-factor of 1.5.
This approximation does not have a significant impact on our derived sensitivities and can be fully addressed in a future analysis.
In order to identify objects, we impose the following basic cuts to select the events [46,75]: where ∆R is the angular distance between any two objects.
In order to choose appropriate kinematic cuts, in Fig. 3  • Cut 2: At least two photons with p γ 1 T > 60 GeV, p γ 2 T > 30 GeV and 0.4 < ∆R γγ < 3.0, since the two photons in the signal and resonant SM backgrounds come from the Higgs boson they have a harder p T spectrum than those in the non-resonant SM backgrounds.
• Cut 3: The invariant mass of the di-photon system, M γγ , is peaked in both the signals and resonant backgrounds, thus we require M γγ to be in the range |M γγ − m h | < 5 GeV.    Tab. II and Tab. III at the HE-LHC and FCC-hh, respectively. One can see that, at the end of the cut flow, the largest SM background is the pp → tth process, which is 0.017 fb and 0.24 fb at HE-LHC and FCC-hh, respectively. Besides, the tjγγ and γγW ± jj processes can also generate significant contributions for the SM background due to the large production cross sections.  To estimate the exclusion significance, Z excl , we use the following expression [76][77][78]: with x = (s + b) 2 − 4δ 2 sb 2 /(1 + δ 2 b). Here, the values of s and b were obtained by multiplying the total signal and SM background cross sections, respectively, by the integrated lumi-nosity. Furthermore, δ is the percentage systematic error on the SM background estimate. In the limit of δ → 0, this expression can be simplified as In this work we choose two cases: no systematics (δ = 0) and a systematic uncertainty of δ = 10% for both the HE-LHC and FCC-hh. We define the regions with Z excl ≤ 1.645 as those that can be excluded at 95% CL (p = 0.05). The limits on the FCNC coupling parameter κ tqh can be directly translated in terms of constraints on BR(t → qh) by using eq. (2).  channel. For the HE-LHC and FCC-hh, the 95% CL upper limits on BR(t → ch) was found to be at the order of 10 −4 with an integrated luminosity of 3 ab −1 and such limits would be increased by an higher integrated luminosity. Finally, at the FCC-hh with an integrated luminosity of 10 ab −1 , Ref. [81] has investigated the t → ch decay and the its BR can be constrained to O(10 −5 ) either with or without considering c-jet tagging.

IV. SUMMARY
In this work, we have analysed the process pp → thj at the HE-LHC and FCC-hh by in the case the SM background is known with negligible uncertainty. When a more realistic 10% systematic uncertainty is considered, the sensitivity decreases to 5.72 (7.96) × 10 −5 at the HE-LHC and 6.62 (8.11) × 10 −5 at the FCC-hh, again, in correspondence to q = u (c). These limits are two orders of magnitude better than the current experimental results obtained from LHC runs at 13 TeV and one order of magnitude better than the existing projections for the HL-LHC at 14 TeV. Therefore, the numerical results presented here for the future HE-LHC and FCC-hh represent good reasons for pursuing further the study of their potential in extracting FCNC effects from NP manifesting themselves in top-Higgs interactions.