Exploring the anomalous top–Higgs FCNC couplings at the electron proton colliders
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Abstract
We perform an updated analysis on the searches for the anomalous FCNC Yukawa interactions between the top quark, the Higgs boson, and either an up or charm quark \({{tqh,\ q=u,\ c}}\)). We probe the observability of the FCNC top–Higgs couplings through the processes \({e^ p\rightarrow \nu _{\mathrm{e}} }\bar{{t}} \rightarrow \nu _{\mathrm{e}} h \bar{{q}}\) signal I) and \(e^ p \rightarrow \nu _{\mathrm{e}} h b\) signal II) at the proposed electron proton ep colliders, where the Higgs boson decays to a \({b}\bar{{b}}\) pair. We find that at the highluminosity (\(1\;{ab}^{1}\)) ep colliders where the electrons have a polarization of \(80\%\) and electron energy is typical 60 GeV, the 2\(\sigma \) upper limits on \({ Br t\rightarrow uh)}\) are \(0.15\times 10^{2}\) \(2.9\times 10^{4}\)) at the 7TeV@LHeC 50TeV@FCCeh) for signal I and \(0.15\times 10^{2}\) \(2.2\times 10^{4}\)) for signal II. We also give an estimate on how the sensitivity (taking signal I as example) would change when we reduce the electron beam energy from 60 to 50 GeV or even 40 GeV due to the cost. The conclusion is that the discovery potential is reduced \(8.7\%\) (\(29.4\%\)) if the electron beam changes from 60 to 50 (40) GeV at the 7 TeV LHeC, and \(16.8\%\) (\(19.8\%\)) at the 50 TeV FCCeh.
1 Introduction
The discovery of the Higgs boson at the Large Hadron Collider LHC) [1, 2] was a major step towards understanding the electroweak symmetry breaking (EWSB) mechanism and marks a new era in particle physics. The precise measurement of the Higgs boson and the top quark properties would provide the possibility of searching for the anomalous flavor changing neutral current (FCNC) Yukawa interactions between them and either an up or charm quark (\({ tqh,\ q=u,\ c}\)). According to the Standard Model (SM), FCNC processes are forbidden at tree level and very much suppressed at higher orders due to the Glashow–Iliopoulos–Maiani (GIM) mechanism [3]. For instance, the \({t\rightarrow qh\ (q=u,c)}\) branching ratio is of the order of \(\sim 10^{10}\) or even below. In models beyond the SM (BSM), the GIM suppression can be relaxed, yielding effective tqh couplings many orders of magnitude larger than those of the SM and therefore being detectable using current experimental data. Observations of such anomalous top–Higgs couplings would provide a clear signal of new physics. Examples of such model extensions [4] are, for instance, the Minimal Supersymmetric Model (MSSM) with/without Rparity violation [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], the two Higgs Doublet Model (2HDM) [20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], the warped extra dimensions model [34, 35], the Alternative Left–Right symmetric Model (ALRM)[36, 37], the Little Higgs with T parity Model (LHT) [38], the Quark Singlet model (QS) [39, 40, 41].
Searches for the anomalous FCNC top–Higgs couplings have been performed at the LHC, and the direct limits on the branching ratio are set from the collider experiments. The most stringent constraint through direct measurements was reported by the CMS and ATLAS collaborations. They have set upper limits on the FCNC couplings in the top sector through the top pair production, with one top decaying to wb and the other assumed to decay to hq. The w boson is considered decaying leptonically and the Higgs decaying either to two photons [42, 43, 44, 45] or to \({b}\bar{{b}}\) [46, 47]. Combining the analysis of the different Higgs decay channels, corresponding to 20.3 (19.7) \(\mathrm{fb}^{1}\) data at the centerofmass energy of 8 TeV for ATLAS (CMS), the 95\(\%\) confidence level (C.L.) upper limits have been found to be \({ Br t\rightarrow u) \le 4.5 5.5)\times 10^{3}}\) [42] and \({ Br t\rightarrow ch) \le 4.6 4.0)\times 10^{3}}\) [48]. In addition to the direct collider measurements, indirect constraints on the anomalous tqh vertex can be obtained from the lowenergy measurements in flavor mixing processes, like, for example, the neutral meson oscillations (\({K^0}\)–\(\bar{{K}}^0\), \({B^0}\)–\(\bar{{B}}^0\) and \({D^0}\)–\(\bar{{D}}^0\)) [49, 50, 51]. Typically, at oneloop level, the \({D^0}\)–\(\bar{{D^0}}\) mixing observable can receive sizable contributions with such an nonvanishing flavor violating tqh coupling [51]. Using data observed on \({D}^0\)–\(\bar{{D^0}}\) mixing, the upper limit of \({Br t\rightarrow qh)\le 5\times 10^{3}}\) can be obtained. The tqh coupling also affects the \({ Z\rightarrow c\bar{c}}\) decay at the loop level and is therefore constrained by the electroweak precision observables of the Z boson [52]. On the phenomenological side the sensitivity to these nonstandard flavor violating couplings in the top sector has been explored in great detail. A lot of work has been done at the LHC, through top pair production [28, 53, 54, 55, 56], single top plus Higgs production [4, 57, 58], and also single top plus W production[59]. Some have been done at the \({ e^+e^}\) colliders [60, 61, 62, 63, 64], and several at the ep colliders [65, 66]. Some other related studies include, for example, Ref. [67], which derives modelindependent constraints on the tqh couplings that arise from the bounds on hadronic electric dipole moments.
In the present paper, we perform an update study of the anomalous FCNC Yukawa interactions at the ep colliders. An earlier study was performed in Ref. [65]. There we briefly reviewed the search of this anomalous couplings at the basic parton level. A comparison between different charge current (CC) and neutral current (NC) production channels was provided. We came to the conclusion that the CC induced \({e^ p\rightarrow \nu _{\mathrm{e}}} \bar{{t}} {\rightarrow \nu _{\mathrm{e}} h} \bar{{q}}\) (signal I) production with \(\gamma \gamma \), \({b}\bar{{b}}\) pair and \(\tau ^+\tau ^\) decays are the favored candidate channels. The \({H}\rightarrow \gamma \gamma \) channel was chosen because of its demonstrated high importance for inclusive Higgs boson studies, with a rather clean signature at the normal LHC. However, for a Higgs boson mass around 125 GeV, \({ e^ p\rightarrow \nu _{\mathrm{e}} }\bar{{t}} \rightarrow \nu _{\mathrm{e}} h \bar{{q}}\) production with \( h\rightarrow \gamma \gamma \) decay at the ep collider, it suffers from its small branching ratio (0.23\(\%\)); thus it is not the one most favored. For the \({h}\rightarrow \tau ^+\tau ^\) channel, the \(\tau \) event reconstruction is not easy, thus we have not concentrated on this issue at this moment. In this paper we choose the \({ h\rightarrow b}\bar{{b}}\) mode which is more interesting than the other channels. In addition to signal I, we consider a second production \({ e^ p \rightarrow \nu _{\mathrm{e}} h b}\) (signal II). Different from signal I, the tqh couplings mainly come from the single top decays; in signal II, the couplings are induced through light quarks that are directly emitted from the protons. We present the discovery potentials from both channels and compare them with each other.
Our paper is organized as follows: Sect. 2 presents a short description of the anomalous top–Higgs FCNC couplings. Section 3 presents the analysis and numerical results in detail. The subsections include signal and background analysis, simulation and the discovery potential, etc. The discovery potentials are compared with the LHC limits and the other studies. Typically, its dependence on the electron beam energy is also presented due to the cost reason. Finally, we summarize and present our conclusion in the last section.
2 The anomalous top–Higgs FCNC couplings
3 Process analysis and numerical calculations
3.1 The signal and background analysis
3.2 The simulation
3.3 The cross sections and distributions

(I) \(\kappa _{\mathrm{tqh}}= \kappa _{\mathrm{tuh}}, \kappa _{\mathrm{tch}} =0 \),

(II) \(\kappa _{\mathrm{tqh}}= \kappa _{\mathrm{tch}}, \kappa _{\mathrm{tuh}} =0 \),

(III) \(\kappa _{\mathrm{tqh}}= \kappa _{\mathrm{tuh}} = \kappa _{\mathrm{tch}} \).
Cross sections (in units of fb) and significance depending on the cut flows for signal I \(\ e^ p \rightarrow \nu _{\mathrm{e}} \bar{t} \rightarrow \nu _{\mathrm{e}} h \bar{q} \rightarrow \nu _{\mathrm{e}} b\bar{b} \bar{q}\) (\(\kappa _{tuh}=0.1\)) and backgrounds at the 7 TeV \(\oplus \) 60 GeV @LHeC and 50 TeV \(\oplus \) 60 GeV @FCCeh. \({\mathcal {SS}}\) is evaluated with \(1\ ab^{1}\) integrated luminosity. Polarization effects and systematic uncertainty are not considered yet
7 TeV \(\oplus \) 60 GeV @LHeC unpol  \(\sigma _{\mathrm{ini}}\) Basic cuts  \(\ge \)3 jets with 2 tagged Bjets  \(M_{\mathrm{j}_1 \mathrm{j}_2 \mathrm{j}_3}\in \) [110, 180]  \(M_{\mathrm{h}}\in \) [105, 130]  HT \(\in [60, 185]\) 

signal I [\(\kappa _{\mathrm{tqh}}=0.1\)]  7.96  1.05  0.87  0.48  0.4 
bakt  1321  60.9  33.82  6.4  3.33 
bakh  92.27  15.8  3.27  1.32  0.82 
bakz  70.73  10.0  2.88  0.08  0.03 
bakjjj  21,730  14.7  6.87  0.70  0.22 
Total BG  –  101.4  46.84  8.5  4.4 
\(\mathcal {SS}[1 ab^{1}\)]  –  3.28  4.0  5.19  5.9 
50 TeV \(\oplus \) 60 GeV @FCCeh unpol  \( \sigma _{\mathrm{ini}}\) Basic cuts  \(\ge \)3 jets with 2 tagged Bjets  HT \(\in \) [60, 175]  \( M_{\mathrm{h}}\in \) [90, 125]  \( M_{\mathrm{j}_1 \mathrm{j}_2 \mathrm{j}_3}\in \) [125, 170] 

signal I [\( \kappa _{\mathrm{tqh}}=0.1\)]  64.24  18.06  11.92  7.9  6.24 
bakt  10660  1296.45  328.2  74.2  34.24 
bakh  507.9  168.36  54.15  35.3  5.58 
bakz  357  104.88  25.97  1.33  0.32 
bakjjj  90,070  203.20  41.79  1.98  1.08 
Total BG  –  1772.89  450.11  112.81  41.22 
\(\mathcal {SS}\,[ 1\ ab^{1}\)]  –  13.54  17.7  23.3  30.0 
Cross sections (in units of fb) and significance depending on the cut flows for signal II \( \ e^ p \rightarrow \nu _{\mathrm{e}} h b \rightarrow \nu _{\mathrm{e}} b\bar{b} b\) (\( \kappa _{\mathrm{tuh}}=0.1\)) and backgrounds at the 7 TeV \(\oplus \) 60 GeV @LHeC and 50 TeV \(\oplus \) 60 GeV @FCCeh. \( {\mathcal {SS}}\) is evaluated with \( 1\ ab^{1}\) integrated luminosity. Polarization effects and systematic uncertainty are not considered yet
7 TeV \(\oplus \) 60 GeV @LHeC unpol  \( \sigma _{\mathrm{ini}}\) Basic cuts  3 tagged Bjets  \(p_{{\mathrm{T}}}^{\mathrm{B}_{\mathrm{j}_3}} \in \) [200, 480]  \( M_{\mathrm{h}}\in \) [100, 140]  \( p_{\mathrm{T}}^{B_{\mathrm{j}_2}} \in \) [40, 140] 

signal II [\( \kappa _{\mathrm{tqh}}=0.1\)]  0.64  0.055  \(6.5 \times 10^{3}\)  \(5.28\times 10^{3}\)  \(3.68\times 10^{3}\) 
bakt  1320  1.806  0  0  0 
bakh  92.27  0.175  \(0.55\times 10^{3}\)  \(0.554 \times 10^{3}\)  \(0.185 \times 10^{3}\) 
bakz  70.73  0.086  \(2.12 \times 10^{3}\)  \(0.283 \times 10^{3}\)  0 
bakjjj  21,730  0.261  0  0  0 
Total BG  –  2.33  \(2.67 \times 10^{3}\)  \(0.837 \times 10^{3} \)  \(0.185 \times 10^{3}\) 
\(\mathcal {SS}[1 ab^{1}\)]  –  1.14  3.1  3.71  4.02 
50 TeV \(\oplus \) 60 GeV @FCCeh unpol  \( \sigma _{\mathrm{ini}}\) Basic cuts  3 tagged Bjets  \( p_{\mathrm{T}}^{\mathrm{B}_{\mathrm{j}_3}} \in \) [265, 455]  \( \Delta R^{\mathrm{hB}_{\mathrm{j}_3}}\) \(\in \) [2.8, 3.5]  \( M_{\mathrm{h}}\in \) [95, 120] 

signal II [\( \kappa _{\mathrm{tqh}}=0.1\)]  3.085  0.54  0.083  0.071  0.044 
bakt  10660.0  101.1  0  0  0 
bakh  507.9  8.82  0.005  0.002  0.0007 
bakz  357.0  3.9  0.035  0.010  0 
bakjjj  90,070.0  12.61  0  0  0 
Total BG  –  126.4  0.04  0.012  0.0007 
\(\mathcal {SS}\,[ 1\ ab^{1}\)]  –  1.51  10.5  13.3  16.70 
Cross sections (in units of fb) and significance depending on the cut flows for signal I \( \ e^ p \rightarrow \nu _{\mathrm{e}} \bar{t} \rightarrow \nu _{\mathrm{e}} h \bar{q} \rightarrow \nu _{\mathrm{e}} b\bar{b} \bar{q}\) (\( \kappa _{\mathrm{tuh}}=0.1\)) and backgrounds at the 7 TeV \(\oplus \) 40 GeV @LHeC and 7 TeV \(\oplus \) 50 GeV @FCCeh. \( {\mathcal {SS}}\) is evaluated with \( 1\ ab^{1}\) integrated luminosity. Polarization effects and systematic uncertainty are not considered yet
7 TeV \(\oplus \) 40 GeV @LHeC unpol  \( \sigma _{\mathrm{ini}}\) Basic cuts  \(\ge \) 3 jets with 2 tagged Bjets  \( M_{\mathrm{top}}\in \) [110, 180]  \( M_{\mathrm{h}}\in \) [100, 130]  ht \(\in \) [85, 190] 

signal I [\( \kappa _{\mathrm{tqh}}=0.1\)]  4.52  0.55  0.46  0.30  0.24 
bakt  749.7  28.0  16.8  3.95  1.92 
bakh  57.68  9.1  2.1  1.07  0.59 
bakz  45.84  6.06  1.94  0.073  0.03 
bakjjj  15,510  9.3  4.6  0.47  0.09 
Total BG  –  52.5  25.42  5.55  2.64 
\(\mathcal {SS}\,[ 1 ab^{1}\)]  –  2.4  2.9  4.0  4.52 
7 TeV \(\oplus \) 50 GeV @LHeC unpol  \( \sigma _{\mathrm{ini}}\) Basic cuts  \(\ge \) 3 jets with 2 tagged Bjets  \( M_{\mathrm{top}}\in \) [115, 180]  \( M_{\mathrm{h}}\in \) [105, 130]  ht \(\in \) [75, 180] 

signal I [\( \kappa _{\mathrm{tqh}}=0.1\)]  6.22  0.79  0.68  0.37  0.31 
bakt  1.032  43.8  25.7  4.6  2.42 
bakh  75.25  12.5  2.8  1.1  0.66 
bakz  58.54  8.1  2.5  0.06  0.026 
bakjjj  18,730  10.5  5.4  0.34  0.075 
Total BG  –  74.8  36.3  6.1  3.2 
\(\mathcal {SS}\,[ 1 ab^{1}\)]  –  2.88  3.54  4.74  5.37 
Cross sections (in units of fb) and significance depending on the cut flows for signal I \( \ e^ p \rightarrow \nu _{\mathrm{e}} \bar{t} \rightarrow \nu _{\mathrm{e}} h \bar{q} \rightarrow \nu _{\mathrm{e}} b\bar{b} \bar{q}\) (\( \kappa _{\mathrm{tuh}}=0.1\)) and backgrounds at the 50 TeV \(\oplus \) 40 GeV @FCCeh and 50 TeV \(\oplus \) 50 GeV @FCCeh. \( {\mathcal {SS}}\) is evaluated with \( 100\ fb^{1}\) integrated luminosity. Polarization effects and systematic uncertainty are not considered yet
50 TeV \(\oplus \) 40 GeV @FCCeh unpol  \( \sigma _{\mathrm{ini}}\) Basic cuts  \(\ge \)3 jets with 2 tagged Bjets  ht \(\in \) [75, 165]  \( M_{\mathrm{h}}\in \) [90, 125]  \( M_{\mathrm{top}}\in \) [120, 170] 

signal I [\( \kappa _{\mathrm{tqh}}=0.1\)]  44.57  11.9  8.2  5.41  4.56 
bakt  7393  762.9  207.8  45.9  25.0 
bakh  377.4  114.0  39.3  25.3  5.2 
bakz  267.8  71.9  19.4  0.9  0.26 
bakjjj  68,370  127.6  32.7  2.3  0.96 
Total BG  –  1076.4  299.2  74.4  31.42 
\(\mathcal {SS}[1\ ab^{1}\)]  –  11.5  15.0  19.6  25.1 
50 TeV \(\oplus \) 50 GeV @FCCeh unpol  \( \sigma _{\mathrm{ini}}\) Basic cuts  \(\ge \)3 jets with 2 tagged Bjets  ht \(\in \) [80, 185]  \( M_{\mathrm{h}}\in \) [90, 125]  \( M_{\mathrm{top}}\in [125, 170]\) 

signal [\( \kappa _{\mathrm{tqh}}=0.1\)]  54.67  15.18  10.4  6.8  6.0 
bakt  9074  1028.6  311.8  72.1  43.2 
bakh  445.5  141.9  52.0  34.3  7.43 
bakz  314.3  89.0  24.9  1.2  0.43 
bakjjj  79,610  170.5  42.2  2.2  1.1 
Total BG  –  1430.0  430.9  109.8  52.16 
\(\mathcal {SS}\,[ 1\ ab^{1}\)]  –  12.7  15.8  20.4  25.8 
3.4 The selections and discovery potential at the ep colliders
3.4.1 The comparison between the two signal channels
The optimized selections for signal II include \( p_\mathrm{T}^{\mathrm{B}_{\mathrm{j}_{ (2,3)}}}\), \( \Delta R^{\mathrm{hB}_{\mathrm{j}_{3}}}\) and mass windows of \( M_\mathrm{h}\). The cut flow dependence is shown in Table 2. Compared with signal I, signal II has one clear advantage, say, the three tagged Bjets selection can reduce the backgrounds strongly. However, its small production rate indicates its disadvantage, only 0.64 (3.085) fb at the LHeC FCCeh) after the basic sample selections. Considering \( 1\ ab^{1}\) luminosity, the significance is calculated to be 4.02 (16.7), not small, showing good potential in the measurement of the anomalous tqh couplings. Actually, soon we may find its discovery potential is already comparable to (at the LHeC) or even better than (at the FCCeh) signal I.
In Fig. 6, the upper limit on \( Br t\rightarrow uh)\) at 99.99, 99.73, 95.40, 68.27\(\%\) C.L. as a function of the integrated luminosity at the 7 (50) TeV LHeC (FCCeh) with 60 GeV electron beam are plotted. The dashed blue, solid black, dotted violet and dashdotted red curves present 1\(\sigma \), 2\(\sigma \), 3\(\sigma \) and 5\(\sigma \) significance, respectively. The first two figures are for signal I and the second two are for signal II. Our conclusion is that, for signal I, at the high luminosity (up to 1\( ab^{1}\)) ep colliders where the electrons have a polarization of \(80\%\) and the electron energy is typical 60 GeV, the 1\(\sigma \), 2\(\sigma \), 3\(\sigma \) and 5\(\sigma \) upper limits on \( Br t\rightarrow uh)\) are \(0.075\times 10^{2}\) (\(0.14\times 10^{3}\)), \(0.15\times 10^{2}\) (\(0.29\times 10^{3}\)), \(0.22\times 10^{2}\) (\(0.43\times 10^{3}\)) and \(0.38\times 10^{2}\) (\(0.72\times 10^{3}\)) at the LHeC (FCCeh). For signal II, the boundaries become \(0.064\times 10^{2}\) (\(0.097\times 10^{3}\)), \(0.15\times 10^{2}\) (\(0.22\times 10^{3}\)), \(0.26\times 10^{2}\) (\(0.35\times 10^{3}\)) and \(0.53\times 10^{2}\) (\(0.68\times 10^{3}\)) at the LHeC (FCCeh), respectively. We can see that signal II can even have better potential than signal I at the FCCeh due to its clean environment. Notice here we use \(5\%\) systematic uncertainty for background yields only at both ep colliders.
3.4.2 The comparison with the other limits
Here we compare our discovery potential with the other studies. Some references present limit on \( Br(t\rightarrow qh)\). For example, Ref. [63] probe the observability of the topHiggs FCNC couplings through the process \( e^e^+\rightarrow t(\rightarrow \ell \nu \ell b)\bar{t}(\rightarrow qh)\). It is shown that the branching ratio can be probed down to \(1.12\times 10^{3}\) at \(95\%\) C.L. at the centerofmass energy of 500 GeV with the integrated luminosity of 3000 \( fb^{1}\). This limit can be further improved when the polarizations of both lepton beams are included [64]. Reference [59], present the study through the process \(pp \rightarrow W^(\rightarrow \ell ^ \bar{\nu }\ell )h(\rightarrow \gamma \gamma )j\), and show that the branching ratios \( Br(t\rightarrow qh)\) can be probed to \(0.16\%\) at \(3\sigma \) level at 14 TeV LHC with an integrated luminosity of 3000 \( fb^{1}\). Through some other channels, this limit can actually be pushed to even lower values. As proposed in [100], at the Highluminosity(HL)LHC, the \(95\%\) CL upper limit \( Br(t\rightarrow qh)\) can be estimated up to the order of \(2\sim 5\times 10^{4}\) by a scaling with the luminosity, based on the studies in Ref. [54].
Some references present the limits on \( Br(t\rightarrow uh)\), which we can easily compare with. As shown in Ref. [56], through \( t\bar{t}\rightarrow W^{+}b + qh \rightarrow \ell ^+\nu b + \gamma \gamma q \) channel at the LHC, the branching ratios \( Br(t\rightarrow uh)\) can be respectively probed to \(0.23\%\) at \(3\sigma \) level at 14 TeV LHC with \( L=3000\ fb^{1}\). This limits can be improved in Ref. [57] where the authors apply a development version of HEPTopTagger algorithm. They found that, through multilepton searches (\( th\rightarrow \ell ^+\nu b+\ell ^+\ell ^ X\)), vector boson plus Higgs search (\( th\rightarrow \ell ^+\nu b + \tau ^+\tau ^\)) and fully hadronic search (\( th\rightarrow jjb+b\bar{b}\)), the limits are found to be \(0.22\%\), \(0.15\%\) and \(0.36\%\) by using \( 100\ fb^{1}\) of 13 TeV data.
3.4.3 The sensitivity dependence on the electron beam energy change
In the above analysis we explore the potentials at the high luminosity up to 1 \(ab^{1}\)) ep colliders where the electrons have a polarization of \(80\%\). The electron energy is typical 60 GeV, but lower energies are interesting due to the cost. Therefore, we give an estimate of how our sensitivity (taking signal I as an example) would change when we reduce the electron beam energy from 60 to 50 GeV or even 40 GeV. In Table 3 we present the results at the 40 and 50 GeV LHeC. Compared with the 60 GeV LHeC, the significance is reduced from 5.9 to 5.37 (4.52) for 50 (40) GeV.
The same comparison is done in Table 4 for the 40 and 50 GeV FCCeh. Compared with the 60 GeV FCCeh, the significance is reduced from 30.0 to 25.8 (25.1) for 50 (40) GeV FCCeh with 1 \( ab^{1}\)). A similar ratio is plotted in Fig. 8. It is found that when the energy of electron beam is reduced from 60 to 50 (40) GeV, the discovery potential is reduced about 16.8 (19.8)% correspondingly.
4 Conclusion
In this paper we present an updated analysis on searches for the anomalous flavor changing neutral current (FCNC) Yukawa interactions between the top quark, the Higgs boson, and either an up or charm quark (\( tqh, q=u, c\)). We probe the observability of the FCNC top–Higgs couplings through the process \( e^ p\rightarrow \nu _{\mathrm{e}} \bar{t} \rightarrow \nu _{\mathrm{e}} h \bar{q}\) (signal I) and \( \ e^ p \rightarrow \nu _{\mathrm{e}} h b\) (signal II) at the ep colliders where the Higgs boson decays to a \( b\bar{b}\) pair. We perform the results from the cutandcount based method. Our results show that with \(80\%\) electron polarization, 1 \( ab^{1}\) integrated luminosity, and \( 5\%\) system uncertainty from background yields only, the \(3\sigma \) limits are \(0.22\times 10^{2}\) at the 7 TeV \(\oplus \) 60 GeV @LHeC and \(3.5\times 10^{4}\) at the 50 TeV \(\oplus \) 60 GeV @FCCeh. These limits are, on one hand, better than the current limits for the experiments; on the other hand, comparable to or even better than some phenomenological studies at the other colliders. We also give an estimate of how our sensitivity (taking signal I as an example) would change when we reduce the electron beam energy from 60 to 50 GeV or even 40 GeV due to the cost. The conclusion is that the discovery potential is reduced to \(8.7\%\) (\(29.4\%\)) if the electron beam changes from 60 to 50 (40) GeV at the 7 TeV LHeC, and \(16.8\%\) (\(19.8\%\)) at the 50 TeV FCCeh. In summary, we give a detailed overview on the search potential for the anomalous top–Higgs couplings at the ep colliders including the LHeC as well as the FCCeh.
Notes
Acknowledgements
The author H. Sun would like to express gratitude for the comments and encouragements from the LHeC/FCCeh (Top and Higgs and BSM) working Group. This work is supported by the National Natural Science Foundation of China (Grant no. 11675033), by the Fundamental Research Funds for the Central Universities (Grant no. DUT15LK22 and Grant no. DUT18LK27).
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