# Production and Decay of Up-Type and Down-Type New Heavy Quarks through Anomalous Interactions at the LHC

Authors: İ. T. Çakır; S. Kuday; O. Çakır
Journal: Advances in High Energy Physics
 (2015)

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## Abstract

We study the processpp→QV+X (where Q=t,b and V=g,γ, and Z) through the anomalous interactions of the new heavy quarks at the LHC. Considering the present limits on the masses and mixings, the signatures of the heavy quark anomalous interactions are discussed and analysed at the LHC for the center of mass energy of 13 TeV. An important sensitivity to anomalous couplings κgt′/Λ=0.10 TeV−1, κγt′/Λ=0.14 TeV−1, κZt′/Λ=0.19 TeV−1 and κgb′/Λ=0.15 TeV−1, κZb′/Λ=0.19 TeV−1, κγb′/Λ=0.30 TeV−1 for the mass of 750 GeV of the new heavy quarks t′ and b′ can be reached for an integrated luminosity of Lint=100 fb−1.


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## Body

## 1. Introduction

The standard model (SM) of the strong and electroweak interactions describes successfully the phenomena of particle physics. However, there are many unanswered questions suggesting the SM to be an effective theory. In order to answer some of the problems with the SM, additional new fermions can be accommodated in many models beyond the SM (see [1–9] and references therein). The new heavy quarks could also be produced in pairs at the LHC with center of mass energy of 13 TeV. However, due to the expected smallness of the mixing between the new heavy quarks and known quarks, the decay modes can be quite different from the one relevant to charged weak interactions. A new symmetry beyond the SM is expected to explain the smallness of these mixings. The arguments given in [10] for anomalous interactions of the top quark are more valid for the new heavy quarks t′ and b′ due to their expected larger masses than the top quark.The ATLAS experiment [11] and CMS experiment [12] have searched for the fourth generation of quarks and set limits on the mass of mb′>480 GeV and mt′>570 GeV at s=7 TeV. The pair production of new heavy quarks has been searched by the ATLAS experiment [13, 14] and the mt′>656 GeV mass limits are set at s=7 TeV. The CMS experiment has excluded t′ masses below 557 GeV [15]. The vector-like quarks have been searched by the ATLAS experiment [16, 17] and set bounds as 900 GeV for charged current channel and 760 GeV for neutral current channel at s=7 TeV. The CMS experiment [18] has set the lower bounds on the mass of 685 GeV at s=8 TeV. Some of the final states in the searches of new phenomena can also be considered in relation with the new heavy quarks.The anomalous resonant productions of the fourth family quarks have been studied in [19, 20] at the LHC with s=14 TeV. The possible single productions of fourth generation quarks via anomalous interactions at Tevatron have also been studied in [21]. The parameter space for the mixing of the fourth generation quarks has been presented in [22]. The CP violating flavor changing neutral current processes of the fourth generation quarks have been analyzed in [23], and the large mixing between fourth generation and first three generations has been excluded under the proposed fit conditions. Investigation of the parameter space favored by the precision electroweak data has been performed for the fourth SM family fermions in [24].In this work, we present the analysis of anomalous productions and decay of new heavy quarkst′ and b′ at the LHC. We have performed the fast simulation for the signal and background. Any observations of the invariant mass peak in the range of 500–1000 GeV and excess in the events with the final states originating from WbV and bV can be interpreted as the signal for the new heavy quarks t′ and b′ via the anomalous interactions.


## 2. New Heavy Quarks Anomalous Interactions

A general theory that includes the standard model (SM) as its low energy limit can be written as an expansion series in powers ofΛ-1 with operators obeying the required symmetries. The dimension six gauge invariant operators can be built from the SM fields and they can induce dimension five operators after spontaneous symmetry breaking. The coefficients of the dimension five terms are related to those of dimension six operators, and they can lead to sizable effects in the heavy quark associated production in high energy collisions [25]. For our study, the effective Lagrangian with dimension five terms for the anomalous interactions among the new heavy quarks (Q′≡t′ or b′), ordinary quarks q, and the gauge bosons V=γ,Z,g can be written explicitly:(1)L=∑qi=u,c,t‍κγqiΛQqiget¯′σμνqiFμν+∑qi=u,c,t‍κzqi2Λgzt¯′σμνqiZμν+∑qi=u,c,t‍κgqi2Λgst¯′σμνλaqiGaμν+∑qi=d,s,b‍κγqiΛQqigeb¯′σμνqiFμν+∑qi=d,s,b‍κzqi2Λgzb¯′σμνqiZμν+∑qi=d,s,b‍κgqi2Λgsb¯′σμνλaqiGaμν+h.c.,where Fμν, Zμν, and Gμν are the field strength tensors of the gauge bosons; σμν=i(γμγν-γνγμ)/2; λa are the Gell-Mann matrices; Qq is the electric charge of the quark (q); ge, gZ, and gs are the electromagnetic, neutral weak, and strong coupling constants, respectively. gZ=ge/cos⁡θwsinθw, where θw is the weak mixing angle. κγ is the anomalous coupling with photon; κz is for the Z boson, and κg is the coupling with gluon. Finally, Λ is the cutoff scale for the new interactions.


## 3. Decay Widths and Branchings

For the decay channelsQ′→Vq where V≡γ, Z, and  g, we use the effective Lagrangian to calculate the anomalous decay widths:(2)Γ(Q′⟶gq)=23κgqΛ2αsmQ′3λ0,ΓQ′⟶γq=12κγqΛ2αeQq2mQ′3λ0,Γ(Q′⟶Zq)=116κZqΛ2αemQ′3sin2θWcos⁡2θWλZλrwith(3)λ0=1-3mq2mQ′2+3mq4mQ′4-mq6mQ′6,λr=1+mZ4mQ′4+mq4mQ′4-2mZ2mQ′2-2mq2mQ′2-2mZ2mq2mQ′4,λZ=2-mZ2mQ′2-4mq2mQ′2+2mq4mQ′4-6mqmZ2mQ′3-mZ2mt2mQ′4-mZ4mQ′4.The anomalous decay widths in different channels are proportional toΛ-2, and they are assumed to be dominant for κ/Λ>0.1 TeV−1 over the charged current channels. In this case, if we take all the anomalous coupling equal then the branching ratios will be nearly independent of κ/Λ. We have used three parametrization sets entitled PI, PII, and PIII. For the PI parametrization, we assume the constant value κi/Λ=0.1 TeV−1, and PII has the parameters κi/Λ=0.1λ4-i TeV−1 with λ=0.5. For PIII we take the couplings κi/Λ=0.5λ4-i TeV−1 with the same value of λ. The index i is the generation number.Tables1 and 2 present the decay width and branching ratios of the new heavy quark t′ through anomalous interactions for the parametrization PI, PII, and PIII, respectively. Taking the anomalous coupling κ/Λ=0.1 TeV−1 we calculate the t′ decay width Γ=0.65 GeV and 1.90 GeV for mt′=700 GeV and 1000 GeV, respectively. The branching into t′→qg channel is the largest and branching into t′→qγ channel is the smallest for equal anomalous couplings with the parametrization PI. On the other hand, PII and PIII parametrization give higher branching ratios into tV (V=g,Z,γ) than qV (q=u,c) channels due to λ4-i factor in the parametrization.Table 1
Branching ratios (%) and decay width of the new heavy quark (t′) with only anomalous interactions for PI parametrization and κ/Λ = 0.1 TeV-1.
Mass(GeV)
g
u
(
c
)
g
t
Z
u
(
c
)
Z
t
γ
u
(
c
)
γ
t
Γ (GeV)
5
00
33.5
22.9
2.86
1.82
0.92
0.63
0.23
600
32.3
25.0
2.86
2.13
0.91
0.70
0.41
700
31.6
26.2
2.87
2.34
0.90
0.75
0.65
800
31.1
27.0
2.89
2.48
0.90
0.78
0.97
900
30.7
27.5
2.91
2.58
0.91
0.81
1.39
1000
30.5
27.8
2.93
2.66
0.91
0.83
1.90Table 2
The same as Table1, but for PII (PIII) parametrization.
Mass (GeV)
g
u
g
c
g
t
Z
u
Z
c
Z
t
γ
u
γ
c
γ
t
Γ (GeV)
5
00
5.66
22.60
61.90
0.48
1.93
4.92
0.15
0.62
1.71
0.021 (0.558)
600
5.17
20.70
63.90
0.46
1.83
5.46
0.14
0.58
1.80
0.040 (1.024)
700
4.90
19.60
64.90
0.44
1.78
5.79
0.14
0.56
1.87
0.066 (1.68)
800
4.73
18.90
65.60
0.44
1.76
6.02
0.14
0.55
1.91
0.100 (2.561)
900
4.61
18.40
65.90
0.44
1.74
6.19
0.13
0.54
1.95
0.145 (3.680)
1000
4.53
18.10
66.20
0.43
1.74
6.32
0.13
0.54
1.98
0.200 (5.070)For the new heavy quarkb′ the decay width and branching ratios are presented in Tables 3 and 4 for the parametrizations PI, PII, and PIII, respectively. We calculate the b′ decay width, by taking the anomalous couplings κ/Λ=0.1 TeV−1, Γ=0.68 GeV, and 1.92 GeV for mb′=700 GeV and 1000 GeV, respectively. The branching for b′→qg is the largest (30%) and it is the smallest for b′→qγ (0.2%) channel for equal anomalous couplings with the parametrization PI. For PII and PIII parametrization the branching ratios into bV (V=g,Z,γ) are larger than qV (q=d,s) channels. The t′ and b′ decay widths are about the same values for PII and PIII parametrization.Table 3
Branching ratios (%) and decay width of the new heavy quark (b′) with only anomalous interactions for PI parametrization and κ/Λ = 0.1 TeV-1.
Mass(GeV)
g
d
(
s
,
b
)
Z
d
(
s
,
b
)
γ
d
(
s
,
b
)
Γ (GeV)
5
00
30.50
2.60
0.21
0.257
600
30.40
2.69
0.21
0.436
700
30.40
2.76
0.22
0.682
800
30.30
2.82
0.22
1.005
900
30.20
2.86
0.22
1.415
1000
30.20
2.90
0.23
1.921Table 4
The same as Table3, but for PII (PIII) parametrization.
Mass (GeV)
g
d
g
s
g
b
Z
d
Z
s
Z
b
γ
d
γ
s
γ
b
Γ (GeV)
5
00
4.36
17.40
69.80
0.37
1.49
5.95
0.030
0.12
0.48
0.028 (0.704)
600
4.35
17.40
69.50
0.38
1.54
6.16
0.030
0.12
0.49
0.047 (1.194)
700
4.34
17.30
69.40
0.39
1.58
6.31
0.031
0.12
0.50
0.074 (1.866)
800
4.33
17.30
69.20
0.40
1.61
6.44
0.031
0.12
0.50
0.110 (2.749)
900
4.32
17.30
69.10
0.41
1.64
6.54
0.032
0.13
0.51
0.154 (3.869)
1000
4.32
17.30
69.00
0.41
1.66
6.63
0.032
0.13
0.52
0.210 (5.253)


## 4. The Cross Sections

In order to study the new heavy quark productions at the LHC, we have used effective anomalous interaction vertices and implemented these vertices into the CalcHEP package [26]. In all of the numerical calculations, the parton distribution functions are set to the CTEQ6L parametrization [27]. The new heavy quarks can be produced through their anomalous couplings to the ordinary quarks and neutral vector bosons as shown in Figure 1.Figure 1
Diagrams for the subprocessgq→VQ with anomalous vertices Q′qV and Q′QV (where Q′ can be the new heavy quark b′ or t′ depending on the type of light (q) or heavy (Q≡t,b) quarks, resp.).
(a)
(b)Total cross sections for the productions of new heavy quarkst′ and b′ are given in Tables 5 and 6 for the parametrizations PI, PII, and PIII, at the center of mass energy of 8 TeV and 13 TeV. For an illustration, taking the mass of new heavy quarks as 700 GeV the cross section of t′b′ production is calculated as 8.50 pb (10.03 pb) for the parametrization PIII at s=13 TeV. It can be seen from Tables 5 and 6 that the cross section decreases while the mass of the new heavy quark increases. The cross section for t′ production is larger than the b′ production with a factor of 1.2–1.8 (0.7–1.0) for PI (PII and PIII) parametrization depending on the considered mass range at s=13 TeV. The general behaviour of the production cross sections depending on the mass of new heavy quarks is presented in Figures 2 and 3 for different parametrizations.Table 5
The cross sections (in pb) of new heavy quarkt′ production without cuts for PI, PII, and PIII parametrizations at the center of mass energy 13 TeV (8 TeV), respectively.
Mass (GeV)
PI
PII
PIII
s = 13 TeV (8 TeV)
s = 13 TeV (8 TeV)
s = 13 TeV (8 TeV)
5
00
13.733 (5.30)
0.664 (0.244)
16.736 (6.113)
600
10.362 (3.72)
0.464 (0.159)
11.770 (4.031)
700
7.825 (2.64)
0.337 (0.109)
8.502 (2.718)
800
5.961 (1.89)
0.250 (0.075)
6.276 (1.882)
900
4.602 (1.36)
0.189 (0.053)
4.701 (1.326)
1000
3.593 (0.98)
0.144 (0.038)
3.609 (0.950)Table 6
The cross sections (in pb) of new heavy quarkb′ production without cuts for PI, PII, and PIII parametrizations at the center of mass energy of 13 TeV (8 TeV), respectively.
Mass (GeV)
PI
PII
PIII
s = 13 TeV (8 TeV)
s = 13 TeV (8 TeV)
s = 13 TeV (8 TeV)
5
00
11.340 (3.913)
0.970 (0.285)
24.474 (7.114)
600
7.495 (2.410)
0.607 (0.162)
15.290 (4.09)
700
5.179 (1.546)
0.412 (0.099)
10.031 (2.483)
800
3.697 (1.025)
0.286 (0.062)
6.832 (1.566)
900
2.707 (0.697)
0.1905 (0.040)
4.791 (1.018)
1000
2.021 (0.482)
0.137 (0.027)
3.441 (0.678)Figure 2
The cross section for the processpp→tV+X depending on the mass for parameter sets PI, PII, and PIII at the center of mass energy s=13 TeV.Figure 3
The cross section for the processpp→bV+X depending on the new heavy quark mass for parameter sets PI, PII, and PII at the center of mass energy s=13 TeV.


### 4.1. Analysis of the Processpp→W+bV+X  (V=g,Z,γ) for t′ Signal

The signal processpp→W+bV+X (V=g,Z,γ) includes the t′ exchange in both the s-channel and t-channel. The s-channel contribution to the signal process would appear itself as resonance around the t′ mass value in the WbV invariant mass. The t-channel gives the nonresonant contribution. We consider that the W boson decays into lepton + missing transverse momentum with the branching ratio of 21% and Z boson decays into dilepton with the branching ratio of  6.7%. In our analyses, we consider the t′ signal in the l+bjet+γ+MET, l+bjet+j+MET, and 3l+bjet+MET channels, where l=e,μ. However, if one takes the hadronic W decay, the signal will be enhanced by a factor of BR(W→hadrons)/BR(W→lν).We have obtained the cross sections by using the cuts pseudorapidityηj,γ<2.5 and transverse momentum pTj,γ>20–200 GeV for jets and photon, in Table 7 (Tables 8 and 9) for PI (PII, PIII) parametrization, respectively. Invariant mass distribution of the tV (where V=γ, g, and Z) system is shown in Figure 4 for PI parametrization of the signal with κ/Λ=0.2 TeV−1 and mt′=700 GeV at the center of mass energy s=13 TeV. It appears from signal significance calculations that the optimized transverse momentum cut is pTj,γ>100 GeV for t′ analyses.Table 7
The cross sections (in pb) fort′ signal in different decay channels for PI parametrization with pT cuts on the jets and photon and |ηj,γ|<2.5 at the center of mass energy s = 13 TeV.
SignalMass (GeV)
PI
p
T
>
20 GeV
p
T
>
50 GeV
p
T
>
100 GeV
p
T
>
200 GeV
p
p
→
W
+
b
γ
+
X
500
2.89
×
1
0
-
1
2.10
×
1
0
-
1
1.24
×
1
0
-
1
1.02
×
1
0
-
4
600
2.43
×
1
0
-
1
1.64
×
1
0
-
1
1.19
×
1
0
-
1
1.23
×
1
0
-
2
700
1.68
×
1
0
-
1
1.2
×
1
0
-
1
1.12
×
1
0
-
1
2.25
×
1
0
-
2
800
1.30
×
1
0
-
1
1.03
×
1
0
-
1
7.53
×
1
0
-
2
3.25
×
1
0
-
2
900
1.02
×
1
0
-
1
8.08
×
1
0
-
2
6.96
×
1
0
-
2
3.02
×
1
0
-
2
1000
7.61
×
1
0
-
2
6.35
×
1
0
-
2
5.07
×
1
0
-
2
2.94
×
1
0
-
2
p
p
→
W
+
b
g
+
X
500
7.78
×
1
0
0
6.02
×
1
0
0
3.63
×
1
0
0
4.74
×
1
0
-
3
600
6.30
×
1
0
0
5.18
×
1
0
0
3.13
×
1
0
0
2.58
×
1
0
-
1
700
4.99
×
1
0
0
3.63
×
1
0
0
3.04
×
1
0
0
9.32
×
1
0
-
1
800
4.01
×
1
0
0
3.45
×
1
0
0
2.76
×
1
0
0
9.91
×
1
0
-
1
900
3.32
×
1
0
0
2.77
×
1
0
0
2.13
×
1
0
0
1.08
×
1
0
0
1000
2.58
×
1
0
0
2.27
×
1
0
0
1.88
×
1
0
0
1.01
×
1
0
0
p
p
→
W
+
b
Z
+
X
500
7.96
×
1
0
-
1
6.01
×
1
0
-
1
3.01
×
1
0
-
1
1.01
×
1
0
-
4
600
4.79
×
1
0
-
1
3.86
×
1
0
-
1
2.45
×
1
0
-
1
2.71
×
1
0
-
3
700
3.99
×
1
0
-
1
3.12
×
1
0
-
1
2.39
×
1
0
-
1
6.96
×
1
0
-
2
800
3.31
×
1
0
-
1
2.89
×
1
0
-
1
2.09
×
1
0
-
1
8.05
×
1
0
-
2
900
2.73
×
1
0
-
1
2.73
×
1
0
-
1
1.91
×
1
0
-
1
9.54
×
1
0
-
2
1000
2.23
×
1
0
-
1
2.02
×
1
0
-
1
1.61
×
1
0
-
1
9.10
×
1
0
-
2Table 8
The same as Table7, but for parametrization PII.
SignalMass (GeV)
PII
p
T
>
20 GeV
p
T
>
50 GeV
p
T
>
100 GeV
p
T
>
200 GeV
p
p
→
W
+
b
γ
+
X
500
6.78
×
1
0
-
3
5.07
×
1
0
-
3
3.45
×
1
0
-
3
2.64
×
1
0
-
7
600
6.57
×
1
0
-
3
5.42
×
1
0
-
3
3.47
×
1
0
-
3
5.34
×
1
0
-
4
700
5.02
×
1
0
-
3
4.31
×
1
0
-
3
3.04
×
1
0
-
3
8.73
×
1
0
-
4
800
3.91
×
1
0
-
3
3.76
×
1
0
-
3
2.56
×
1
0
-
3
1.03
×
1
0
-
3
900
3.03
×
1
0
-
3
2.68
×
1
0
-
3
2.11
×
1
0
-
3
1.01
×
1
0
-
3
1000
2.40
×
1
0
-
3
2.43
×
1
0
-
3
1.77
×
1
0
-
3
9.98
×
1
0
-
4
p
p
→
W
+
b
g
+
X
500
3.47
×
1
0
-
1
2.68
×
1
0
-
1
1.52
×
1
0
-
1
5.30
×
1
0
-
6
600
2.51
×
1
0
-
1
2.12
×
1
0
-
1
1.35
×
1
0
-
1
2.01
×
1
0
-
2
700
1.87
×
1
0
-
1
1.6
×
1
0
-
1
1.16
×
1
0
-
1
3.42
×
1
0
-
2
800
1.46
×
1
0
-
1
1.25
×
1
0
-
1
9.39
×
1
0
-
2
4.03
×
1
0
-
2
900
1.12
×
1
0
-
1
1.08
×
1
0
-
1
7.80
×
1
0
-
2
3.86
×
1
0
-
2
1000
9.35
×
1
0
-
2
8.37
×
1
0
-
2
6.62
×
1
0
-
2
3.68
×
1
0
-
2
p
p
→
W
+
b
Z
+
X
500
2.10
×
1
0
-
2
1.77
×
1
0
-
2
1.16
×
1
0
-
2
2.64
×
1
0
-
7
600
1.95
×
1
0
-
2
1.75
×
1
0
-
2
1.14
×
1
0
-
2
1.34
×
1
0
-
3
700
1.73
×
1
0
-
2
1.43
×
1
0
-
2
1.00
×
1
0
-
2
2.9
×
1
0
-
3
800
1.34
×
1
0
-
2
1.19
×
1
0
-
2
8.89
×
1
0
-
3
3.42
×
1
0
-
3
900
1.06
×
1
0
-
2
9.55
×
1
0
-
3
7.63
×
1
0
-
3
3.37
×
1
0
-
3
1000
8.09
×
1
0
-
3
7.58
×
1
0
-
3
6.31
×
1
0
-
3
3.23
×
1
0
-
3Table 9
The same as Table7, but for parametrization PIII.
SignalMass (GeV)
PIII
p
T
>
20 GeV
p
T
>
50 GeV
p
T
>
100 GeV
p
T
>
200 GeV
p
p
→
W
+
b
γ
+
X
500
2.60
×
1
0
-
1
2.78
×
1
0
-
1
1.08
×
1
0
-
1
1.59
×
1
0
-
4
600
1.78
×
1
0
-
1
1.61
×
1
0
-
1
1.01
×
1
0
-
1
1.42
×
1
0
-
2
700
1.56
×
1
0
-
1
1.35
×
1
0
-
1
9.33
×
1
0
-
2
2.72
×
1
0
-
2
800
1.17
×
1
0
-
1
1.06
×
1
0
-
1
7.84
×
1
0
-
2
3.32
×
1
0
-
2
900
9.04
×
1
0
-
2
8.42
×
1
0
-
2
6.68
×
1
0
-
2
3.25
×
1
0
-
2
1000
7.60
×
1
0
-
2
6.76
×
1
0
-
2
5.16
×
1
0
-
2
3.17
×
1
0
-
2
p
p
→
W
+
b
g
+
X
500
8.39
×
1
0
0
6.49
×
1
0
0
3.86
×
1
0
0
4.65
×
1
0
-
3
600
6.10
×
1
0
0
5.78
×
1
0
0
3.81
×
1
0
0
5.56
×
1
0
-
1
700
5.39
×
1
0
0
4.64
×
1
0
0
3.41
×
1
0
0
9.70
×
1
0
-
1
800
3.94
×
1
0
0
3.54
×
1
0
0
2.73
×
1
0
0
1.05
×
1
0
0
900
3.24
×
1
0
0
2.76
×
1
0
0
2.27
×
1
0
0
1.07
×
1
0
0
1000
2.33
×
1
0
0
2.29
×
1
0
0
1.84
×
1
0
0
9.98
×
1
0
-
1
p
p
→
W
+
b
Z
+
X
500
7.72
×
1
0
-
1
1.01
×
1
0
0
2.17
×
1
0
-
1
6.27
×
1
0
-
4
600
6.24
×
1
0
-
1
3.85
×
1
0
-
1
2.92
×
1
0
-
1
3.20
×
1
0
-
2
700
5.00
×
1
0
-
1
3.05
×
1
0
-
1
2.86
×
1
0
-
1
5.80
×
1
0
-
2
800
3.78
×
1
0
-
1
2.50
×
1
0
-
1
2.42
×
1
0
-
1
9.64
×
1
0
-
2
900
3.04
×
1
0
-
1
1.67
×
1
0
-
1
2.06
×
1
0
-
1
9.62
×
1
0
-
2
1000
2.51
×
1
0
-
1
1.29
×
1
0
-
1
1.48
×
1
0
-
1
9.61
×
1
0
-
2Figure 4
Invariant mass distributionsmtV (where V=γ, g, and Z) for PI parametrization of the signal with κ/Λ=0.2 TeV−1 and mt′=700 GeV at the center of mass energy s=13 TeV.The backgrounds for the final stateW+b(b¯)V (where V≡photon, jet, and Z boson) are given in Table 10. We apply the following cuts to the final state photon and jets as |ηj,γ|<2.5 and pTj,γ>20–200 GeV. For the background cross section estimates, we assume the efficiency for b-tagging to be εb=50% and the rejection ratios to be 10% for c(c¯) quark jets and 1% for light quark jets since they are assumed to be mistagged as b-jets.Table 10
The cross sections (in pb) for the relevant backgrounds (W+b(b-)V, W+c(c-)V, and W+jV, where V = photon, jet, and Z boson) with pT cuts on the jets at the center of mass energy s = 13 TeV.
Background
p
T
>
20 GeV
p
T
>
50 GeV
p
T
>
100 GeV
p
T
>
200 GeV
p
p
→
W
+
b
γ
+
X
2.37
×
1
0
-
3
3.62
×
1
0
-
4
6.17
×
1
0
-
5
6.99
×
1
0
-
6
p
p
→
W
+
c
-
γ
+
X
4.15
×
1
0
0
4.59
×
1
0
-
1
6.25
×
1
0
-
2
6.21
×
1
0
-
3
p
p
→
W
+
j
γ
+
X
2.63
×
1
0
1
4.30
×
1
0
0
7.33
×
1
0
-
1
1.27
×
1
0
-
1
p
p
→
W
+
b
(
b
-
)
j
+
X
7.26
×
1
0
1
3.02
×
1
0
1
6.11
×
1
0
0
9.74
×
1
0
-
1
p
p
→
W
+
c
(
c
-
)
j
+
X
5.98
×
1
0
2
9.65
×
1
0
1
1.79
×
1
0
1
2.42
×
1
0
0
p
p
→
W
+
j
j
+
X
7.31
×
1
0
3
7.78
×
1
0
2
1.61
×
1
0
2
2.58
×
1
0
1
p
p
→
W
+
b
Z
+
X
6.26
×
1
0
-
4
3.99
×
1
0
-
4
1.93
×
1
0
-
4
4.71
×
1
0
-
5
p
p
→
W
+
c
-
Z
+
X
5.29
×
1
0
-
1
3.40
×
1
0
-
1
1.66
×
1
0
-
1
4.15
×
1
0
-
2
p
p
→
W
+
j
Z
+
X
8.59
×
1
0
0
4.83
×
1
0
0
2.49
×
1
0
0
7.91
×
1
0
-
1In order to find the discovery limits we use the statistical significance [28] defined as(4)SS=2(S+B)ln⁡(1+SB)-S,where S and B are the numbers of the signal and background events, respectively. In Figures 5–7, the integrated luminosity required to reach 3σ significance for the signal of t′ anomalous interactions is shown for parametrizations PI, PII, and PIII at the LHC with s=13 TeV. It is seen from these figures that the channel t′→tZ requires more integrated luminosity than the other channels. By requiring the signal significance SS=3, the contour plots of κ/Λ and mass of t′ quark are presented in Figure 8. The results show that one can discover the t′ quark anomalous couplings κ/Λ down to 0.1 TeV−1 in the tg channel for mt′=750 GeV.Figure 5
Integrated luminosity required to reach3σ significance for the signal of t′ anomalous interactions for parametrization PI at the LHC with s=13 TeV.Figure 6
The same as Figure5, but for parametrization PII.Figure 7
The same as Figure5, but for parametrization PIII.Figure 8
The contour plot of anomalous coupling and mass of new heavy quarkt′ for the dynamical parametrization explained in the text with a significance of  3σ at s=13 TeV and Lint=100 fb−1.


#### 4.1.1. Simulation fort′ Signal

In order to include detector effects in the simulation, we have generatedtV (where V=γ, g, and Z) signal events for each subprocess and they are mixed using the “event_mixer” script which can be found within the CALCHEP package [26]. For further decay and hadronization these events are passed to PYTHIA [29] and simulated with the PGS4 program [30] using generic LHC detector parameters. This fast simulation includes the important detector effects such as tracking, smearing effects of the calorimeters, resolution, and tag efficiencies. The EXROOTANALYSIS package [31] is used for the simulated events and the output is analyzed and histogrammed with the ROOT [32] macros. We consider jets (up to five), leptons (electrons or muons), photons, and missing transverse momentum within the simulated events for the tγ, tj, and tZ events generation. The typical kinematical distributions are shown in Figures 9-10.Figure 9
Transverse momentum distributions of leading jet (Jet 1) and other jets (Jet 2 and Jet 3) and photon for signal (tγ production) after detector simulation.Figure 10
Transverse momentum distributions of leading jet (Jet 1) and other jets (Jet 2 and Jet 3) and photon for background (Wjγ production).In the analysis, the signal (withκ/Λ=0.2 TeV−1 and mt′=700 GeV) and the corresponding background (WjV) are taken into account. The s-channel contribution to the signal process appears as a resonance around the t′ mass value in the reconstructed invariant mass mt′rec. The reconstructed mass distribution for the t′ signal (reconstructed from a top quark and a vector boson) is shown in Figure 11.Figure 11
The reconstructed mass distributions for background and signal (tγ) with mt′=700 GeV and κ/Λ=0.15 TeV−1.Similar to the single top processes, the top quark in the final state is reconstructed from a leading jet (commonlybjet) and a W boson (which can be reconstructed from its leptonic or hadronic decay). For the tγ production we require systematically the large transverse momentum of photon (pTγ>100 GeV), minimum jet transverse momentum (pTj>20 GeV), and the pseudorapidity range (ηj,γ<2.5) in addition to the requirements on mass reconstruction of W-boson and top quark. The large pTγ and the requirement of single b-tagging allow a better separation of the signal (for tγ channel) from the background. Other channels for tg and tZ productions are more challenging due to a large number of jets, which require additional discriminators such as angular and/or total transverse energy variables. However, in order to get rid of the backgrounds from Wt and tt¯ production (for a similar framework the production cross sections are about 25 pb and 340 pb, resp.), one can consider the channel 3l+bjet+MET for a distinctive signal from the t′→tZ. An analysis of the investigation of single top production with similar backgrounds at the LHC can be found in [33–35].


### 4.2.  Analysis of the Processpp→bV+X  (V=g,Z,γ) for b′ Signal

The signal processpp→bV+X (V=g,Z,γ) includes the new heavy quark b′ exchange in both the s-channel and the t-channel. The s-channel contributes to the signal process as resonance around the b′ mass value in the bV invariant mass, while the t-channel contributes to the nonresonant behaviour. For this process, we consider the leptonic decay of Z boson. In the analyses, we consider the b′ signal to be bjet+γ, bjet+j, and bjet+dilepton.We have obtained the cross sections by using the pseudorapidity cutsηj,γ<2.5 and transverse momentum cuts pTj,γ>20–200 GeV for jets and photon, in Table 11 (Tables 12 and 13) for PI (PII, PIII) parametrizations, respectively. Invariant mass distribution of the bV (where V=γ, g, and Z) system is shown in Figure 12 for PI parametrization of the signal with κ/Λ=0.2 TeV−1 and mb′=700 GeV at the center of mass energy s=13 TeV. It appears from signal significance calculation that the optimized transverse momentum cut is pT>200 GeV for b′ analyses.Table 11
The cross sections (in pb) forb′ signal in different decay channel for parametrization PI with pT cuts on the jets and photon and |ηj,γ|<2.5 at the center of mass energy s = 13 TeV.
SignalMass (GeV)
PI
p
T
>
20 GeV
p
T
>
50 GeV
p
T
>
100 GeV
p
T
>
200 GeV
p
p
→
b
γ
+
X
500
5.64
×
1
0
-
2
5.62
×
1
0
-
2
5.49
×
1
0
-
2
3.95
×
1
0
-
2
600
3.96
×
1
0
-
2
3.96
×
1
0
-
2
3.90
×
1
0
-
2
3.33
×
1
0
-
2
700
2.87
×
1
0
-
2
2.87
×
1
0
-
2
2.86
×
1
0
-
2
2.59
×
1
0
-
2
800
2.12
×
1
0
-
2
2.13
×
1
0
-
2
2.12
×
1
0
-
2
1.99
×
1
0
-
2
900
1.60
×
1
0
-
2
1.60
×
1
0
-
2
1.60
×
1
0
-
2
1.53
×
1
0
-
2
1000
1.22
×
1
0
-
2
1.22
×
1
0
-
2
1.22
×
1
0
-
2
1.19
×
1
0
-
2
p
p
→
b
g
+
X
500
8.13
×
1
0
0
8.13
×
1
0
0
7.93
×
1
0
0
5.96
×
1
0
0
600
5.59
×
1
0
0
5.59
×
1
0
0
5.53
×
1
0
0
4.88
×
1
0
0
700
3.98
×
1
0
0
3.98
×
1
0
0
3.96
×
1
0
0
3.73
×
1
0
0
800
2.91
×
1
0
0
2.91
×
1
0
0
2.90
×
1
0
0
2.81
×
1
0
0
900
2.16
×
1
0
0
2.16
×
1
0
0
2.16
×
1
0
0
2.14
×
1
0
0
1000
1.64
×
1
0
0
1.63
×
1
0
0
1.63
×
1
0
0
1.62
×
1
0
0
p
p
→
b
Z
+
X
500
7.87
×
1
0
-
1
7.81
×
1
0
-
1
7.50
×
1
0
-
1
4.79
×
1
0
-
1
600
5.48
×
1
0
-
1
5.48
×
1
0
-
1
5.31
×
1
0
-
1
4.27
×
1
0
-
1
700
3.95
×
1
0
-
1
3.94
×
1
0
-
1
3.86
×
1
0
-
1
3.39
×
1
0
-
1
800
2.92
×
1
0
-
1
2.91
×
1
0
-
1
2.86
×
1
0
-
1
2.61
×
1
0
-
1
900
2.18
×
1
0
-
1
2.18
×
1
0
-
1
2.15
×
1
0
-
1
2.02
×
1
0
-
1
1000
1.66
×
1
0
-
1
1.66
×
1
0
-
1
1.64
×
1
0
-
1
1.56
×
1
0
-
1Table 12
The same as Table11, but for parametrization PII.
SignalMass (GeV)
PII
p
T
>
20 GeV
p
T
>
50 GeV
p
T
>
100 GeV
p
T
>
200 GeV
p
p
→
b
γ
+
X
500
5.18
×
1
0
-
3
5.26
×
1
0
-
3
5.04
×
1
0
-
3
3.54
×
1
0
-
3
600
3.38
×
1
0
-
3
3.37
×
1
0
-
3
3.36
×
1
0
-
3
2.77
×
1
0
-
3
700
2.32
×
1
0
-
3
2.31
×
1
0
-
3
2.30
×
1
0
-
3
2.05
×
1
0
-
3
800
1.71
×
1
0
-
3
1.63
×
1
0
-
3
1.64
×
1
0
-
3
1.50
×
1
0
-
3
900
1.17
×
1
0
-
3
1.16
×
1
0
-
3
1.17
×
1
0
-
3
1.11
×
1
0
-
3
1000
8.60
×
1
0
-
4
8.58
×
1
0
-
4
8.55
×
1
0
-
4
8.24
×
1
0
-
4
p
p
→
b
g
+
X
500
7.40
×
1
0
-
1
7.39
×
1
0
-
1
7.21
×
1
0
-
1
5.16
×
1
0
-
1
600
4.83
×
1
0
-
1
4.80
×
1
0
-
1
4.81
×
1
0
-
1
3.98
×
1
0
-
1
700
3.22
×
1
0
-
1
3.22
×
1
0
-
1
3.20
×
1
0
-
1
2.89
×
1
0
-
1
800
2.24
×
1
0
-
1
2.21
×
1
0
-
1
2.21
×
1
0
-
1
2.04
×
1
0
-
1
900
1.5
×
1
0
-
1
1.58
×
1
0
-
1
1.58
×
1
0
-
1
1.49
×
1
0
-
1
1000
1.14
×
1
0
-
1
1.14
×
1
0
-
1
1.13
×
1
0
-
1
1.10
×
1
0
-
1
p
p
→
b
Z
+
X
500
6.89
×
1
0
-
2
6.85
×
1
0
-
2
6.45
×
1
0
-
2
4.23
×
1
0
-
2
600
4.52
×
1
0
-
2
4.51
×
1
0
-
2
4.34
×
1
0
-
2
3.53
×
1
0
-
2
700
3.12
×
1
0
-
2
3.11
×
1
0
-
2
3.05
×
1
0
-
2
2.65
×
1
0
-
2
800
2.19
×
1
0
-
2
2.18
×
1
0
-
2
2.15
×
1
0
-
2
1.95
×
1
0
-
2
900
1.56
×
1
0
-
2
1.56
×
1
0
-
2
1.55
×
1
0
-
2
1.44
×
1
0
-
2
1000
1.14
×
1
0
-
2
1.13
×
1
0
-
2
1.13
×
1
0
-
2
1.07
×
1
0
-
2Table 13
The same as Table11, but for parametrization PIII.
SignalMass (GeV)
PIII
p
T
>
20 GeV
p
T
>
50 GeV
p
T
>
100 GeV
p
T
>
200 GeV
p
p
→
b
γ
+
X
500
13.1
×
1
0
-
2
13.14
×
1
0
-
2
12.75
×
1
0
-
2
8.92
×
1
0
-
2
600
8.59
×
1
0
-
2
8.58
×
1
0
-
2
8.44
×
1
0
-
2
7.03
×
1
0
-
2
700
5.82
×
1
0
-
2
5.82
×
1
0
-
2
5.77
×
1
0
-
2
5.17
×
1
0
-
2
800
4.07
×
1
0
-
2
4.07
×
1
0
-
2
4.06
×
1
0
-
2
3.77
×
1
0
-
2
900
2.92
×
1
0
-
2
2.92
×
1
0
-
2
2.91
×
1
0
-
2
2.77
×
1
0
-
2
1000
2.14
×
1
0
-
2
2.13
×
1
0
-
2
2.13
×
1
0
-
2
2.06
×
1
0
-
2
p
p
→
b
g
+
X
500
19.04
×
1
0
0
18.96
×
1
0
0
18.43
×
1
0
0
12.86
×
1
0
0
600
12.19
×
1
0
0
12.13
×
1
0
0
11.93
×
1
0
0
9.92
×
1
0
0
700
8.08
×
1
0
0
8.07
×
1
0
0
8.02
×
1
0
0
7.17
×
1
0
0
800
5.57
×
1
0
0
5.57
×
1
0
0
5.55
×
1
0
0
5.15
×
1
0
0
900
3.94
×
1
0
0
3.94
×
1
0
0
3.94
×
1
0
0
3.74
×
1
0
0
1000
2.85
×
1
0
0
2.85
×
1
0
0
2.85
×
1
0
0
2.74
×
1
0
0
p
p
→
b
Z
+
X
500
1.76
×
1
0
0
1.75
×
1
0
0
1.65
×
1
0
0
1.05
×
1
0
0
600
1.15
×
1
0
0
1.14
×
1
0
0
1.11
×
1
0
0
8.80
×
1
0
-
1
700
7.83
×
1
0
-
1
7.80
×
1
0
-
1
7.60
×
1
0
-
1
6.61
×
1
0
-
1
800
5.47
×
1
0
-
1
5.41
×
1
0
-
1
5.31
×
1
0
-
1
4.80
×
1
0
-
1
900
3.92
×
1
0
-
1
3.90
×
1
0
-
1
3.82
×
1
0
-
1
3.60
×
1
0
-
1
1000
2.86
×
1
0
-
1
2.82
×
1
0
-
1
2.80
×
1
0
-
1
2.62
×
1
0
-
1Figure 12
Invariant mass distribution of thebV (where V=γ, g, and Z) system is shown in Figure 5 for PI parametrization of the signal with κ/Λ=0.2 TeV−1 and mb′=700 GeV at the center of mass energy s=13 TeV.The backgrounds for the final stateb(b¯)V (where V≡ photon, jet, and Z boson) are given in Table 14. We apply the following cuts to the final state photon and jets as ηj,γ<2.5 and pTj,γ>20–200 GeV. It can be noted that the background cross section decreases as the pT cuts increase. We assume the efficiency for b-tagging to be εb=50% and the rejection ratios to be 10% for c(c¯) quark jets and 1% for light quark jets.Table 14
The cross sections (in pb) for the backgrounds (b(b-)V, c(c-)V, and jV, where V = photon, jet, and Z boson) with pT cuts on the jets and photon at the center of mass energy s = 13 TeV.
Background
p
T
>
20 GeV
p
T
>
50 GeV
p
T
>
100 GeV
p
T
>
200 GeV
p
p
→
b
(
b
-
)
γ
+
X
2.99
×
1
0
3
1.35
×
1
0
2
9.04
×
1
0
0
4.02
×
1
0
-
1
p
p
→
c
(
c
-
)
γ
+
X
1.87
×
1
0
4
8.15
×
1
0
2
5.40
×
1
0
1
2.43
×
1
0
0
p
p
→
j
γ
+
X
5.43
×
1
0
4
3.27
×
1
0
3
3.38
×
1
0
2
2.85
×
1
0
1
p
p
→
b
(
b
-
)
j
+
X
7.83
×
1
0
6
3.05
×
1
0
5
1.92
×
1
0
4
8.93
×
1
0
2
p
p
→
c
(
c
-
)
j
+
X
1.22
×
1
0
7
4.55
×
1
0
5
2.89
×
1
0
4
1.35
×
1
0
3
p
p
→
j
j
+
X
2.43
×
1
0
8
8.54
×
1
0
6
5.44
×
1
0
5
2.80
×
1
0
4
p
p
→
b
(
b
-
)
Z
+
X
5.02
×
1
0
2
1.35
×
1
0
2
2.25
×
1
0
1
1.56
×
1
0
0
p
p
→
c
(
c
-
)
Z
+
X
5.96
×
1
0
2
1.58
×
1
0
2
2.64
×
1
0
1
1.83
×
1
0
0
p
p
→
j
Z
+
X
8.00
×
1
0
3
2.08
×
1
0
3
4.08
×
1
0
2
4.12
×
1
0
1In order to reach3σ significance for the signal of b′ anomalous interactions the required integrated luminosity is shown in Figures 13–15 for parametrizations PI, PII, and PIII at the LHC with s=13 TeV. The channel b′→bγ requires more integrated luminosity than the other channels. By requiring the signal significance SS=3, the contour plots of κ/Λ and mass of b′ quark are presented in Figure 16. The results show that one can discover the b′ quark anomalous couplings down to 0.1 in the bg channel for mb′=500 GeV.Figure 13
Integrated luminosity required to reach3σ significance for the signal of b′ anomalous interactions for parametrization PI at the LHC with s=13 TeV.Figure 14
The same as Figure13, but for parametrization PII.Figure 15
The same as Figure13, but for parametrization PIII.Figure 16
The contour plot of anomalous coupling and mass of new heavy quarkb′ for the dynamical parametrization explained in the text with a significance of  3σ at s=13 TeV and Lint=100 fb−1.


#### 4.2.1. Simulation forb′ Signal

In the simulation, we have generatedbV (where V=γ, g, and Z) events for each subprocess and these events are simulated using generic detector parameters to include detector effects such as tracking, tagging efficiencies, and smearing effects. After the simulation, the typical kinematical distributions are shown in Figures 17-18.Figure 17
Transverse momentum distributions of leading jet and photon (bγ production) for signal after detector simulation.Figure 18
Transverse momentum distributions of leading jet and photon (jγ production) for background at the given conditions mentioned in the text.In the analysis, the signal (withκ/Λ=0.3 TeV−1 and mb′=700 GeV) and the corresponding background are taken into account. The invariant mass of the new heavy quark b′ can be reconstructed from a bjet and a neutral gauge boson (where the Z boson can also be reconstructed from its dilepton or hadronic decay). For the bγ production, we require a large pTγ (>100 GeV) for photon and large pTj (>100 GeV) for jet and pseudorapidity ηj,γ (<2.5). For the bγ signal channel, the invariant mass distributions for signal and background events are shown in Figure 19. The large pTj,γ and the requirement of single b-tagging allow a better separation of the signal (for bγ channel) from the background, and then we find a precise limit for the anomalous coupling in this channel. For the bg and bZ production, we require two high pT jets (one b-jet) and a high pT jet in addition to the reconstructed mass mZrec, respectively. The main character of the signal is the high pTj and/or pTγ and single b-tagged jet. We calculate the signal and background events in the range mb′recGeV-700GeV<50 GeV and we find a similar significance as shown in Figure 16.Figure 19
The reconstructed mass distributions for background and signal (bγ) with mb′=700 GeV and κ/Λ=0.3 TeV−1.


## 4.1. Analysis of the Processpp→W+bV+X  (V=g,Z,γ) for t′ Signal

The signal processpp→W+bV+X (V=g,Z,γ) includes the t′ exchange in both the s-channel and t-channel. The s-channel contribution to the signal process would appear itself as resonance around the t′ mass value in the WbV invariant mass. The t-channel gives the nonresonant contribution. We consider that the W boson decays into lepton + missing transverse momentum with the branching ratio of 21% and Z boson decays into dilepton with the branching ratio of  6.7%. In our analyses, we consider the t′ signal in the l+bjet+γ+MET, l+bjet+j+MET, and 3l+bjet+MET channels, where l=e,μ. However, if one takes the hadronic W decay, the signal will be enhanced by a factor of BR(W→hadrons)/BR(W→lν).We have obtained the cross sections by using the cuts pseudorapidityηj,γ<2.5 and transverse momentum pTj,γ>20–200 GeV for jets and photon, in Table 7 (Tables 8 and 9) for PI (PII, PIII) parametrization, respectively. Invariant mass distribution of the tV (where V=γ, g, and Z) system is shown in Figure 4 for PI parametrization of the signal with κ/Λ=0.2 TeV−1 and mt′=700 GeV at the center of mass energy s=13 TeV. It appears from signal significance calculations that the optimized transverse momentum cut is pTj,γ>100 GeV for t′ analyses.Table 7
The cross sections (in pb) fort′ signal in different decay channels for PI parametrization with pT cuts on the jets and photon and |ηj,γ|<2.5 at the center of mass energy s = 13 TeV.
SignalMass (GeV)
PI
p
T
>
20 GeV
p
T
>
50 GeV
p
T
>
100 GeV
p
T
>
200 GeV
p
p
→
W
+
b
γ
+
X
500
2.89
×
1
0
-
1
2.10
×
1
0
-
1
1.24
×
1
0
-
1
1.02
×
1
0
-
4
600
2.43
×
1
0
-
1
1.64
×
1
0
-
1
1.19
×
1
0
-
1
1.23
×
1
0
-
2
700
1.68
×
1
0
-
1
1.2
×
1
0
-
1
1.12
×
1
0
-
1
2.25
×
1
0
-
2
800
1.30
×
1
0
-
1
1.03
×
1
0
-
1
7.53
×
1
0
-
2
3.25
×
1
0
-
2
900
1.02
×
1
0
-
1
8.08
×
1
0
-
2
6.96
×
1
0
-
2
3.02
×
1
0
-
2
1000
7.61
×
1
0
-
2
6.35
×
1
0
-
2
5.07
×
1
0
-
2
2.94
×
1
0
-
2
p
p
→
W
+
b
g
+
X
500
7.78
×
1
0
0
6.02
×
1
0
0
3.63
×
1
0
0
4.74
×
1
0
-
3
600
6.30
×
1
0
0
5.18
×
1
0
0
3.13
×
1
0
0
2.58
×
1
0
-
1
700
4.99
×
1
0
0
3.63
×
1
0
0
3.04
×
1
0
0
9.32
×
1
0
-
1
800
4.01
×
1
0
0
3.45
×
1
0
0
2.76
×
1
0
0
9.91
×
1
0
-
1
900
3.32
×
1
0
0
2.77
×
1
0
0
2.13
×
1
0
0
1.08
×
1
0
0
1000
2.58
×
1
0
0
2.27
×
1
0
0
1.88
×
1
0
0
1.01
×
1
0
0
p
p
→
W
+
b
Z
+
X
500
7.96
×
1
0
-
1
6.01
×
1
0
-
1
3.01
×
1
0
-
1
1.01
×
1
0
-
4
600
4.79
×
1
0
-
1
3.86
×
1
0
-
1
2.45
×
1
0
-
1
2.71
×
1
0
-
3
700
3.99
×
1
0
-
1
3.12
×
1
0
-
1
2.39
×
1
0
-
1
6.96
×
1
0
-
2
800
3.31
×
1
0
-
1
2.89
×
1
0
-
1
2.09
×
1
0
-
1
8.05
×
1
0
-
2
900
2.73
×
1
0
-
1
2.73
×
1
0
-
1
1.91
×
1
0
-
1
9.54
×
1
0
-
2
1000
2.23
×
1
0
-
1
2.02
×
1
0
-
1
1.61
×
1
0
-
1
9.10
×
1
0
-
2Table 8
The same as Table7, but for parametrization PII.
SignalMass (GeV)
PII
p
T
>
20 GeV
p
T
>
50 GeV
p
T
>
100 GeV
p
T
>
200 GeV
p
p
→
W
+
b
γ
+
X
500
6.78
×
1
0
-
3
5.07
×
1
0
-
3
3.45
×
1
0
-
3
2.64
×
1
0
-
7
600
6.57
×
1
0
-
3
5.42
×
1
0
-
3
3.47
×
1
0
-
3
5.34
×
1
0
-
4
700
5.02
×
1
0
-
3
4.31
×
1
0
-
3
3.04
×
1
0
-
3
8.73
×
1
0
-
4
800
3.91
×
1
0
-
3
3.76
×
1
0
-
3
2.56
×
1
0
-
3
1.03
×
1
0
-
3
900
3.03
×
1
0
-
3
2.68
×
1
0
-
3
2.11
×
1
0
-
3
1.01
×
1
0
-
3
1000
2.40
×
1
0
-
3
2.43
×
1
0
-
3
1.77
×
1
0
-
3
9.98
×
1
0
-
4
p
p
→
W
+
b
g
+
X
500
3.47
×
1
0
-
1
2.68
×
1
0
-
1
1.52
×
1
0
-
1
5.30
×
1
0
-
6
600
2.51
×
1
0
-
1
2.12
×
1
0
-
1
1.35
×
1
0
-
1
2.01
×
1
0
-
2
700
1.87
×
1
0
-
1
1.6
×
1
0
-
1
1.16
×
1
0
-
1
3.42
×
1
0
-
2
800
1.46
×
1
0
-
1
1.25
×
1
0
-
1
9.39
×
1
0
-
2
4.03
×
1
0
-
2
900
1.12
×
1
0
-
1
1.08
×
1
0
-
1
7.80
×
1
0
-
2
3.86
×
1
0
-
2
1000
9.35
×
1
0
-
2
8.37
×
1
0
-
2
6.62
×
1
0
-
2
3.68
×
1
0
-
2
p
p
→
W
+
b
Z
+
X
500
2.10
×
1
0
-
2
1.77
×
1
0
-
2
1.16
×
1
0
-
2
2.64
×
1
0
-
7
600
1.95
×
1
0
-
2
1.75
×
1
0
-
2
1.14
×
1
0
-
2
1.34
×
1
0
-
3
700
1.73
×
1
0
-
2
1.43
×
1
0
-
2
1.00
×
1
0
-
2
2.9
×
1
0
-
3
800
1.34
×
1
0
-
2
1.19
×
1
0
-
2
8.89
×
1
0
-
3
3.42
×
1
0
-
3
900
1.06
×
1
0
-
2
9.55
×
1
0
-
3
7.63
×
1
0
-
3
3.37
×
1
0
-
3
1000
8.09
×
1
0
-
3
7.58
×
1
0
-
3
6.31
×
1
0
-
3
3.23
×
1
0
-
3Table 9
The same as Table7, but for parametrization PIII.
SignalMass (GeV)
PIII
p
T
>
20 GeV
p
T
>
50 GeV
p
T
>
100 GeV
p
T
>
200 GeV
p
p
→
W
+
b
γ
+
X
500
2.60
×
1
0
-
1
2.78
×
1
0
-
1
1.08
×
1
0
-
1
1.59
×
1
0
-
4
600
1.78
×
1
0
-
1
1.61
×
1
0
-
1
1.01
×
1
0
-
1
1.42
×
1
0
-
2
700
1.56
×
1
0
-
1
1.35
×
1
0
-
1
9.33
×
1
0
-
2
2.72
×
1
0
-
2
800
1.17
×
1
0
-
1
1.06
×
1
0
-
1
7.84
×
1
0
-
2
3.32
×
1
0
-
2
900
9.04
×
1
0
-
2
8.42
×
1
0
-
2
6.68
×
1
0
-
2
3.25
×
1
0
-
2
1000
7.60
×
1
0
-
2
6.76
×
1
0
-
2
5.16
×
1
0
-
2
3.17
×
1
0
-
2
p
p
→
W
+
b
g
+
X
500
8.39
×
1
0
0
6.49
×
1
0
0
3.86
×
1
0
0
4.65
×
1
0
-
3
600
6.10
×
1
0
0
5.78
×
1
0
0
3.81
×
1
0
0
5.56
×
1
0
-
1
700
5.39
×
1
0
0
4.64
×
1
0
0
3.41
×
1
0
0
9.70
×
1
0
-
1
800
3.94
×
1
0
0
3.54
×
1
0
0
2.73
×
1
0
0
1.05
×
1
0
0
900
3.24
×
1
0
0
2.76
×
1
0
0
2.27
×
1
0
0
1.07
×
1
0
0
1000
2.33
×
1
0
0
2.29
×
1
0
0
1.84
×
1
0
0
9.98
×
1
0
-
1
p
p
→
W
+
b
Z
+
X
500
7.72
×
1
0
-
1
1.01
×
1
0
0
2.17
×
1
0
-
1
6.27
×
1
0
-
4
600
6.24
×
1
0
-
1
3.85
×
1
0
-
1
2.92
×
1
0
-
1
3.20
×
1
0
-
2
700
5.00
×
1
0
-
1
3.05
×
1
0
-
1
2.86
×
1
0
-
1
5.80
×
1
0
-
2
800
3.78
×
1
0
-
1
2.50
×
1
0
-
1
2.42
×
1
0
-
1
9.64
×
1
0
-
2
900
3.04
×
1
0
-
1
1.67
×
1
0
-
1
2.06
×
1
0
-
1
9.62
×
1
0
-
2
1000
2.51
×
1
0
-
1
1.29
×
1
0
-
1
1.48
×
1
0
-
1
9.61
×
1
0
-
2Figure 4
Invariant mass distributionsmtV (where V=γ, g, and Z) for PI parametrization of the signal with κ/Λ=0.2 TeV−1 and mt′=700 GeV at the center of mass energy s=13 TeV.The backgrounds for the final stateW+b(b¯)V (where V≡photon, jet, and Z boson) are given in Table 10. We apply the following cuts to the final state photon and jets as |ηj,γ|<2.5 and pTj,γ>20–200 GeV. For the background cross section estimates, we assume the efficiency for b-tagging to be εb=50% and the rejection ratios to be 10% for c(c¯) quark jets and 1% for light quark jets since they are assumed to be mistagged as b-jets.Table 10
The cross sections (in pb) for the relevant backgrounds (W+b(b-)V, W+c(c-)V, and W+jV, where V = photon, jet, and Z boson) with pT cuts on the jets at the center of mass energy s = 13 TeV.
Background
p
T
>
20 GeV
p
T
>
50 GeV
p
T
>
100 GeV
p
T
>
200 GeV
p
p
→
W
+
b
γ
+
X
2.37
×
1
0
-
3
3.62
×
1
0
-
4
6.17
×
1
0
-
5
6.99
×
1
0
-
6
p
p
→
W
+
c
-
γ
+
X
4.15
×
1
0
0
4.59
×
1
0
-
1
6.25
×
1
0
-
2
6.21
×
1
0
-
3
p
p
→
W
+
j
γ
+
X
2.63
×
1
0
1
4.30
×
1
0
0
7.33
×
1
0
-
1
1.27
×
1
0
-
1
p
p
→
W
+
b
(
b
-
)
j
+
X
7.26
×
1
0
1
3.02
×
1
0
1
6.11
×
1
0
0
9.74
×
1
0
-
1
p
p
→
W
+
c
(
c
-
)
j
+
X
5.98
×
1
0
2
9.65
×
1
0
1
1.79
×
1
0
1
2.42
×
1
0
0
p
p
→
W
+
j
j
+
X
7.31
×
1
0
3
7.78
×
1
0
2
1.61
×
1
0
2
2.58
×
1
0
1
p
p
→
W
+
b
Z
+
X
6.26
×
1
0
-
4
3.99
×
1
0
-
4
1.93
×
1
0
-
4
4.71
×
1
0
-
5
p
p
→
W
+
c
-
Z
+
X
5.29
×
1
0
-
1
3.40
×
1
0
-
1
1.66
×
1
0
-
1
4.15
×
1
0
-
2
p
p
→
W
+
j
Z
+
X
8.59
×
1
0
0
4.83
×
1
0
0
2.49
×
1
0
0
7.91
×
1
0
-
1In order to find the discovery limits we use the statistical significance [28] defined as(4)SS=2(S+B)ln⁡(1+SB)-S,where S and B are the numbers of the signal and background events, respectively. In Figures 5–7, the integrated luminosity required to reach 3σ significance for the signal of t′ anomalous interactions is shown for parametrizations PI, PII, and PIII at the LHC with s=13 TeV. It is seen from these figures that the channel t′→tZ requires more integrated luminosity than the other channels. By requiring the signal significance SS=3, the contour plots of κ/Λ and mass of t′ quark are presented in Figure 8. The results show that one can discover the t′ quark anomalous couplings κ/Λ down to 0.1 TeV−1 in the tg channel for mt′=750 GeV.Figure 5
Integrated luminosity required to reach3σ significance for the signal of t′ anomalous interactions for parametrization PI at the LHC with s=13 TeV.Figure 6
The same as Figure5, but for parametrization PII.Figure 7
The same as Figure5, but for parametrization PIII.Figure 8
The contour plot of anomalous coupling and mass of new heavy quarkt′ for the dynamical parametrization explained in the text with a significance of  3σ at s=13 TeV and Lint=100 fb−1.


### 4.1.1. Simulation fort′ Signal

In order to include detector effects in the simulation, we have generatedtV (where V=γ, g, and Z) signal events for each subprocess and they are mixed using the “event_mixer” script which can be found within the CALCHEP package [26]. For further decay and hadronization these events are passed to PYTHIA [29] and simulated with the PGS4 program [30] using generic LHC detector parameters. This fast simulation includes the important detector effects such as tracking, smearing effects of the calorimeters, resolution, and tag efficiencies. The EXROOTANALYSIS package [31] is used for the simulated events and the output is analyzed and histogrammed with the ROOT [32] macros. We consider jets (up to five), leptons (electrons or muons), photons, and missing transverse momentum within the simulated events for the tγ, tj, and tZ events generation. The typical kinematical distributions are shown in Figures 9-10.Figure 9
Transverse momentum distributions of leading jet (Jet 1) and other jets (Jet 2 and Jet 3) and photon for signal (tγ production) after detector simulation.Figure 10
Transverse momentum distributions of leading jet (Jet 1) and other jets (Jet 2 and Jet 3) and photon for background (Wjγ production).In the analysis, the signal (withκ/Λ=0.2 TeV−1 and mt′=700 GeV) and the corresponding background (WjV) are taken into account. The s-channel contribution to the signal process appears as a resonance around the t′ mass value in the reconstructed invariant mass mt′rec. The reconstructed mass distribution for the t′ signal (reconstructed from a top quark and a vector boson) is shown in Figure 11.Figure 11
The reconstructed mass distributions for background and signal (tγ) with mt′=700 GeV and κ/Λ=0.15 TeV−1.Similar to the single top processes, the top quark in the final state is reconstructed from a leading jet (commonlybjet) and a W boson (which can be reconstructed from its leptonic or hadronic decay). For the tγ production we require systematically the large transverse momentum of photon (pTγ>100 GeV), minimum jet transverse momentum (pTj>20 GeV), and the pseudorapidity range (ηj,γ<2.5) in addition to the requirements on mass reconstruction of W-boson and top quark. The large pTγ and the requirement of single b-tagging allow a better separation of the signal (for tγ channel) from the background. Other channels for tg and tZ productions are more challenging due to a large number of jets, which require additional discriminators such as angular and/or total transverse energy variables. However, in order to get rid of the backgrounds from Wt and tt¯ production (for a similar framework the production cross sections are about 25 pb and 340 pb, resp.), one can consider the channel 3l+bjet+MET for a distinctive signal from the t′→tZ. An analysis of the investigation of single top production with similar backgrounds at the LHC can be found in [33–35].


## 4.1.1. Simulation fort′ Signal

In order to include detector effects in the simulation, we have generatedtV (where V=γ, g, and Z) signal events for each subprocess and they are mixed using the “event_mixer” script which can be found within the CALCHEP package [26]. For further decay and hadronization these events are passed to PYTHIA [29] and simulated with the PGS4 program [30] using generic LHC detector parameters. This fast simulation includes the important detector effects such as tracking, smearing effects of the calorimeters, resolution, and tag efficiencies. The EXROOTANALYSIS package [31] is used for the simulated events and the output is analyzed and histogrammed with the ROOT [32] macros. We consider jets (up to five), leptons (electrons or muons), photons, and missing transverse momentum within the simulated events for the tγ, tj, and tZ events generation. The typical kinematical distributions are shown in Figures 9-10.Figure 9
Transverse momentum distributions of leading jet (Jet 1) and other jets (Jet 2 and Jet 3) and photon for signal (tγ production) after detector simulation.Figure 10
Transverse momentum distributions of leading jet (Jet 1) and other jets (Jet 2 and Jet 3) and photon for background (Wjγ production).In the analysis, the signal (withκ/Λ=0.2 TeV−1 and mt′=700 GeV) and the corresponding background (WjV) are taken into account. The s-channel contribution to the signal process appears as a resonance around the t′ mass value in the reconstructed invariant mass mt′rec. The reconstructed mass distribution for the t′ signal (reconstructed from a top quark and a vector boson) is shown in Figure 11.Figure 11
The reconstructed mass distributions for background and signal (tγ) with mt′=700 GeV and κ/Λ=0.15 TeV−1.Similar to the single top processes, the top quark in the final state is reconstructed from a leading jet (commonlybjet) and a W boson (which can be reconstructed from its leptonic or hadronic decay). For the tγ production we require systematically the large transverse momentum of photon (pTγ>100 GeV), minimum jet transverse momentum (pTj>20 GeV), and the pseudorapidity range (ηj,γ<2.5) in addition to the requirements on mass reconstruction of W-boson and top quark. The large pTγ and the requirement of single b-tagging allow a better separation of the signal (for tγ channel) from the background. Other channels for tg and tZ productions are more challenging due to a large number of jets, which require additional discriminators such as angular and/or total transverse energy variables. However, in order to get rid of the backgrounds from Wt and tt¯ production (for a similar framework the production cross sections are about 25 pb and 340 pb, resp.), one can consider the channel 3l+bjet+MET for a distinctive signal from the t′→tZ. An analysis of the investigation of single top production with similar backgrounds at the LHC can be found in [33–35].


## 4.2.  Analysis of the Processpp→bV+X  (V=g,Z,γ) for b′ Signal

The signal processpp→bV+X (V=g,Z,γ) includes the new heavy quark b′ exchange in both the s-channel and the t-channel. The s-channel contributes to the signal process as resonance around the b′ mass value in the bV invariant mass, while the t-channel contributes to the nonresonant behaviour. For this process, we consider the leptonic decay of Z boson. In the analyses, we consider the b′ signal to be bjet+γ, bjet+j, and bjet+dilepton.We have obtained the cross sections by using the pseudorapidity cutsηj,γ<2.5 and transverse momentum cuts pTj,γ>20–200 GeV for jets and photon, in Table 11 (Tables 12 and 13) for PI (PII, PIII) parametrizations, respectively. Invariant mass distribution of the bV (where V=γ, g, and Z) system is shown in Figure 12 for PI parametrization of the signal with κ/Λ=0.2 TeV−1 and mb′=700 GeV at the center of mass energy s=13 TeV. It appears from signal significance calculation that the optimized transverse momentum cut is pT>200 GeV for b′ analyses.Table 11
The cross sections (in pb) forb′ signal in different decay channel for parametrization PI with pT cuts on the jets and photon and |ηj,γ|<2.5 at the center of mass energy s = 13 TeV.
SignalMass (GeV)
PI
p
T
>
20 GeV
p
T
>
50 GeV
p
T
>
100 GeV
p
T
>
200 GeV
p
p
→
b
γ
+
X
500
5.64
×
1
0
-
2
5.62
×
1
0
-
2
5.49
×
1
0
-
2
3.95
×
1
0
-
2
600
3.96
×
1
0
-
2
3.96
×
1
0
-
2
3.90
×
1
0
-
2
3.33
×
1
0
-
2
700
2.87
×
1
0
-
2
2.87
×
1
0
-
2
2.86
×
1
0
-
2
2.59
×
1
0
-
2
800
2.12
×
1
0
-
2
2.13
×
1
0
-
2
2.12
×
1
0
-
2
1.99
×
1
0
-
2
900
1.60
×
1
0
-
2
1.60
×
1
0
-
2
1.60
×
1
0
-
2
1.53
×
1
0
-
2
1000
1.22
×
1
0
-
2
1.22
×
1
0
-
2
1.22
×
1
0
-
2
1.19
×
1
0
-
2
p
p
→
b
g
+
X
500
8.13
×
1
0
0
8.13
×
1
0
0
7.93
×
1
0
0
5.96
×
1
0
0
600
5.59
×
1
0
0
5.59
×
1
0
0
5.53
×
1
0
0
4.88
×
1
0
0
700
3.98
×
1
0
0
3.98
×
1
0
0
3.96
×
1
0
0
3.73
×
1
0
0
800
2.91
×
1
0
0
2.91
×
1
0
0
2.90
×
1
0
0
2.81
×
1
0
0
900
2.16
×
1
0
0
2.16
×
1
0
0
2.16
×
1
0
0
2.14
×
1
0
0
1000
1.64
×
1
0
0
1.63
×
1
0
0
1.63
×
1
0
0
1.62
×
1
0
0
p
p
→
b
Z
+
X
500
7.87
×
1
0
-
1
7.81
×
1
0
-
1
7.50
×
1
0
-
1
4.79
×
1
0
-
1
600
5.48
×
1
0
-
1
5.48
×
1
0
-
1
5.31
×
1
0
-
1
4.27
×
1
0
-
1
700
3.95
×
1
0
-
1
3.94
×
1
0
-
1
3.86
×
1
0
-
1
3.39
×
1
0
-
1
800
2.92
×
1
0
-
1
2.91
×
1
0
-
1
2.86
×
1
0
-
1
2.61
×
1
0
-
1
900
2.18
×
1
0
-
1
2.18
×
1
0
-
1
2.15
×
1
0
-
1
2.02
×
1
0
-
1
1000
1.66
×
1
0
-
1
1.66
×
1
0
-
1
1.64
×
1
0
-
1
1.56
×
1
0
-
1Table 12
The same as Table11, but for parametrization PII.
SignalMass (GeV)
PII
p
T
>
20 GeV
p
T
>
50 GeV
p
T
>
100 GeV
p
T
>
200 GeV
p
p
→
b
γ
+
X
500
5.18
×
1
0
-
3
5.26
×
1
0
-
3
5.04
×
1
0
-
3
3.54
×
1
0
-
3
600
3.38
×
1
0
-
3
3.37
×
1
0
-
3
3.36
×
1
0
-
3
2.77
×
1
0
-
3
700
2.32
×
1
0
-
3
2.31
×
1
0
-
3
2.30
×
1
0
-
3
2.05
×
1
0
-
3
800
1.71
×
1
0
-
3
1.63
×
1
0
-
3
1.64
×
1
0
-
3
1.50
×
1
0
-
3
900
1.17
×
1
0
-
3
1.16
×
1
0
-
3
1.17
×
1
0
-
3
1.11
×
1
0
-
3
1000
8.60
×
1
0
-
4
8.58
×
1
0
-
4
8.55
×
1
0
-
4
8.24
×
1
0
-
4
p
p
→
b
g
+
X
500
7.40
×
1
0
-
1
7.39
×
1
0
-
1
7.21
×
1
0
-
1
5.16
×
1
0
-
1
600
4.83
×
1
0
-
1
4.80
×
1
0
-
1
4.81
×
1
0
-
1
3.98
×
1
0
-
1
700
3.22
×
1
0
-
1
3.22
×
1
0
-
1
3.20
×
1
0
-
1
2.89
×
1
0
-
1
800
2.24
×
1
0
-
1
2.21
×
1
0
-
1
2.21
×
1
0
-
1
2.04
×
1
0
-
1
900
1.5
×
1
0
-
1
1.58
×
1
0
-
1
1.58
×
1
0
-
1
1.49
×
1
0
-
1
1000
1.14
×
1
0
-
1
1.14
×
1
0
-
1
1.13
×
1
0
-
1
1.10
×
1
0
-
1
p
p
→
b
Z
+
X
500
6.89
×
1
0
-
2
6.85
×
1
0
-
2
6.45
×
1
0
-
2
4.23
×
1
0
-
2
600
4.52
×
1
0
-
2
4.51
×
1
0
-
2
4.34
×
1
0
-
2
3.53
×
1
0
-
2
700
3.12
×
1
0
-
2
3.11
×
1
0
-
2
3.05
×
1
0
-
2
2.65
×
1
0
-
2
800
2.19
×
1
0
-
2
2.18
×
1
0
-
2
2.15
×
1
0
-
2
1.95
×
1
0
-
2
900
1.56
×
1
0
-
2
1.56
×
1
0
-
2
1.55
×
1
0
-
2
1.44
×
1
0
-
2
1000
1.14
×
1
0
-
2
1.13
×
1
0
-
2
1.13
×
1
0
-
2
1.07
×
1
0
-
2Table 13
The same as Table11, but for parametrization PIII.
SignalMass (GeV)
PIII
p
T
>
20 GeV
p
T
>
50 GeV
p
T
>
100 GeV
p
T
>
200 GeV
p
p
→
b
γ
+
X
500
13.1
×
1
0
-
2
13.14
×
1
0
-
2
12.75
×
1
0
-
2
8.92
×
1
0
-
2
600
8.59
×
1
0
-
2
8.58
×
1
0
-
2
8.44
×
1
0
-
2
7.03
×
1
0
-
2
700
5.82
×
1
0
-
2
5.82
×
1
0
-
2
5.77
×
1
0
-
2
5.17
×
1
0
-
2
800
4.07
×
1
0
-
2
4.07
×
1
0
-
2
4.06
×
1
0
-
2
3.77
×
1
0
-
2
900
2.92
×
1
0
-
2
2.92
×
1
0
-
2
2.91
×
1
0
-
2
2.77
×
1
0
-
2
1000
2.14
×
1
0
-
2
2.13
×
1
0
-
2
2.13
×
1
0
-
2
2.06
×
1
0
-
2
p
p
→
b
g
+
X
500
19.04
×
1
0
0
18.96
×
1
0
0
18.43
×
1
0
0
12.86
×
1
0
0
600
12.19
×
1
0
0
12.13
×
1
0
0
11.93
×
1
0
0
9.92
×
1
0
0
700
8.08
×
1
0
0
8.07
×
1
0
0
8.02
×
1
0
0
7.17
×
1
0
0
800
5.57
×
1
0
0
5.57
×
1
0
0
5.55
×
1
0
0
5.15
×
1
0
0
900
3.94
×
1
0
0
3.94
×
1
0
0
3.94
×
1
0
0
3.74
×
1
0
0
1000
2.85
×
1
0
0
2.85
×
1
0
0
2.85
×
1
0
0
2.74
×
1
0
0
p
p
→
b
Z
+
X
500
1.76
×
1
0
0
1.75
×
1
0
0
1.65
×
1
0
0
1.05
×
1
0
0
600
1.15
×
1
0
0
1.14
×
1
0
0
1.11
×
1
0
0
8.80
×
1
0
-
1
700
7.83
×
1
0
-
1
7.80
×
1
0
-
1
7.60
×
1
0
-
1
6.61
×
1
0
-
1
800
5.47
×
1
0
-
1
5.41
×
1
0
-
1
5.31
×
1
0
-
1
4.80
×
1
0
-
1
900
3.92
×
1
0
-
1
3.90
×
1
0
-
1
3.82
×
1
0
-
1
3.60
×
1
0
-
1
1000
2.86
×
1
0
-
1
2.82
×
1
0
-
1
2.80
×
1
0
-
1
2.62
×
1
0
-
1Figure 12
Invariant mass distribution of thebV (where V=γ, g, and Z) system is shown in Figure 5 for PI parametrization of the signal with κ/Λ=0.2 TeV−1 and mb′=700 GeV at the center of mass energy s=13 TeV.The backgrounds for the final stateb(b¯)V (where V≡ photon, jet, and Z boson) are given in Table 14. We apply the following cuts to the final state photon and jets as ηj,γ<2.5 and pTj,γ>20–200 GeV. It can be noted that the background cross section decreases as the pT cuts increase. We assume the efficiency for b-tagging to be εb=50% and the rejection ratios to be 10% for c(c¯) quark jets and 1% for light quark jets.Table 14
The cross sections (in pb) for the backgrounds (b(b-)V, c(c-)V, and jV, where V = photon, jet, and Z boson) with pT cuts on the jets and photon at the center of mass energy s = 13 TeV.
Background
p
T
>
20 GeV
p
T
>
50 GeV
p
T
>
100 GeV
p
T
>
200 GeV
p
p
→
b
(
b
-
)
γ
+
X
2.99
×
1
0
3
1.35
×
1
0
2
9.04
×
1
0
0
4.02
×
1
0
-
1
p
p
→
c
(
c
-
)
γ
+
X
1.87
×
1
0
4
8.15
×
1
0
2
5.40
×
1
0
1
2.43
×
1
0
0
p
p
→
j
γ
+
X
5.43
×
1
0
4
3.27
×
1
0
3
3.38
×
1
0
2
2.85
×
1
0
1
p
p
→
b
(
b
-
)
j
+
X
7.83
×
1
0
6
3.05
×
1
0
5
1.92
×
1
0
4
8.93
×
1
0
2
p
p
→
c
(
c
-
)
j
+
X
1.22
×
1
0
7
4.55
×
1
0
5
2.89
×
1
0
4
1.35
×
1
0
3
p
p
→
j
j
+
X
2.43
×
1
0
8
8.54
×
1
0
6
5.44
×
1
0
5
2.80
×
1
0
4
p
p
→
b
(
b
-
)
Z
+
X
5.02
×
1
0
2
1.35
×
1
0
2
2.25
×
1
0
1
1.56
×
1
0
0
p
p
→
c
(
c
-
)
Z
+
X
5.96
×
1
0
2
1.58
×
1
0
2
2.64
×
1
0
1
1.83
×
1
0
0
p
p
→
j
Z
+
X
8.00
×
1
0
3
2.08
×
1
0
3
4.08
×
1
0
2
4.12
×
1
0
1In order to reach3σ significance for the signal of b′ anomalous interactions the required integrated luminosity is shown in Figures 13–15 for parametrizations PI, PII, and PIII at the LHC with s=13 TeV. The channel b′→bγ requires more integrated luminosity than the other channels. By requiring the signal significance SS=3, the contour plots of κ/Λ and mass of b′ quark are presented in Figure 16. The results show that one can discover the b′ quark anomalous couplings down to 0.1 in the bg channel for mb′=500 GeV.Figure 13
Integrated luminosity required to reach3σ significance for the signal of b′ anomalous interactions for parametrization PI at the LHC with s=13 TeV.Figure 14
The same as Figure13, but for parametrization PII.Figure 15
The same as Figure13, but for parametrization PIII.Figure 16
The contour plot of anomalous coupling and mass of new heavy quarkb′ for the dynamical parametrization explained in the text with a significance of  3σ at s=13 TeV and Lint=100 fb−1.


### 4.2.1. Simulation forb′ Signal

In the simulation, we have generatedbV (where V=γ, g, and Z) events for each subprocess and these events are simulated using generic detector parameters to include detector effects such as tracking, tagging efficiencies, and smearing effects. After the simulation, the typical kinematical distributions are shown in Figures 17-18.Figure 17
Transverse momentum distributions of leading jet and photon (bγ production) for signal after detector simulation.Figure 18
Transverse momentum distributions of leading jet and photon (jγ production) for background at the given conditions mentioned in the text.In the analysis, the signal (withκ/Λ=0.3 TeV−1 and mb′=700 GeV) and the corresponding background are taken into account. The invariant mass of the new heavy quark b′ can be reconstructed from a bjet and a neutral gauge boson (where the Z boson can also be reconstructed from its dilepton or hadronic decay). For the bγ production, we require a large pTγ (>100 GeV) for photon and large pTj (>100 GeV) for jet and pseudorapidity ηj,γ (<2.5). For the bγ signal channel, the invariant mass distributions for signal and background events are shown in Figure 19. The large pTj,γ and the requirement of single b-tagging allow a better separation of the signal (for bγ channel) from the background, and then we find a precise limit for the anomalous coupling in this channel. For the bg and bZ production, we require two high pT jets (one b-jet) and a high pT jet in addition to the reconstructed mass mZrec, respectively. The main character of the signal is the high pTj and/or pTγ and single b-tagged jet. We calculate the signal and background events in the range mb′recGeV-700GeV<50 GeV and we find a similar significance as shown in Figure 16.Figure 19
The reconstructed mass distributions for background and signal (bγ) with mb′=700 GeV and κ/Λ=0.3 TeV−1.


## 4.2.1. Simulation forb′ Signal

In the simulation, we have generatedbV (where V=γ, g, and Z) events for each subprocess and these events are simulated using generic detector parameters to include detector effects such as tracking, tagging efficiencies, and smearing effects. After the simulation, the typical kinematical distributions are shown in Figures 17-18.Figure 17
Transverse momentum distributions of leading jet and photon (bγ production) for signal after detector simulation.Figure 18
Transverse momentum distributions of leading jet and photon (jγ production) for background at the given conditions mentioned in the text.In the analysis, the signal (withκ/Λ=0.3 TeV−1 and mb′=700 GeV) and the corresponding background are taken into account. The invariant mass of the new heavy quark b′ can be reconstructed from a bjet and a neutral gauge boson (where the Z boson can also be reconstructed from its dilepton or hadronic decay). For the bγ production, we require a large pTγ (>100 GeV) for photon and large pTj (>100 GeV) for jet and pseudorapidity ηj,γ (<2.5). For the bγ signal channel, the invariant mass distributions for signal and background events are shown in Figure 19. The large pTj,γ and the requirement of single b-tagging allow a better separation of the signal (for bγ channel) from the background, and then we find a precise limit for the anomalous coupling in this channel. For the bg and bZ production, we require two high pT jets (one b-jet) and a high pT jet in addition to the reconstructed mass mZrec, respectively. The main character of the signal is the high pTj and/or pTγ and single b-tagged jet. We calculate the signal and background events in the range mb′recGeV-700GeV<50 GeV and we find a similar significance as shown in Figure 16.Figure 19
The reconstructed mass distributions for background and signal (bγ) with mb′=700 GeV and κ/Λ=0.3 TeV−1.


## 5. Conclusion

The new heavy quarks of up-type and down-type can be produced with large numbers at the LHC if they have the anomalous couplings (via flavor changing neutral current) that well dominate over the charged current interactions. The single production of new heavy quarks can be achieved through the anomalous interactions at the LHC withs=13 TeV. The anomalous vertices could appear significantly at leading order processes due to the possibility of new heavy quarks. From the results of signal significance calculations for t′ (b′) anomalous productions, the sensitivity to the anomalous couplings κt′/Λ (κb′/Λ) can be reached down to 0.10 TeV−1 (0.15 TeV−1) in the lepton+bjet+jet+MET (bjet + jet) channel at s=13 TeV, assuming a dynamical parametrization for the anomalous couplings and the mass of 750 GeV for the new heavy quarks. The observability limits on the anomalous couplings obtained after the simulation are comparable with the partonic level analysis in the photon and Z boson associated channels, whereas the productions tg and bg are less comparable due to the fast simulation method. In any case the single b tagging will play an important role in probing new heavy quarks and reducing the background.



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*Source: 134898-2015-03-08.xml*