# Probing the Anomalous FCNCtqγ Couplings at Large Hadron Electron Collider

Authors: I. Turk Cakir; A. Yilmaz; H. Denizli; A. Senol; H. Karadeniz; O. Cakir
Journal: Advances in High Energy Physics
 (2017)

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## Abstract

We investigate the anomalous flavour changing neutral current (FCNC) interactions of top quark through the processe-p→e-W±q+X. We calculate the signal and background cross sections in electron-proton collisions at Large Hadron electron Collider (LHeC) with a 7 TeV proton beam from the LHC and a new 60 GeV electron beam from energy recovery linac (ERL). We study the relevant background processes including one electron and three jets in the final state. The distributions of the invariant mass of two jets and an additional jet tagged as b-jet are used to account for signal and background events after the analysis cuts. We find upper bounds on anomalous FCNC couplings λ of the order of 10-2 at LHeC for a luminosity projection of 500 fb-1 together with the fast simulation of detector effects. As a matter of interest, we analyze the sensitivity to the couplings (λu, λc) and find an enhanced sensitivity to λc at the LHeC when compared to the results from the HERA.


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## Body

## 1. Introduction

The top quark is the most massive of all observed elementary particles. The top quark interacts with the other quarks of Standard Model (SM) via gauge and Yukawa couplings. It interacts primarily by the strong interaction, but can only decay through the weak interaction. The top quark decays to aW boson and either a bottom quark (most frequently), a strange quark, or a down quark (rarely). It is also a unique probe to search for the dynamics of electroweak symmetry breaking. Being the heaviest quark, effects of new physics on its couplings are expected to be larger than that for other fermions; hence it is expected that possible deviations with respect to predictions of the SM might be found with precise measurements of its couplings. It is known that the flavour changing neutral current (FCNC) transitions are absent at tree level and highly suppressed at loop level due to the Glashow-Iliopoulos-Maiani (GIM) mechanism [1]. The branching ratios for the top quark FCNC decays through the process t→qγ are of the order 10-14-10-12 in the SM [2]. However, various scenarios beyond the standard model (BSM), such as two Higgs doublet model, supersymmetry, and technicolor, predict much larger rates at the order of 10-6-10-5 [3, 4]. Therefore, an observation of the large FCNC induced couplings would indicate the existence of the BSM.The experimental limits on the branching ratios of the rare top quark decays were established by the experiments at Tevatron and LHC. The CDF experiment set upper bound on branching ratio for top quark FCNC decay asBR(t→qγ)<3.2×10-2 [5]. Presently, the most powerful upper limits on top quark FCNC branching ratios from different channels are BR(t→uγ)<1.61×10-4 and BR(t→cγ)<1.82×10-3 at 95% confidence level (CL) given by the CMS experiment [6].The direct single top quark production channels through the photon emission at the LHC have been studied to probe the top quark FCNCtqγ interactions [7, 8]. Search for flavour changing neutral currents in the single top association with a photon at the LHC has been studied in [9]. In the same sign top quark production at the LHC the top FCNC couplings have been studied in [10]. The top FCNC couplings at future circular hadron electron colliders have been studied in [11].The main physics goals of future high energy particle colliders are to examine the fundamental interactions within the SM and to search for possible effects of new physics beyond the SM. The electron-proton colliders are based on a ring type proton accelerator with an intersecting electron beam accelerator. Currently, a projected futureep collider, namely, Large Hadron electron Collider (LHeC), has been discussed [12–14]. It comprises a 60 GeV electron beam that will collide with the 7 TeV proton beam, having an integrated luminosity of Lint=100fb-1 per year, and it is planned to collect 1 ab-1 over the years. Recently, the new physics capability and potential of ep colliders through di-Higgs boson production have been studied in [15].When we study anomalous top quark FCNC interactions at the future colliders, we take also into account bounds from measured low energy processes where the loops include top quarks. For example, the FCNC transition processesb→sγ are considered to be the valuable probe of top quark anomalous couplings [16, 17]. The bounds [18] on the top quark real FCNC couplings are lower than the current direct limit but still accessible at the high luminosity run of LHC.In this work, we study the physics potential of LHeC collider two parameters for probing top quarktqγ FCNC couplings through single top production. We focus on two parameters analysis of the signal and background including Delphes detector simulation. We discuss the sensitivity and bounds for anomalous top quark couplings (λu, λc) for different luminosity projections.


## 2. Calculation Framework

The top quark FCNC interactions would be a good test of new physics at present and future colliders. The new physics effects can be described by a set of higher order effective operators in a model independent framework. The anomalous FCNC interactions of top quark with up-type quarks (u, c) and a photon can be described in a model independent effective Lagrangian(1)Leff=ge2mtt-σμνλuLPL+λuRPRuAμν+ge2mtt-σμνλcLPL+λcRPRcAμν+h.c.,where ge is the electromagnetic coupling constant, λqL(R) are the strength of anomalous FCNC couplings and the values of these vanish at the lowest order in the SM, and PL(R) denotes the left (right) handed projection operators. The photon field strength tensor is Aμν and anomalous term is related to σμν=i/2[γμ,γν]. The effective Lagrangian is used to calculate both production cross section and the decay widths for the t→qγ channels. At the ep colliders anomalous single top quark production can be achieved through the scattering of incoming electron beam with the quark current of the proton via the production channel (t-channel) as shown in diagrams, Figure 1. For the event generation and cross section calculations, we have used event generator MadGraph5_aMC@NLO [19] with built in parton distribution function NNPDF23 [20]. The effective interactions described by (1) have been implemented through FeynRules [21] and the model file is used within MadGraph5_aMC@NLO. This event generator provides the tools to perform the simulation of both signal and backgrounds within the same framework. In this study, an allowed range of values for the FCNC parameters λqL(R)≤0.05 is taken into account.Figure 1
Leading order diagrams for single top quark production via flavour changing neutral currents and its subsequent decay. The similar diagrams for single anti-top production can be obtained by exchangingu↔u- and c↔c- and its corresponding subsequent decay.


## 3. Cross Section for the Signal

The contributions from new interactions of the BSM physics can modify the production rate and properties of the top quark expected within the SM. The relative contribution of the left and right currents is determined byλqL and λqR as given in (1); no specific chirality is assumed for the FCNC interaction vertices (tqγ); here we use a simplified scenario with λqL=λqR=λq throughout the study. We study single top quark (or anti-top quark) production through the FCNC interactions at the LHeC. The signal cross sections for the processes e-p→e-t+X and e-p→e-t-+X are σ(t)=196.90fb and σ(t-)=40.21 fb for equal coupling scenario λ=λu=λc=0.05 at the center of mass energy sep≃1.29 TeV of the LHeC for the electron beam energy of 60 GeV and proton beam energy of 7 TeV, respectively. In order to enrich the statistics, we take into account both single top and single anti-top production processes.The signal cross sections for the processe-p→(e-t+e-t-)+X for different values of couplings λu and λc at the LHeC are given in Table 1. In order to estimate the sensitivity to FCNC coupling parameters in the range, we plot contours corresponding to different values of signal cross sections as shown in Figure 2. A realistic and detailed analysis of the signal and background for one electron, two jets, and one b-tagged jet in the final state is given in the following section including a fast detector simulation.Table 1
The signal cross section values (in pb) for processe-p→(e-t+e-t-)+X at LHeC.
LHeC
λ
c
=
1
0
-
2
λ
c
=
1
0
-
3
λ
c
=
0
λ
u
=
1
0
-
2
9.468
×
1
0
-
3
8.368
×
1
0
-
3
8.357
×
1
0
-
3
λ
u
=
1
0
-
3
1.188
×
1
0
-
3
9.460
×
1
0
-
5
8.365
×
1
0
-
5
λ
u
=
0
1.103
×
1
0
-
3
1.104
×
1
0
-
5
0Figure 2
Contour plot for plane of FCNC couplingsλu and λc depending on signal cross sections at LHeC.


## 4. Analysis

In this section, we study the sensitivity to anomalous top FCNC couplings through the signal and background processe-p→e-W±q+X at LHeC. This process includes the off-shell single top quark production and interfering background with the signal. We calculate the cross section for this process to normalize the distributions from the signal and background events. The cross section values depending on the FCNC couplings are shown in Table 2 with the generator level preselection cuts (ne≥1 and nj≥3). We generate signal and background (interfering with signal) events by using MadGraph5_aMC@NLO [19] with the effective Lagrangian implemented through FeynRules [21] model including the CKM matrix elements. Parton showering and fast detector simulations are subsequently performed with Pythia 6 [22] and Delphes 3 [23], respectively. For the analysis of signal and background events, following the generator based preselection cuts, we also apply selection cuts as shown in Table 3.Table 2
The cross section (in pb) for the processe-p→e-W±q+X depending on the FCNC couplings λu and λc. The values correspond to the case that only one of the couplings is allowed to change at a time.
λ
u or λc→
0.05
0.03
0.02
0.01
0
λ
c
=
0
2.493
2.368
2.329
2.307
2.298
λ
u
=
0
2.324
2.308
2.303
2.299
2.298
λ
u
=
λ
c
2.519
2.378
2.333
2.307
2.298Table 3
The preselection and a set of cuts for the analysis of signal and background events at LHeC.
Cut-0
Preselection:ne≥1 and njets≥3
Cut-1
b-tag: one b-tagged jet (jb)
Cut-2
Transverse momentum:pT(j2,j3)>30 GeV and pT(jb)>40 GeV and pT(e)>20 GeV
Cut-3
Pseudo-rapidity:-4<η(jb,j2,j3)<0 and |η(e)|<2.5
Cut-4
W boson mass: 50<Minvrec(j2,j3)<100 GeV
Cut-5
Top quark mass:130<Minvrec(jb+j2+j3)<190 GeVConcerning our processe-p→e-W±q+X, with the hadronic decay mode of the W boson we will have at least three jets and one electron in the final state. We take into account eWq (B1) and eZq (B2) backgrounds which have the same final state after W and Z decays hadronically, as that of the signal process. Here, multijet QCD backgrounds are not included in the analysis. The transverse momentum and pseudo-rapidity distributions of the leading jet and second and third jets are presented in Figure 3 for the signal and interfering background together, and in Figure 4 only the backgrounds B1 and B2. The distribution has similar shape for signal and considers backgrounds. In order to select signal events, each event is required to have one electron, two jets, and one b-jet with the highest pT. The number of selected objects in the signal events can help to suppress the background events effectively. The kinematical distributions (pT(e) and η(e)) for the electron in the event are shown in Figure 5 for S + B1 and in Figure 6 for only B1 and B2. One of the specific signatures of the signal is the presence of an electron with high transverse momentum (pT(e)>20 GeV) and central pseudo-rapidity (|η(e)|<2.5). The leading jet with pT(j)>40 GeV and other two jets with pT(j)>30 GeV are considered in our analysis, as the cuts flow shown in Table 3. Since the LHeC has an energy asymmetry, the jets from the process mainly peaked in the backward region according to the ep collisions; therefore the pseudo-rapidity range for jets is taken to be -4<η(j)<0 for the analysis.Figure 3
Transverse momentum and pseudo-rapidity distributions of three jets from the processe-p→e-W±q+X which includes both the interfering background and signal for λu=λc=0.05 at the LHeC.Figure 4
Transverse momentum and pseudo-rapidity distributions of three jets from the processe-p→e-W±q+X for background (B1) (a) and the process e-p→e-Zq+X for background (B2) (b) at the LHeC.
(a)
(b)Figure 5
Transverse momentum and pseudo-rapidity distribution of electron from the processe-p→e-W±q+X which includes both the background and signal for λu=λc=0.05 at the LHeC.Figure 6
Transverse momentum and pseudo-rapidity distribution of electron from the processe-p→e-W±q+X for background (B1) (a) and the process e-p→e-Zq+X for background (B2) (b) at the LHeC.
(a)
(b)In the fast simulation, the detector card includesb-tagging efficiency to be 70%, with mistagging efficiencies for c-jets and light jets of 10% and 0.3%, respectively, in the considered (pT, η) range of the jets. These are consistent with the typical values used by the LHC experiments [24]. The top quark mass is reconstructed from three jets (with one b-tagged jet) after selection cuts. At each cut step we calculate the cut efficiencies as shown in Figure 7 for different FCNC coupling parameter. This figure shows that the cut efficiency changes from 6% to 1% for interfering backgrounds eWq (B1) and eZq (B2) with cut steps from Cut-1 to Cut-5 when the FCNC coupling (λ) is set to zero. For the signal the cut efficiency depends on the value of the couplings, for example, it decreases from 10% to 2.5% for the couplings λu=λc=0.05.Figure 7
Efficiency plot for the cuts applied at each step for the analysis of signal (S) + background (B1) and background (B2) events. The cut efficiencies are calculated with respect to the preselection cuts for each coupling value.The number of events for signal and backgrounds after Cut-5 at LHeC with an integrated luminosity ofLint=100 fb-1 are given in Table 4. The respective number of events after each cut can be obtained from Table 4 with a relative factor.Table 4
The number of events for backgroundB1 (B2) and signal with FCNC couplings λu and λc at LHeC with Lint=100 fb-1.
λ
c
=
0
λ
c
=
0.01
λ
c
=
0.03
λ
c
=
0.05
λ
u
=
0
584 (149)
592
609
640
λ
u
=
0.01
617
621
692
763
λ
u
=
0.03
943
969
1003
1209
λ
u
=
0.05
1502
1744
1758
1792We plot the invariant mass of top quark (reconstructed from three jets, one isb-tagged) as shown in Figure 8. The Cut-4 for W boson mass window reduces e-Zq background (B2) effectively, while keeping the signal less affected. The invariant mass (Mjjj) distribution after Cut-4 and ratio (S + B1 + B2)/(B1 + B2) plot for equal coupling scenario (λu=λc=0.05) are presented in Figure 8, where the main contribution comes from the B1 background.Figure 8
Invariant mass distributions of three jets (one of the jets is required asb-jet) for the signal + background (S + B1 + B2) and backgrounds (B1, B2). The ratio plot presents the signal (for equal coupling scenario λ=0.05) strength which peaks at the top mass.The statistical significance (SS) is calculated at the final stage of the cuts using the signal (S) and total background (B) events(2)SS=2S+Bln⁡1+SB-S.For different coupling scenario (λu≠λc), we calculate the significance and search for the sensitivity to the FCNC couplings λu and λc. The SS reach for FCNC tqγ couplings is presented in Figures 9 and 10 depending on the integrated luminosity ranging from 1 fb-1 to 1 ab-1 at the LHeC. It includes the contribution from the main background on the predicted results. The signal significance corresponding to 2σ, 3σ, and 5σ lines is also shown. In Figure 11 we also present a plot showing the 3σ and 5σ contours in the λu-λc plane at LHeC for an integrated luminosity of 500 fb-1. In this study, we have calculated the cross section with the theoretical uncertainties for the PDF scale variation which is in the range ±2.5%. The LHeC collider would be clear environment and the systematics would be less than that of the LHC. For the sake of clarity, only uncertainties from statistics are taken into account, while the uncertainties from systematics are ignored in the present discussions.Figure 9
Estimated statistical significance (SS) reach of flavour changing neutral currenttuγ coupling (λu) depending on the integrated luminosity ranging from 1 fb-1 to 1 ab-1 at the LHeC. It includes the contribution from the main background (B1) on the predicted results. The signal significance corresponding to 2σ, 3σ, and 5σ lines is also shown.Figure 10
Estimated statistical significance (SS) reach of flavour changing neutral currenttcγ coupling (λc) depending on the integrated luminosity ranging from 1 fb-1 to 1 ab-1 at the LHeC. It includes the contribution from the main background (B1) on the predicted results. The signal significance corresponding to 2σ, 3σ, and 5σ lines is also shown.Figure 11
The contour plot for the couplingsλu and λc at LHeC for an integrated luminosity of 500 fb-1.In the literature, there are alternative uses of effective coupling constants appearing in the effective Lagrangian. It is also useful to express our results in terms of branching ratios which can be comparable with the results of other studies. In order to translate the bounds, we define the branching ratio as(3)BRt⟶qγ=Γt⟶qγΓt⟶q′W++Γt⟶uγ+Γt⟶cγ.Since the Vtb element of CKM matrix is much larger than Vts and Vtd, the main contribution to Γ(t→q′W+) comes from the decay t→bW for a value of about Γ(t→bW)=1.41 GeV [25]. We calculate the partial widths for the FCNC decay channels t→qγ as Γ(t→qγ)=(1/8)αeλq2mt.In this study, we find3σ significance results to reach upper limits λu=0.012 and λc=0.032 with an integrated luminosity of 500 fb-1 at LHeC. These limits on the couplings can also be translated to the upper bounds on branching ratios BR(t→uγ)<1.62×10-5 and BR(t→cγ)<1.15×10-4, respectively. Previous experimental constraints on the branching fractions of t→qγ (with q representing an up or charm quark) from the ep collider HERA are 0.29% from ZEUS [26] and 0.64% from H1 [27] at the 95% confidence level (CL). At LHeC energy region the c-quark contribution to the process becomes comparable with the u-quark contribution; hence the sensitivity to λc will be enhanced comparing to HERA results. We can also compare our results with the recent results from the CMS experiment with an integrated luminosity of 19.8 fb-1 which place an upper bound on top quark FCNC branching ratios BR(t→uγ)<1.61×10-4 and BR(t→cγ)<1.82×10-3 at 95% confidence level [6]. Our results show that an order of magnitude improvement can be achieved for the top quark FCNC branching.


## 5. Conclusion

The LHeC projected as an ep collider, especially due to its respective clean environment when compared to high energy hadron colliders and the electron beam polarization possibility, will provide important results for some certain processes. In this study, we focused on the physics potential of the LHeC promoting its complementary and competitive role. We have analyzed the processe-p→e-W±q+X with the signature including one isolated electron and one b-jet together with two jets in the final state. The signal for this process includes the top quark flavour changing neutral current couplings (tqγ) through photon exchanges in electron-proton collisions. We set upper limits on the top quark FCNC couplings from the analysis of signal and background including detector effects through the fast simulation. The expected limits on tqγ couplings at HL-LHC have already been reported in [28]; the branching ratios for t→qγ are 8×10-5 and 2.5×10-5 for Lint= 300 fb-1 and 3000 fb-1, respectively. The LHeC with the high luminosity of 1 ab-1 has the potential of probing the top FCNC couplings (λu, λc), which can be comparable or even better when compared to the bounds from the HL-LHC.



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