Search for pair production of the heavy vectorlike top partner in same-sign dilepton signature at the HL-LHC

Although the Standard Model (SM) has proved itself with great success, a theory beyond the SM (BSM) is necessary from both the theoretical and experimental points of view, one of which is the so-called gauge hierarchy problem DeSimone:2012fs . Many new physics models BSM, such as little Higgs ArkaniHamed:2002qy ; Han:2003wu ; Chang:2003vs , composite Higgs Agashe:2004rs , and other extended models He:1999vp ; Wang:2013jwa ; He:2001fz ; He:2014ora , have been proposed to solve this problem by introducing a spontaneously broken global symmetry, leading the Higgs boson to be a pseudo Goldstone boson. New vectorlike top partners (VLQ-$T$) are generally predicted in these BSM models, which are color-triplet fermions but with its left- and right-handed components transforming in the same way under the gauge group $SU(2)\times U(1)$ Buchkremer:2013bha ; Aguilar-Saavedra:2013qpa . A common feature is that they are assumed to decay into a SM quark and a gauge boson or Higgs boson, which can generate characteristic signatures at hadron colliders (see, for example Cacciapaglia:2011fx ; Okada:2012gy ; Backovic:2014uma ; Barducci:2017xtw ; Cacciapaglia:2018qep ; Liu:2017rjw ; Liu:2017sdg ; Liu:2019jgp ; Tian:2021oey ; Tian:2021nmj ; Yang:2021btv ; Moretti:2016gkr ; Moretti:2017qby ; Carvalho:2018jkq ; Benbrik:2019zdp ; Aguilar-Saavedra:2019ghg ; Buckley:2020wzk ; Brown:2020uwk ; Deandrea:2021vje ; Belyaev:2021zgq ; Dasgupta:2021fzw ; Han:2022npb ; Cacciapaglia:2021uqh ; Bhardwaj:2022wfz ; Han:2022jcp ; Verma:2022nyd ).

From the experimental point of view, vectorlike quarks (VLQs) are still allowed by present searches, unlike the fourth generation of quarks with chiral couplings, which is ruled out by electroweak precision measurements Kribs:2007nz ; Banerjee:2013hxa ; Cao:2022mif , and by the measured properties of the SM Higgs boson ATLAS:2016neq ; Eberhardt:2012sb ; CMS:2013zma . VLQs can evade such exclusion bounds because they are not chiral, a priori, and do not have to acquire their mass via the Higgs mechanism. Therefore, such new particles are receiving a lot of attention at the LHC. Up to now, searches at the LHC for VLQ-$T$ have been performed and presented by the ATLAS and CMS Collaborations, with the lower mass bounds on $T$ reaching up to about $740-1370$ GeV at 95% confidence level (C.L.), depending on the $SU(2)$ multiplets they belong to and different decay modes  Aaboud:2018pii ; CMS:2019eqb . Besides, such VLQ-$T$ can also be singly produced at the LHC via their electroweak (EW) coupling with SM quarks and weak bosons, which depends on the strength of the interaction between the VLQ-$T$ and the weak gauge bosons. Current searches for single production of VLQ-$T$ have placed limits on the production cross sections for their masses between 1 and 2 TeV at 95% C.L. for various EW coupling parameters CMS:2017gsh ; CMS:2017voh ; CMS:2019afi ; ATLAS:2022ozf .

Typically, most of the phenomenological studies are based on the assumption that the VLQ-$T$ only couple to the third-generation quarks, since this is the scenario least constrained by previous measurements Buchkremer:2013bha . Considering the constraints from flavor physics Cacciapaglia:2010vn ; Botella:2012ju ; Cacciapaglia:2015ixa ; Alok:2015iha ; Ishiwata:2015cga ; Botella:2016ibj ; Vatsyayan:2020jan ; Branco:2021vhs ; Accomando:2022ouo ; Balaji:2021lpr , the VLQ-$T$ can mix in a sizable way with lighter quarks, which could have a severe impact on electroweak vectorlike quark processes at the LHC Atre:2011ae ; Basso:2014apa ; Liu:2016jho and the Large Hadron Electron Collider Han:2017cvu ; Zhang:2017nsn ; Gong:2020ouh . This is particularly of interest for couplings to first-generation quarks, where amplitudes involving VLQ-$T$ couplings direct to initial-state up quark become significant due to large high-$x$ valence-quark densities. The future high-luminosity LHC (HL-LHC) is expected to reach 3000 fb ^-1 Apollinari:2015wtw , which will be very beneficial for discovering possible new physical signals even for small production rates. Recently, Zhou and Liu Zhou:2020ovl ; Zhou:2020byj studied a new decay channel of the top partner mediated by the heavy Majorana neutrino ($T\to b\ell^{+}\ell^{+}jj$), which can be used to probe the top partner and test the seesaw mechanism simultaneously at the HL-LHC by searching for final same-sign dileptons. In this work, we study the pair production of the VLQ-$T$ at the HL-LHC in a model-independent way through the process $pp\to TT$ with the decay channel $T\to W^{+}q(\to\ell^{+}\nu_{\ell}q)$, which induced the final states with two leptons of the same electric charge (electrons or muons), two jets, and missing transverse momentum.

The paper is arranged as follows. In Sec. II, we briefly review the simplified model including the singlet VLQ-$T$ and calculate its pair production involving the mixing with both the first- and third-generate quarks. In Sec. III, we discuss the observability of the VLQ-$T$ through the process $pp\to TT\to\ell^{+}\ell^{+}jj+\not{E}_{T}$ at the HL-LHC. Finally, conclusions are presented in Sec. IV.

Next, we perform the Monte Carlo simulation and explore the sensitivity of the VLQ-$T$ at the 14 TeV LHC through the channel,

where $\ell=e,\mu$.

For the above same-sign dilepton final states, the major SM backgrounds at the LHC come from prompt multileptons (mainly from events with $t\bar{t}W^{+}$ and $W^{+}W^{+}+$jets) and nonprompt leptons (mainly from events with jets of heavy flavor, such as $t\bar{t}$). Other processes, such as the $t\bar{t}Z$, triboson events, $ZZjj$, and $W^{\pm}+$jets are not included in the analysis owing to the negligible cross sections resulting from application of the cuts. To be exact, opposite-sign dileptons, one of which is mismeasured, should also constitute our backgrounds but, as the rate of mismeasurement for muons, is generally low enough that we ignore its effects. The QCD next-to-leading-order (NLO) prediction for pair production is calculated in Ref. Fuks:2016ftf . Here we take the conservative value of the $K$-factor as 1.3 for the signal. To account for contributions from higher-order QCD corrections, the cross sections of dominant backgrounds at LO are adjusted to NLO by means of $K$ factors, which are 1.04 for $W^{+}W^{+}jj$ Jager:2009xx ; Melia:2010bm and 1.22 for $t\bar{t}W^{+}$ Campbell:2012dh . The dominant $t\bar{t}$ background is normalized to the NNLO QCD cross section of 953.6 pb Czakon:2013goa . It should be noted that we assume that the kinematic distributions are only mildly affected by these higher-order QCD effects. Therefore, for simplicity, we rescale the above distributions by using constant bin-independent $K$ factors.

Signal and background events are generated at LO using MadGraph5-aMC$@$NLO. As a reference point, we set a benchmark value of $g^{\ast}=0.1$ and $R_{L}=1$. Analogously, our benchmark points in the mass axis read $M_{T}=$1500 and 2000 GeV. However, we will present the reach later in the $g^{\ast}-R_{L}$ plane. Then we pass the parton-level events to Pythia 8.20 pythia8 and Delphes 3.4.2 deFavereau:2013fsa for performing the parton shower and fast detector simulations, respectively. The anti-$k_{t}$ algorithm Cacciari:2008gp with parameter $\Delta R=0.4$ is used to reconstruct jets. Finally, event analysis is performed by using MadAnalysis5 ma5 .

To identify objects, we choose the basic cuts at parton level for the signals and SM backgrounds as follows:

where $\Delta R=\sqrt{\Delta\Phi^{2}+\Delta\eta^{2}}$ is the separation in the rapidity-azimuth plane and $p_{T}^{\ell/j}$ and $|\eta_{\ell/j}|$ are the transverse momentum and pseudorapidity of the leptons and jets, respectively.

Owing to the larger mass of VLQ-$T$, the decay products are highly boosted. Therefore, the $p_{T}^{l/j}$ peaks of the signals are larger than those of the SM backgrounds. In Fig. 4, we plot some differential distributions for signals and SM backgrounds at the LHC, such as the transverse momentum distributions of the leading and subleading leptons ($p_{T}^{\ell_{1,2}}$), the transverse momentum distributions of the leading and subleading jets ($p_{T}^{j_{1,2}}$), the missing transverse energy $\not{E}_{T}$, and the invariant mass distribution for the final $j\ell$ system $M_{\ell j}$. Based on these kinematical distributions, we apply the following kinematic cuts to the events to distinguish the signal from the SM backgrounds.

1. (a)

   Cut 1: There are exactly two same-sign isolated leptons $[N(\ell^{+})=2]$ and at least two jets $[N(j)\geq 2]$

2. (b)

   Cut 2: The transverse momenta of the leading and subleading leptons and jets are required $p_{T}^{l_{1,2}}>200~{}(100)\rm~{}GeV$ and $p_{T}^{j_{1,2}}>300~{}(150)\rm~{}GeV$. Besides, the invariant mass of two jets are required $M_{jj}>200\rm~{}GeV$ to reduce the background from $W$-boson decays.

3. (c)

   Cut 3: The transverse missing energy is required $\not{E}_{T}>200\rm~{}GeV$.

4. (d)

   Cut 4: The invariant mass of final system $M_{\ell j}$ is required to have $M_{\ell j}>600\rm~{}GeV$.

We present the cross sections of three typical signal ($M_{T}=1500,2000$ GeV) and the relevant backgrounds after imposing the cuts in Table 1. Among the three kinds of SM backgrounds, we can see from Table 1 that the dominant one is the $t\bar{t}$ events with the basic cut. The first two cuts on numbers of final same-sign leptons and transverse momenta of leptons and jets can greatly suppress the $t\bar{t}$ events, and other SM backgrounds to the same order as the signal remain. Then the large $\not{E}_{T}$ requirement can cut about 70% SM backgrounds while keeping 80% signal events. All backgrounds are suppressed very efficiently at the end of the cut flow, while the signals still have a relatively good efficiency. The dominant SM background comes from the $W^{+}W^{+}jj$ process, with a cross section of $1.4\times 10^{-3}$ fb.

It should be noted that we have not considered the pileup effects, which is important for a fully realistic simulation and needs appropriate removal techniques Cacciari:2007fd ; Krohn:2013lba ; Berta:2014eza . However, we expect that such effects can be limited on our results since the event selection is based on two same-sign hard leptons.

The median expected significance for discovery and exclusion can be approximated by Cowan:2010js

with

In the idealized limit of a perfectly known background prediction, $\delta=0$, these expressions would reduce to

Here $s$ and $b$ denote the event numbers after the above cuts for the signal and background, respectively. $\delta$ denotes the percentage systematic error on the SM background estimate. The integrated luminosity at the HL-LHC is set at 3000 fb^-1.

In Fig. 5, we plot the excluded $2\sigma$ and $5\sigma$ discovery reaches in the plane of $g^{\ast}-R_{L}$ for two fixed VLQ-$T$ masses and $\delta=30\%$ at HL-LHC. In Fig. 5, one can see that the $5\sigma$ level discovery sensitivity of $g^{\ast}$ is 0.11 (0.12) for $M_{T}=1500~{}(2000)$ GeV and $R_{L}=1$, and it changes as $0.27~{}(0.29)$ for $R_{L}=0.1$. On the other hand, from the $2\sigma$ exclusion limits one can see that the upper limits on the size of $g^{\ast}$ are given as $g^{\ast}\leq 0.08~{}(0.09)$ for $R_{L}=1$, and that they change as $g^{\ast}\leq 0.42~{}(0.45)$ for the smaller value $R_{L}=0.02$.

As mentioned earlier, the case of $R_{L}\rightarrow\infty$ means that the singlet VLQ-$T$ is coupled only to the first-generation SM quarks. Based on the cuts adopted in the above discussion, we extend our analysis in this case with the VLQ-$T$ masses ranging from 1500 to 2500 GeV in steps of 100 GeV. Figure 6 shows the $2\sigma$ exclusion limits as a function of $M_{T}$ and $g^{\ast}$ with two systematic error cases of $\delta=0$ and $\delta=30\%$. We observe that our signals are not very sensitive to the values of the systematic uncertainties. Assuming a realistic 30% systematic error, the sensitivities are slightly weaker than those without any systematic error. For the considered mass range of 1500 to 2500 GeV, the upper limit on allowed values of $g^{\ast}$ rises from a minimum value of 0.056 starting at $M_{T}=1500$ GeV, up to 0.074 for $M_{T}=2500$ GeV. These results are slightly better than the noncollider limits ($\kappa=g^{\ast}/\sqrt{2}\simeq 0.07$) conservatively estimated in Ref. Buchkremer:2013bha for a mass scale of the order of a TeV from atomic parity violation measurements Deandrea:1997wk .

The new heavy vectorlike $T$ quark of charge 2/3 appears in many new physics models beyond the SM. In this paper, we exploited a simplified model with only two free parameters: the electroweak coupling parameter $g^{\ast}$ and the generation mixing parameter $R_{L}$. We presented a search strategy at the future HL-LHC for a distinguishable signal with a same-sign dilepton plus two jets and missing energy. The $2\sigma$ exclusion limits, as well as the $5\sigma$ discovery reach in the parameter plane of the two variables $g^{\ast}-R_{L}$, were obtained for two typical heavy $T$ quark masses. For two typical VLQ-$T$ masses $M_{T}=1500~{}(2000)$ GeV, the upper limits on the size of $g^{\ast}$ were given as $g^{\ast}\leq 0.42~{}(0.45)$ for the smaller value $R_{L}=0.02$, and $g^{\ast}\leq 0.08~{}(0.09)$ for $R_{L}=1$. Assuming that the VLQ-$T$ with mass of TeV scale couples to the first-generation quarks only, the correlated region $g^{\ast}\in[0.056,0.074]$ and $M_{T}\in[1500,2500]$ GeV can be excluded at the $2\sigma$ level at the future HL-LHC, which is slightly better than the noncollider limits from atomic parity violation measurements.