Search for single production of vector-like top partners at the Large Hadron Electron Collider

TL;DR

This paper proposes a search strategy for single production of vector-like top partners at the LHeC, analyzing decay channels and estimating exclusion limits on couplings for different masses and luminosities.

Contribution

It introduces a novel search approach for vector-like top partners at the LHeC, focusing on specific decay channels and providing sensitivity estimates for various parameters.

Findings

Potential to exclude $TWb$ couplings at 3σ level for masses up to 1 TeV.

Analysis of decay channels $T o Wb$ and $T o th$ at the LHeC.

Sensitivity estimates for different integrated luminosities.

Abstract

The new vector-like top partners with charge $2/3$ are a typical feature of many new physics models beyond the Standard Model (SM). We propose a search strategy for single production of top partners $T$ focusing on both the $T\to Wb$ and $T\to th$ decay channels at the Large Hadron Electron Collider (LHeC). Our analysis is based on a simplified model in which the top partner is an $SU(2)$ singlet, with couplings only to the third generation of SM quarks. We study the observability of the single $T$ through the processes $e^{+}p \to T(\to bW^{+})\bar{\nu}_{e}\to b\ell^{+}+ \not E_T^{miss}$ and $e^{+}p \to T(\to th)\bar{\nu}_{e}\to t(\to jj'b)h(\to b\bar{b}) \not E_T^{miss}$ at the LHeC with the proposed 140 GeV electron beam (with $80\%$ polarization) and 7 TeV proton beam. For three typical $T$-quark masses (800, 900 and 1000 GeV), the $3\sigma$ exclusion limits on the $TWb$ coupling are respectively presented for various values of the integrated luminosity.

Tables

Table 1. Table 1: The cut flow of the cross sections (in fb) for the signal and backgrounds at the LHeC with E e = 140 subscript 𝐸 𝑒 140 E_{e}=140 GeV and E p = 7 subscript 𝐸 𝑝 7 E_{p}=7 TeV. Here we take g ∗ = 0.2 superscript 𝑔 ∗ 0.2 g^{\ast}=0.2 .

Cuts	signal			backgrounds
	800 GeV	900 GeV	1000 GeV	$\nu Wb$	$\nu Wj$	total
Basic cuts	0.3	0.13	0.05	768	34	802
Cut 1	0.13	0.077	0.036	0.006	0.61	0.62
Cut 2	0.12	0.07	0.032	0.006	0.31	0.32
Cut 3	0.1	0.064	0.031	0.003	0.23	0.23

Table 2. Table 2: The cut flow of the cross sections (in 10 − 2 superscript 10 2 10^{-2} fb) for the signal and backgrounds at the LHeC with E e = 140 subscript 𝐸 𝑒 140 E_{e}=140 GeV and E p = 7 subscript 𝐸 𝑝 7 E_{p}=7 TeV. Here we take g ∗ = 0.2 superscript 𝑔 ∗ 0.2 g^{\ast}=0.2 .

Cuts	signal			backgrounds
	800 GeV	900 GeV	1000 GeV	${\overline{\nu }}_{e}th$	${\overline{\nu }}_{e}tZ$	$t+2b$	$W+3b$	total
Basic cuts	5.2	1.92	0.64	9.5	23	27	28	87.5
Cut 1	4.4	1.84	0.6	0.16	0.39	0.43	0.47	1.45
Cut 2	1.0	0.4	0.12	0.04	0.026	0.03	0.03	0.13

Equations

$${\mathcal{L}}_T=$$

$$e^{+}p\to T(\to b{W}^{+}){\bar{\nu }}_e\to b{W}^{+}(\to {\ell }^{+}{\bar{\nu }}_{\ell }){\bar{\nu }}_e.$$

$$e^{+}p$$

$$p_T^{\ell ,b}>20\mathrm{GeV},|{\eta }_{\mathrm{\ell }}|<2.5,|{\eta }_{\mathrm{b}}|<5,/{\mathrm{E}}_{\mathrm{T}}^{\mathrm{miss}}>20GeV.$$

$$e^{+}p\to T(\to th){\bar{\nu }}_e\to t(\to W^{+}b\to j{j}^{\prime }b)h(\to b\bar{b}){\bar{\nu }}_e.$$

$$e^{+}p$$

$$g^{\ast }$$

Full text

I Introduction

With the discovery of the 125 GeV Higgs boson at the Large Hadron Collider (LHC) lhc-higgs , our understanding of electroweak symmetry breaking (EWSB) has been significantly enhanced. However, some unanswered questions remain which forces us to look for new physics (NP) beyond the Standard Model (SM). One of the intriguing issues that needs immediate attention is the naturalness problem hmass . Many popular models have been proposed and different solutions can be categorized based on the objects which cancel the largest Higgs radiative corrections from the top quark. Some of these models postulate the existence of new heavy fermions, such as little Higgs models littlehiggs , extra dimensions ED and composite Higgs models twinhiggs ; Agashe:2004rs . In many cases, these new fermions are vector-like top partners, whose common feature is to decay into a SM quark and a gauge boson, or a Higgs boson. Many phenomenology studies for these new fermions have been made in the literature, see for example p-lh ; p-cp ; p-twin ; p1 ; p2 ; p3 ; NP ; single ; jhep1304-004 ; NP-shu ; jhep1501-088 .

Here we mainly focus on the $SU(2)$ singlet $T$-quarks with charge $2/3$. Due to the Goldstone-boson equivalence theorem, the branching ratios of $T$ into $bW$, $tZ$ and $th$ have a good approximation 2:1:1 in the limit $m_{T}\rightarrow\infty$. Previous studies of ATLAS and CMS Collaborations, relying on signatures induced by both the vector-like $T$-quark pair-production and single-production modes, impose strong constraints on the masses of the heavy quarks that are now bounded to be above about 550-950 GeV atlas-1 ; cms-1 ; atlas-cms-13 , depending on the assumed branching ratios. For the $Wb$ channel, the current constraint from the ATLAS Collaboration set a upper limit on the parameter $C^{Wb}_{L}<0.45$ which performed the search for singly produced vector-like $T$ quark at 13 TeV with 3.2 fb*-1* atlas13 . Besides, the top partner couplings to the SM particles are rather severely constrained by the electroweak precision observables ew ; rb , various SM-like Higgs decay channels higgs-decay and the other indirect constraints (see for example Refs. Buchkremer:2013bha ; bound ). On the other hand, the crucial point is that even a small mixing to the first generation may have a severe impact on single $T$-quark production processes jhep2015-02-032 ; jhep1108-080 . In the previous studies single ; NP-shu ; jhep1501-088 , it has been recognized that the single production of top partners at the LHC will provide the most promising channel in searching for a heavy top partner. In fact, the collider search for top partners has become and will remain an important constraint on wide classes of new physics models. Thus it is highly motivated to investigate all sensitive search strategies within the possibly available accelerator and detector designs.

In our present paper, we study the observability of a single $T$-quark production at the proposed Large Hadron-Electron Collider (LHeC). The LHeC LHeC would be the next high-energy $e$-$p$ collider which is designed to collide an electron beam with a typical energy range, 60-150 GeV with a 7 TeV or higher proton beam from the LHC. Its luminosity is projected to be as high as possibly 1 ab*-1*, with a default value of 100 fb*-1* LHeC1 . Furthermore, the electron beam can be polarized and has an enormous scope to probe electroweak and Higgs boson physics LHeC2 ; LHeC3 . Certainly, it is possible that the new vector-like $T$-quarks can mix sizably with the SM light quarks and their production cross section will be very large due to the mixing with valence quarks, but then their masses are not connected to EWSB and thus we do not consider this case. Although the $T\to tZ(\to\ell^{+}\ell^{-})$ channel is a primary option for most experimental searches, it has small number of events at the LHeC even for a high luminosity plb-liu . We expect that other channels will give a better constraint on the parameters of our model than the considered $T\to tZ$ channel. In this paper, we mainly study the observability of a single $T$-quark production at LHeC combine both the $bW$ and $th$ decay channels for three typical masses of top partners.

This paper is organized as follows. In Sec. II, we give a brief description of the simplified model including the vector-like $T$-quark with charge $2/3$. In Sec. III we study the prospects of observing the single $T$ production by performing a detailed analysis of the signal and backgrounds in each channel. Finally, we draw our conclusions in Sec. IV.

II Top partner in a simplified model

It is clear that many extensions of the SM contain vector-like quark partners (and in particular top-partners), which can be classified according to their $SU(2)\times U(1)$ quantum numbers, where at least one of the partners needs to have the same electro-magnetic charge $2/3$ as the corresponding SM quark. A generic parametrization of an effective Lagrangian for top partners has been recently proposed in Ref. Buchkremer:2013bha , where the vector-like quarks are embedded in different representations of the weak $SU(2)$ group. We here consider a simplified model where the vector-like $T$-quark is an $SU(2)$ singlet, with couplings only to the third generation of SM quarks. The benefit of using the simplified effective theory is that the results of the studies could be used to make predictions for more complex models including various types of top partners. The top partner sector of the model is described by the general effective Lagrangian Buchkremer:2013bha

[TABLE]

where $m_{T}$ is the top partner mass and $g^{\ast}$ parametrizes the single production coupling in association with a $b$ or a top-quark. $g$ is the $SU(2)_{L}$ gauge coupling constant, $c_{W}=\cos\theta_{W}$ and $\theta_{W}$ is the Weinberg angle.

In this simplified model, the top partner couplings to the SM particles are rather severely constrained by electroweak constraints as well as by the direct measurement of $V_{tb}$ vtb . However, such constraints can be significantly altered in most realistic models including the vector-like quark with two or more partner multiplets bound . Here we take a conservative range for the coupling parameter atlas13 ; vtb : $g^{\ast}\leq 0.5$.

III Event generation and analysis

During the simulation, we first extract the model file web of the singlet vector-like top partners by using the FeynRules package feynrules . The leading order cross sections are calculated using MadGraph5-aMC$@$NLO mg5 with CTEQ6L parton distribution function (PDF) cteq and the renormalization and factorization scales are set dynamically by default. The collider parameter is taken to be $E_{e}=140$ GeV and $E_{p}=7$ TeV, corresponding to a c.m. energy of approximately $\sqrt{s}=1.98$ TeV. The SM input parameters relevant in our study are taken from pdg .

In Fig. 1, we show the single production cross sections of the vector-like $T$ depending on their masses at the LHeC for $g^{\ast}=0.2$ and positron beam polarization $p_{e}=0,0.8$. We can see that the cross section for polarized can be about 1.8 times larger than that for unpolarized case. For $g^{\ast}=0.2$ and $p_{e}=0.8$, the cross sections are about 3.1, 1.3 and 0.5 fb for $m_{T}=800,900$ and 1000 GeV, respectively.

Next, we analyze the observation potential of each channel by performing a Monte Carlo simulation of the signal and background events and applying the suitable selection cuts to maximize the significance. The Feynman diagram of production and decay chain is presented in Fig. 2.

For the fixed $T$-quark mass, the corresponding free parameters are the coupling parameter $g^{\ast}$. We take three typical values of the $T$ quark mass: $m_{T}=800,900,1000$ GeV with $g^{\ast}=0.2$. We generate all event samples in this analysis at the leading order using MadGraph5-aMC$@$NLO. Parton shower (both initial and final) and hadronization effects have been dealt with by PYTHIA6 pythia . For all the considered signals and backgrounds, the K-factors are taken to be 1 prd81-054018 . We apply jet and lepton energy smearing according to the following energy resolution formula LHeC $\delta E/E=a/\sqrt{E/\rm GeV}\oplus b$, where a is a sampling term and b is a constant term. For jets we take $a=45\%$ and $b=3\%$, and for leptons we take $a=8.5\%$ and $b=0.3\%$. In our analysis, we assume a b-jet tagging efficiency of $\epsilon_{b}=60\%$ and a corresponding mistagging rate of $\epsilon_{g,u,d,s}=1\%$ for light jets and $\epsilon_{c}=10\%$ for a $c$-jet. Event analysis is performed by using MadAnalysis5 ma5 .

III.1 The $T\to Wb$ channel

In this section, we analyze the observation potential by performing a Monte Carlo simulation of the signal and background events and explore the sensitivity of single top partner at the LHeC through the channel

[TABLE]

For this channel, the typical signal is exactly one charged lepton, one $b$ jet and missing energy. The main SM background are the processes containing a $W$ boson in the final state, such as

[TABLE]

where one light jet might be faked as $b$ jet. For the $\nu Wb$ process, the dominant process is the single top production process in which the top quark decay in to $Wb$. We also checked that other background processes, such as the di-boson production are negligible with the selection cuts.

To reduce the backgrounds, we pick up the events that included exactly one isolated lepton and one b-tagged jet, then impose the following basic cuts:

[TABLE]

In Fig. 3, we show the normalized distributions of the scalar sum of the transverse momenta ($\rm sP_{T}$) of the $b$-tagged jet and the lepton, the transverse momentums $p_{T}^{\ell,b}$ and the variable $\Delta R(b,\ell)$ for the signals and backgrounds. Here $\Delta R=\sqrt{(\Delta\phi)^{2}+(\Delta\eta)^{2}}$ is the particle separation with $\Delta\phi$ and $\Delta\eta$ being the separation in the azimuth angle and rapidity respectively. Based on these kinematical distributions, we impose the following cuts to get a high significance:

• •

Cut 1: $\rm sP_{T}>500\rm~{}GeV$.

• •

Cut 2: $p_{T}^{\ell}>100\rm~{}GeV$, $p_{T}^{b}>250\rm~{}GeV$ and $2.8<\Delta R(b,\ell)<3.5$.

In Fig. 4, we show the transverse mass distribution for the $b\ell\not{E}_{T}$ system, which has been defined in Ref. epjc-74-3103 . From this figure, we can see that the distributions of signal have peaks around the $T$-quark mass while background distributions turn over at lower masses. Thus we can further reduce the backgrounds by the following cut:

• •

Cut 3: $M_{T}>700\rm~{}GeV$.

We present the cross sections of the signal and backgrounds after imposing the cuts in Table 1. From the numerical results, one can see that the backgrounds are suppressed very efficiently after imposing the selections. For example, the production cross section of the $\nu Wb$ background drops from 768 fb to 0.006 fb, with a reject efficiency more than $99\%$. The dominant SM background come from the $\nu Wj$ production process and is about 0.23 fb after imposing the selections.

III.2 The $T\to th$ channel

Next, we analyze the observation potential and explore the sensitivity of single $T$-quark at the LHeC through the channel

[TABLE]

The main SM background are the processes:

[TABLE]

Besides, the single top and single $W$ plus jets production processes are also the backgrounds, where one light jet might be faked as $b$ jet.

The event selection in the 3b-tagging case first requires at least five jets satisfying the following basic cuts:

• •

$p_{T}^{j}>20\rm~{}GeV$, $|\eta_{j}|<5$, $\Delta R_{jj}>0.4$.

• •

There are at least three b-tagged jets with $|\eta_{b}|<5$.

• •

Events with additional charged leptons are vetoed.

In Fig. 5, we show the $H_{T}$ distribution for the different considered processes, where $H_{T}$ denotes the scalar sum of the transverse momenta of the final state jets. The signal distribution has a considerable tail for larger values of $H_{T}$ compared to background events. Therefore we choose the $H_{T}$ cut

• •

Cut 1: $H_{T}>600\rm~{}GeV$.

Fig. 6 illustrates the distribution of the reconstructed Higgs boson mass of the signal and backgrounds. In order to suppress the $tZ\bar{\nu}_{e}$, $tbb$ and $Wbbj$ backgrounds, we require the mass of the Higgs boson to satisfy

• •

Cut 2: $|m_{bb}-m_{h}|<20\rm~{}GeV$.

We list the results after imposing various kinematic cuts in Table 2. From the numerical results, one can see that all the backgrounds are also suppressed efficiently after imposing these selections. However, due to the small production cross section for the signals, the large value of the coupling parameter $g^{\ast}$ and the high integrated luminosity are needed to produce more final events. Note that here our results are conservative, the analysis presented can be further improved in several aspects. First is of course a more realistic estimation of the signal and backgrounds including parton shower and more detailed detector effects. Secondly, we have only applied a cut-based analysis with very simple variables. A further multivariate analysis may deliver additional gain in sensitivity. Furthermore, other techniques such as Boosted Decision Trees(BDT), Heidelberg-Eugene-Paris top-tagger (HEPtopTagger) and jet dipolarity BDRS ; top-tagger ; Hook-jhep may be more useful to enhance the significance.

To estimate the observability quantitatively, we adopt the significance measurement ss : $SS=\sqrt{2L[(\sigma_{S}+\sigma_{B})\ln(1+\sigma_{S}/\sigma_{B})-\sigma_{S}]}$, where $L$ is the integrated luminosity, $\sigma_{S}$ and $\sigma_{B}$ are the cross sections of signal and background, respectively. In Fig. 7, we show the excluded $3\sigma$ reaches in the plane of the integrated luminosity and the coupling parameter $g^{\ast}$ for two channels. For $m_{T}=800$, 900 and 1000 GeV, we can see that the upper limits for the $T\to Wb$ channel on the size of $g^{\ast}$ are respectively given as about 0.2, 0.24 and 0.34 for $L=300$ fb*-1*, and changed as about 0.15, 0.18 and 0.25 when the integrated luminosity is 1000 fb*-1*. For the $T\to th$ channel, the high integrated luminosity is needed to enhance the production events due to the small production rates. For the same three top partner masses, we can see that the upper limits on the size of $g^{\ast}$ are respectively given as about 0.15, 0.23 and 0.4 when the integrated luminosity is 1000 fb*-1*.

IV conclusion and discussion

The new heavy vector-like top partners with charge $2/3$ appear in many new physics models beyond the SM. In order to be as model-independent as possible we exploited a simplified model with only two free parameters, the heavy top mass and an electroweak coupling constant. In this paper we described the future LHeC potential to search for the heavy vector-like $T$-quark via the $T\to bW^{+}$ and $T\to th$ decay modes. We investigated the observability of the heavy vector-like top partner $T$ production through the processes $e^{+}p\to T(\to bW^{+})\bar{\nu}_{e}\to bW^{+}(\to\ell^{+}\bar{\nu}_{\ell})\bar{\nu}_{e}$ and $e^{+}p\to T(\to th)\bar{\nu}_{e}\to t(\to jj^{\prime}b)h(\to b\bar{b})\bar{\nu}_{e}$ at the LHeC with $E_{e}=140$ GeV (with 0.8 polarization) and $E_{p}=7$ TeV. Since the single $T$ production depends on the $TWb$ coupling and the $T$-quark mass, we constrain the parameter space in the plane of the integrated luminosity and the coupling parameter $g^{\ast}$. In the $bW$ channel, we rely on the large $p_{T}$ of the lepton, the $b$-jet and large missing energy to suppress the backgrounds. In the $th$ channel, we consider the all-hadronic final states and a large $H_{T}$ cut can efficiently suppress the backgrounds. For $m_{T}$= 800, 900 and 1000 GeV, the upper limits on the size of $g^{\ast}$ are respectively given as about 0.15, 0.18 and 0.25 with the high luminosity of 1000 fb*-1*. We expect our analysis can represent a complementary candidate to pursue the search of a possible singlet top partner below $\sim 1$ TeV.

In some typical models such as the minimal Composite Higgs (CH) models jhep1304-004 and the littlest Higgs model with T-parity (LHT) lht , the heavy $T$-quark couplings only to the third generation of SM quarks. Our results can be straightforwardly mapped within the context of the CH model and the LHT model, namely with

[TABLE]

where $y$, $R$ and $f$ are the model parameters (for more detail, see e.g.jhep1304-004 ; lht ). For the low mass reign (i.e., m_{T}{\ \lower-1.2pt\vbox{\hbox{\hbox to0.0pt{<\hss}\lower 6.0pt\vbox{\hbox{\sim}}}}\ }1 TeV), we expect our analysis can represent a viable and complementary candidate to pursue the search of the singlet vector-like $T$-quarks.

Now we compare the discovery reach in our results with other phenomenological studies at the LHC. In a simplified composite Higgs model, the authors of Ref. NP-shu project at $\sqrt{s}=8$ TeV and 25 fb*-1* of integrated luminosity the exclusion potential with $Br(T\to Wb)=0.5$, obtaining a strong constraint on the $TWb$ coupling ($g_{TbW}/g^{SM}_{TbW}<0.2\sim 0.3$) for $m_{T}\subset(700,1000)$ GeV. For the $T\to tZ$ channel, the authors of Ref. jhep1501-088 studied the dilepton signals at $\sqrt{s}=13$ TeV with 300 fb*-1* of integrated luminosity and the results show that the signal from the $T\to tZ\to(qq^{\prime}b)(\ell^{+}\ell^{-})$ channel is within the range of possible evidence for top partner masses up to roughly 1450 GeV with g^{\ast}{\ \lower-1.2pt\vbox{\hbox{\hbox to0.0pt{<\hss}\lower 6.0pt\vbox{\hbox{\sim}}}}\ }0.5, while being still sensitive to $g^{\ast}$ couplings down to 0.05 for $m_{T}=0.8$ TeV. Analogously, the authors of Ref. jhep2015-02-032 studied the trilepton signals from the $T\to tZ\to(b\ell\nu)(\ell^{+}\ell^{-})$ channel at the LHC with $\sqrt{s}=13$ TeV, the results show that the trilepton signal can probe possible top partner masses up to roughly 1700 GeV with g^{\ast}{\ \lower-1.2pt\vbox{\hbox{\hbox to0.0pt{<\hss}\lower 6.0pt\vbox{\hbox{\sim}}}}\ }0.5, while being still sensitive to $g^{\ast}$ couplings down to 0.1 for $m_{T}=0.8$ TeV. Thus we can see that, for the typical mass parameter $m_{T}=0.8$ TeV, the LHeC sensitivity for the $TbW$ coupling strength is smaller than the sensitivity limits of LHC as g^{\ast}{\ \lower-1.2pt\vbox{\hbox{\hbox to0.0pt{<\hss}\lower 6.0pt\vbox{\hbox{\sim}}}}\ }0.1(0.05) with an integrated luminosity of 300 fb*-1* at $\sqrt{s}=13$ TeV jhep1501-088 ; jhep2015-02-032 . In our previous study plb-liu , the decay of $T\to t(\to bjj^{\prime})Z(\to\ell^{+}\ell^{-})$ channel from the single top partner produced at the LHeC are investigated by considering the mixing between the top partner with the first and the third generation quarks. For a high integrated luminosity of 1 ab*-1*, the upper limits on the size of $g^{\ast}$ are given as $g^{\ast}\leq 0.29$ for $R_{L}=0$ (only couplings with the third generation SM quarks) and $m_{T}=0.8$ TeV. Thus we expect our analysis can represent a viable and complementary candidate to pursue the search of a possible vector-like top partner with low masses (i.e., m_{T}{\ \lower-1.2pt\vbox{\hbox{\hbox to0.0pt{<\hss}\lower 6.0pt\vbox{\hbox{\sim}}}}\ }1 TeV).

Acknowledgements.

This work is supported by the Joint Funds of the National Natural Science Foundation of China (Grant No. U1304112), the Foundation of He nan Educational Committee (Grant No. 2015GGJS-059) and the Foundation of Henan Institute of Science and Technology (Grant No. 2016ZD01).