# Searches for the Anomalous FCNC Top-Higgs Couplings with Polarized Electron Beam at the LHeC

Authors: XiaoJuan Wang; Hao Sun; Xuan Luo
Journal: Advances in High Energy Physics
 (2017)

---

## Abstract

We study the single top and Higgs associated productione-p→νet-→νehq-(h→bb-) in the top-Higgs FCNC couplings at the LHeC with the electron beam energy of Ee=60 GeV and Ee=120 GeV and combination of a 7 TeV and 50 TeV proton beam. With the possibility of e-beam polarization (pe=0, ±0.6), we distinct the cut-based method and the multivariate analysis- (MVA-) based method and compare with the current experimental and theoretical limits. It is shown that the branching ratio Br(t→uh) can be probed to 0.113 (0.093%), 0.071 (0.057%), 0.030 (0.022%), and 0.024 (0.019%) with the cut-based (MVA-based) analysis at (Ep, Ee) = (7 TeV, 60 GeV), (Ep, Ee) = (7 TeV, 120 GeV), (Ep, Ee) = (50 TeV, 60 GeV), and (Ep, Ee) = (50 TeV, 120 GeV) beam energy and 1σ level. With the possibility of e-beam polarization, the expected limits can be probed down to 0.090 (0.073%), 0.056 (0.045%), 0.024 (0.018%), and 0.019 (0.015%), respectively.


---

## Body

## 1. Introduction

The Large Hadron Electron Collider (LHeC) is the second electron-hadron collider following HERA [1]. With remarkable higher energy and luminosity, the LHeC is a major step towards understanding the Higgs physics and QCD. For the LHeC colliding energy, the 7 TeV proton beam at the LHC as well as the 50 TeV proton beam at the future FCC-he [2] and a new 60 GeV electron beam [1] are envisaged. To probe new physics, the anomalous flavor changing neutral current (FCNC) Yukawa interactions, between the top-Higgs and either an up or charm quark, would provide a clear signal. The SM Lagrangian can be extended by the following terms:(1)L=κtuht¯uh+κtcht¯ch+h.c.,where the real parameters κtuh and κtch denote the FCNC couplings of the Higgs to up-type quarks. The total decay width of the top quark Γt is(2)Γt=Γt→W-bSM+Γt→ch+Γt→uh, where the decay width Γt→W-bSM and Γt→u(c)h can be found in [3, 4], respectively. Thus, the branching ratio for t→u(c)h can be approximately given by(3)Brt⟶uch=κtuch22GFmt21-τh221-τW221+2τW2≈0.512κtuch2, where GF is the Fermi constant and τW=mW/mt. The W boson and top quark masses are chosen to be mW=79.82GeV and mt=173.2GeV, respectively.Up to now, the investigation oft→qh anomalous couplings has been experimented by many groups, which gives the strong limits on the top-Higgs FCNC couplings. For instance, according to the ATLAS and CMS collaborations, the upper limits of Br(t→qh)<0.79% [5, 6] and Br(t→qh)<0.45% [7] have been set at 95% confidence level (CL). At one-loop level, the D0-D0¯ mixing observable can receive sizeable contributions with such an unvanishing flavor violating tqH coupling [8]. Using data observed on D0-D0¯, the upper limit of Br(t→qh)<5×10-3 can be achieved. Furthermore, through Z→cc¯ decay and electroweak observables, the upper limit of Br(t→qh)<0.21% [9] can be obtained.On the other hand, based on the experimental data, many phenomenological studies are performed from different channels. For instance, [10] found that the branching ratios Br(t→qh) can be probed to 0.24% at 3σ level at 14 TeV LHC with integrated luminosity of 3000 fb-1 through the process Wt→Whq→lνbγγq. Reference [11] explored the top-Higgs FCNC couplings through tt¯→Wbqh→lνbγγq and found that the branching ratios Br(t→uh) can be probed to 0.23% at 3σ sensitivity at 14 TeV LHC with =3000 fb-1. And [12] obtained Br(t→qh) to be 0.112% based on the process of tt¯→tqh→lνbbb¯q. The process of th→lνbτ+τ- has been studied in [13] and the authors therein estimated the upper limits of Br(t→uh)<0.15% at 100 fb-1 of 13 TeV data for multilepton searches. The results from different experiments and theoretical channels are summarized in Table 1.Table 1
The results from different experimental and phenomenological channels.
Channels
Data set
Limits
tt-→Wbqh→lνbγγq
ATLAS, 4.7 (20.3)fb-1 @ 7 (8) TeV
B
r
(
t
→
q
h
)
<
0.79% [5, 6]
tt-→Wbqh→lνbγγq
CMS, 19.5fb-1 @ 8 TeV
B
r
(
t
→
u
h
)
<
0.45% [7]
D
0
-
D
0
- mixing data
—
B
r
(
t
→
q
h
)
<
0.5% [8]
Z
→
c
c
- and EW observables
—
B
r
(
t
→
q
h
)
<
0.21% [9]
Wt→Whq→lνbγγq
LHC, 3000fb-1 @ 14 TeV, 3σ
B
r
(
t
→
q
h
)
<
0.24% [10]
tt-→Wbqh→lνbγγq
LHC, 3000fb-1 @ 14 TeV
B
r
(
t
→
u
h
)
<
0.23% [11]
tt-→tqh→lνbbb-q
ILC, 3000fb-1 @ 500 GeV
B
r
(
t
→
q
h
)
<
0.112% [12]
th→lνbτ+τ-
LHC, 100fb-1 @ 13 TeV
B
r
(
t
→
u
h
)
<
0.15% [13]
th→lνbl+l-X
LHC, 100fb-1 @ 13 TeV
B
r
(
t
→
u
h
)
<
0.22% [13]
th→jjbbb-
LHC, 100fb-1 @ 13 TeV
B
r
(
t
→
u
h
)
<
0.36
% [13]In this study, we examinede-p→νet¯→νehq¯ at the LHeC, where the Higgs boson decays to bb¯ at 7 (50) TeV with 60 (120) GeV electron beam and 1000 fb-1 integrated luminosity. The possibility of e-beam polarization is also considered. The Feynman diagram is plotted in Figure 1. The main backgrounds which yield the same or similar final states to the signal are listed as follows:(4)e-p⟶νet¯⟶W-⟶jjb¯,e-p⟶e-jjj,e-p⟶νejjj,e-p⟶νeh⟶bb¯j,e-p⟶νez⟶bb¯j, where j=g,u,u¯,d,d¯,c,c¯,s,s¯,b, and b¯ if possible. Notice that e-p→e-jjj is the neutral current multijet QCD background, and all the others belong to charged current (CC) productions. For the single top background e-p→νe(t¯→(W-→jj)b¯), the produced top quark will decay to a W boson and a b-jet. The W boson continues to decay to non-b-jet final states, which might be mistagged as a b-jet. With the same final states, e-p→νe(h→bb¯)j and e-p→νe(z→bb¯)j are the irreducible backgrounds corresponding to associated Higgs jet and Z jet which contain three QED couplings. e-p→νejjj is the CC multijet QCD background. Similar to the single top background, misidentification of one or more of the final state light jets to b-jet makes this process a reducible background.Figure 1
Feynman diagram for the partonic processe-b¯→νet¯→νehq¯→νebb¯q¯ at the LHeC through flavor changing top-Higgs interactions.


## 2. Tools and Method

During the simulation, we first extract the Feynman Rules by using the FeynRules package [14] and generate the event with MadGraph@NLO [15]. PYTHIA6.4 [16] was set to solve the initial and final state parton shower, hadronization, heavy hadron decays, and so forth. We use CTEQ6L [17, 18] as the parton distribution function and set the renormalization and factorization scale to be μr=μf. We take the input heavy particle masses as mh=125.7GeV, mt=173.2GeV, mZ=91.1876GeV, and mW=79.82GeV, respectively. We employ the following basic preselections cuts to select the events: (5)ETmissing≥15GeV,pTk0≥15GeV,k0=j,b,l,ηj<5,ηb<5,ηl≤3,ΔRk1k2>0.4,k1k2=jj,jl,jb,bb,bl,where ΔR=ΔΦ2+Δη2 is the separation with Δη and ΔΦ in the rapidity-azimuth plane and pTjet,b,l and |ηjet,b,l| are the transverse momentum and the pseudorapidity of jets, b-jets, and leptons, while ETmissing is the missing transverse momentum. Then we adopt a cut-based method and a multivariate analysis- (MVA-) based method for signal and background analysis, respectively.


### 2.1. Cut-Based Method

In order to distinguish between signal-related events and background-related events as much as possible, we set a series of cuts. We list all the cut-based selections here:(i)
Cut 1: the basic preselection cuts(ii)
Cut 2: the selectione-p→ETmissing+0l+≥3jets,(withatleast2taggedb-jets)(iii)
Cut 3: missing transverse energyETmissing>20GeV(iv)
Cut 4: the reconstructed top quark mass windowmt∈[148GeV,178GeV](v)
Cut 5: the reconstructedW boson mass window mW<50GeVormW>90GeV(vi)
Cut 6: the reconstructedZ boson mass window mZ<55GeVormZ>95GeV(vii)
Cut 7: the reconstructed Higgs mass windowmh∈[100GeV,130GeV]


### 2.2. MVA-Based Method

We implemented the MVA method using the Root Toolkit for Multivariate Analysis (TMVA) [19]. After cut 1, cut 2, and cut 3, we especially select several input variables to discriminate the signal and background events, thus resulting in better signal significance. Specifically, we define a set of totally 44 kinematic variables and choose the most effective ones for Boosted Decision Trees (BDT) training, which are the b-jet number (Nbjet), the separation in the Φ-η plane between jets (ΔRB1B2, ΔRB1J1), the difference in azimuthal angle between jets (ΔΦB1B2, ΔΦB1J1), the transverse momentum of the jet (pTJ1), and the difference in |η| within Higgs jet system (ΔηhJ1). It is worth noting that e-beam polarization is considered in both cut-based method and MVA-based method.


## 2.1. Cut-Based Method

In order to distinguish between signal-related events and background-related events as much as possible, we set a series of cuts. We list all the cut-based selections here:(i)
Cut 1: the basic preselection cuts(ii)
Cut 2: the selectione-p→ETmissing+0l+≥3jets,(withatleast2taggedb-jets)(iii)
Cut 3: missing transverse energyETmissing>20GeV(iv)
Cut 4: the reconstructed top quark mass windowmt∈[148GeV,178GeV](v)
Cut 5: the reconstructedW boson mass window mW<50GeVormW>90GeV(vi)
Cut 6: the reconstructedZ boson mass window mZ<55GeVormZ>95GeV(vii)
Cut 7: the reconstructed Higgs mass windowmh∈[100GeV,130GeV]


## 2.2. MVA-Based Method

We implemented the MVA method using the Root Toolkit for Multivariate Analysis (TMVA) [19]. After cut 1, cut 2, and cut 3, we especially select several input variables to discriminate the signal and background events, thus resulting in better signal significance. Specifically, we define a set of totally 44 kinematic variables and choose the most effective ones for Boosted Decision Trees (BDT) training, which are the b-jet number (Nbjet), the separation in the Φ-η plane between jets (ΔRB1B2, ΔRB1J1), the difference in azimuthal angle between jets (ΔΦB1B2, ΔΦB1J1), the transverse momentum of the jet (pTJ1), and the difference in |η| within Higgs jet system (ΔηhJ1). It is worth noting that e-beam polarization is considered in both cut-based method and MVA-based method.


## 3. Results

In Figure2 ((60) GeV) and Figure 3 ((120) GeV), we show the dependence of the cross section σ on the top-Higgs FCNC couplings κtqh at Ee = 60 (120) GeV with pe = ±0.6 electron beam polarization and combination of a 7 (50) GeV proton beam for three different cases: (I) κtqh=κtuh,κtch=0, (II) κtqh=κtch,κtuh=0, and (III) κtqh=κtuh=κtch. Obviously, the cross section of κtqh=0.1 can be 100 times larger than that of κtqh=0.01, and the cross section of 50 TeV can be 9.1 (6.6) times larger than that of 7 TeV with a 60 (120) GeV electron beam. We also find that the cross sections between polarized and unpolarized electron beam cases are related as σer-=σe0-·(1-per-) and σel-+σer-=2σe0-, independent of being case I, case II, or caseIII. Here σer-, σel-, and σe0- represent the right, left, and without electron beam polarization, respectively.Figure 2
The cross sectionsσtqh on the top-Higgs FCNC couplings κtqh at the 7 (50) TeV and 60 GeV LHeC with e-beam polarization pe=0,±0.6.Figure 3
The same as Figure2 but for Ee = 120 GeV.The cross section of the signal and backgrounds (in units of fb) are summarized in Table2 (cut-based method) and Table 3 (MVA-based method). From these tables, we calculate the signal significance S/S+B as 4.191 (15.341) and 6.652 (19.236) for 7 and 50 TeV by cut-based method and 4.921 (16.934) and 7.874 (20.785) by MVA-based method after imposing all the relevant event selections (only the first three selections in MVA-based method), respectively. Obviously, compared to the cut-based method, the MVA-based method can get better signal significance. As expected, with the p2=-0.6  e-beam polarization, the results are improved as 5.302 (19.404) and 8.414 (24.335) for cut-based method and 6.224 (21.420) and 9.960 (26.291) for MVA-based method. In addition to effective cuts, enhancing the b-tagging efficiency together with reducing the jet misidentification rates is one of the other ways to improve the signal significance. It is confirmed that the signal significance can be increased from 4.191, 6.652, 15.341, and 19.238 to 8.366, 13.840, 33.750, and 44.154 with ϵb=80%, ϵc=1%, and ϵlight=0.1% with the same value of the input parameters and kinematic cuts.Table 2
Expected cross sections after all the selections for signal and backgrounds at the LHeC with integrated luminosity of1000fb-1, b-tagging efficiency ϵb = 60%, jet misidentification rates ϵc = 10%, and ϵlight = 1% by cut-based method. In particular, we select e-beam polarization as p0 = 0, p1 = 0.6, and p2=-0.6.
S
B
SS
60 GeV⊕ 7 TeV @ LHeC
p0
0.14
0.93
4.191
p1
0.05
0.37
2.651
p2
0.22
1.49
5.302
120 GeV⊕ 7 TeV @ LHeC
p0
0.32
1.98
6.652
p1
0.13
0.79
4.207
p2
0.51
3.16
8.414
60 GeV⊕ 50 TeV @ LHeC
p0
1.29
5.80
15.341
p1
0.52
2.32
9.702
p2
2.07
9.28
19.404
120 GeV⊕ 50 TeV @ LHeC
p0
2.14
10.26
19.238
p1
0.86
4.10
12.167
p2
3.43
16.42
24.335Table 3
The same as Table2 but for MVA-based method. We select e-beam polarization as p0 = 0, p1 = 0.6, and p2=-0.6.
S
B
SS
60 GeV⊕ 7 TeV @ LHeC
p0
0.125
0.520
4.921
p1
0.050
0.208
3.112
p2
0.200
0.833
6.224
120 GeV⊕ 7 TeV @ LHeC
p0
0.281
0.992
7.874
p1
0.112
0.397
4.980
p2
0.450
1.588
9.960
60 GeV⊕ 50 TeV @ LHeC
p0
0.652
0.830
16.934
p1
0.261
0.332
10.710
p2
1.043
1.328
21.420
120 GeV⊕ 50 TeV@ LHeC
p0
1.082
1.629
20.785
p1
0.433
0.652
13.145
p2
1.732
2.606
26.291In order to estimate the sensitivity to the anomalous tqH couplings, we used chi-square (χ2) function [20, 21]:(6)χ2=σtot-σBσBδ2, where σtot is the total cross section and δ is the statistical error. In Figure 4 (cut-based analysis) and Figure 5 (MVA-based analysis) [19], we plot the contours of 1σ limits to κtqH at 7 (50) GeV LHeC and 60 (120) GeV electron beam with different polarization. The red, blue, and black curves represent the 0.6, -0.6, and without electron beam polarization. From these figures, we can see that the branching ratio Br(t→uh) can be probed to 0.113(0.093%), 0.071(0.057%), 0.030(0.022%), and 0.024 (0.019%) with the cut-based (MVA-based) analysis at (Ep, Ee) = (7 TeV, 60 GeV), (Ep, Ee) = (7 TeV, 120 GeV), (Ep, Ee) = (50 TeV, 60 GeV), and (Ep, Ee) = (50 TeV, 120 GeV) beam energy. As expected, the MVA-based method has a great advantage and also the 50 TeV high energy can get better results compared to the 7 TeV ones. Furthermore, it is clear that the limits can be probed down to 0.090 (0.073%), 0.056 (0.045%), 0.024 (0.018%), and 0.019 (0.015%) with the e-beam polarization of p2=-0.6.Figure 4
The upper limit from cut-based method at 1σ level at 7 (50) GeV LHeC with 60 (120) GeV electron beam. The red, blue, and black curves represent the 0.6, -0.6, and without electron beam polarization.Figure 5
The same as Figure4 but for MVA.Finally, we give precise integrated luminosity (L) corresponding to the critical limits obtained by the experimental results (Table 4) and other phenomenological studies (Table 5). With the e-beam polarization p2=-0.6, L needed to get the upper bounds on Br(t→qh) is reduced significantly. A detailed comparison between the LHeC collider(s) and the LHC or linear colliders is given.Table 4
The integrated luminosity (L) needed to get the upper bounds on Br(t→qh) at 95% CL obtained from the experiments. Both the cut- (MVA-) based results and 1σ (2σ) limits with e-beam polarization are presented.
Channels and limits
Method
L
[
f
b
-
1
]
1
σ
L
[
f
b
-
1
]
2
σ
p
0
p
1
p
2
p
0
p
1
p
2
t
t
-
→
W
b
q
h
→
l
ν
b
γ
γ
q ATLAS, 4.7 (20.3) fb-1 @ 7 (8) TeV Br(t→qh)<0.79% [5, 6]
CutMVA
0.930.58
2.321.44
0.580.36
3.602.24
9.005.60
2.251.40
t
t
-
→
W
b
q
h
→
l
ν
b
γ
γ
q CMS, 19.5 fb-1 @ 8 TeV  Br(t→uh)<0.45% [7]
CutMVA
2.861.78
7.154.45
1.791.11
11.106.91
27.7617.27
6.944.32
D
0
-
D
0
- mixing data Br(t→qh)<0.5% [8]
CutMVA
2.321.44
5.793.60
1.450.90
8.995.60
22.4813.99
5.623.50
Z
→
c
c
- and EW observables  Br(t→qh)<0.21% [9]
CutMVA
13.138.17
32.8320.43
8.215.11
51.0131.74
127.5379.35
31.8819.84Table 5
The same as Table4 but for some other phenomenological studies.
Channels and limits
Method
L
[
f
b
-
1
]
1
σ
L
[
f
b
-
1
]
2
σ
p
0
p
1
p
2
p
0
p
1
p
2
W
t
→
W
h
q
→
l
ν
b
γ
γ
q LHC, 3000 fb-1 @ 14 TeV 3σ,  Br(t→qh)<0.24% [10]
CutMVA
10.056.26
25.1415.64
6.283.91
39.0524.30
97.6360.75
24.4115.19
t
t
-
→
W
b
q
h
→
l
ν
b
γ
γ
q LHC, 3000 fb-1 @ 14 TeV Br(t→uh)<0.23% [11]
CutMVA
10.956.81
27.3717.03
6.844.26
42.5226.46
106.3166.15
26.5816.54
t
t
-
→
t
q
h
→
l
ν
b
b
b
-
q ILC, 3000 fb-1 @ 500 GeV Br(t→qh)<0.112% [12]
CutMVA
46.2028.75
115.5071.86
28.8717.97
179.44111.65
448.60279.13
112.1569.78
t
h
→
l
ν
b
τ
+
τ
- LHC, 100 fb-1 @ 13 TeV Br(t→uh)<0.15 % [13]
CutMVA
25.7516.02
64.3740.05
16.0910.01
100.0162.23
250.03155.58
62.5138.89
t
h
→
l
ν
b
l
+
l
-
X LHC, 100 fb-1 @ 13 TeV Br(t→uh)<0.22% [13]
CutMVA
11.977.45
29.9218.61
7.484.65
46.4828.92
116.2072.30
29.0518.08
t
h
→
j
j
b
b
b
- LHC, 100 fb-1 @ 13 TeV Br(t→uh)<0.36% [13]
CutMVA
4.472.78
11.176.95
2.791.74
17.3510.80
43.3826.99
10.846.75


## 4. Conclusion

In this paper, we investigated the anomalous FCNC Yukawa interactions between the top quark, the Higgs boson, and either an up or charm quark with a channele-p→νet¯→νehq¯(h→bb¯) at the LHeC. The signal significance S/S+B can be obtained as 4.191 (4.921), 6.652 (7.874), 15.341 (16.934), and 19.238 (20.785) with the cut-based (MVA-based) method at (Ep, Ee) = (7 TeV, 60 GeV), (Ep, Ee) = (7 TeV, 120 GeV), (Ep, Ee) = (50 TeV, 60 GeV), and (Ep, Ee) = (50 TeV, 120 GeV). Similarly, our results show that the branching ratio Br(t→uh) can be probed to 0.113 (0.093%), 0.071 (0.057%), 0.030 (0.022%), and 0.024 (0.019%), and with the e-beam polarization p2=-0.6, the expected limits can be greatly reduced. Finally, a detailed comparison between our study and the critical limits obtained by the experiments and other phenomenological studies is shown. We thus give an overview of the search potential on the anomalous top-Higgs couplings with polarized electron beam at the LHeC.



---

*Source: 4693213-2017-03-16.xml*