Boosting vector leptoquark searches with boosted tops

Arvind Bhaskar,1, ∗ Tanumoy Mandal,2, † and Subhadip Mitra1, ‡

1Center for Computational Natural Sciences and Bioinformatics,International Institute of Information Technology, Hyderabad 500 032, India

2Indian Institute of Science Education and Research Thiruvananthapuram, Vithura, Kerala, 695551, India(Dated: July 6, 2020)

At the LHC, a TeV-scale leptoquark (LQ) that decays dominantly to a top quark (t) and a light chargedlepton (` = e, µ) would form a resonance system of boosted-t + high-pT-`. We consider all possiblevector LQ models within the Buchmüller-Rückl-Wyler classifications with the desired decay. We proposesimple phenomenological Lagrangians that are suitable for bottom-up/experimental studies and, at thesame time, can cover the relevant parameter spaces of these models. In this simplified framework, westudy the pair and single production channels of vector LQs at the LHC. Interestingly, we find that, likethe pair production, the cross sections of some single production processes also depend on the parameterκ that appears in the gluon-vector LQ coupling. We adopt a search strategy of selecting events with atleast one boosted hadronic top quark and exactly two high-pT leptons of the same flavor and oppositesign. This combines events from the pair and single production processes and, therefore, can enhancethe discovery potential beyond that of the pair-production-only searches. For 5σ discovery we find thatvector LQs can be probed up to 2.55 TeV for 100% branching ratio in the t` decay mode and O(1) newcouplings at the 14 TeV LHC with 3 ab−1 of integrated luminosity.

I. INTRODUCTION

In the recent past, several experimental collaborations have re-ported some hints of lepton flavor universality violation in theheavy meson decays. Collectively, these point toward the ex-istence of some physics beyond the Standard Model (SM) asthe SM gauge interactions are flavor-blind. Intriguingly, theseseem to be quite tenacious and have created a lot of excitementin the particle physics community. Initially, the BaBar collabo-ration found two significant anomalies in the flavor-changingcharged current decays of the B-meson via the b → cτν tran-sition. They reported the anomalies in terms of excesses inthe RD(∗) observables defined as the ratios of branching ra-tios (BRs) to reduce some systematic and hadronic uncertain-ties [1, 2]. Since then, the excesses have survived the latermeasurements by the LHCb [3–5] and Belle [6–9] collabora-tions. The statistical average of these two observables obtainedin the RD-RD∗ plane by the HFLAV Group puts the anoma-lies away from the corresponding SM predictions [10–13] bya combined significance of ∼ 3.1σ. The LHCb Collaborationhas also observed downward deviations of about 2.5σ [14–18]from the SM predictions [19, 20] in the flavor-changing neu-tral current transition b→ sµµmeasured in terms of theRK(∗)

observables. Similarly, an excess of about ∼ 2σ was found inanother observable, RJ/ψ [21]. In addition, a long-standingdiscrepancy of about ∼ 3.5σ exists in the muon anomalousmagnetic moment measurement [22].

It is known that TeV-scale leptoquarks (LQs) are good can-didates to address the flavor anomalies. Moreover, their phe-nomenology has been explored in various other contexts aswell [23–77]. LQs are color-triplet bosons [either scalars(sLQs) or vectors (vLQs)] predicted by many beyond-the-SMtheories [78–82]. They have fractional electric charges andcarry both lepton and baryon numbers. In general, a LQ cancouple to a quark and a lepton of either the same or differ-ent generations. The flavor anomalies suggest that LQs cou-

∗ arvind.bhaskar@research.iiit.ac.in† tanumoy@iisertvm.ac.in‡ subhadip.mitra@iiit.ac.in

ple more strongly to the third-generation fermions than theother two. Cross-generational couplings of LQs could generateflavor-changing neutral currents; those involving the first andsecond generations are tightly constrained. However, boundsare relatively weaker when a fermion of the third-generationis involved.

The search for LQs is an important research program at theLHC. Usually, the LHC searches are done for LQs that coupleto quarks and leptons of the same generation and are labeledaccordingly. For example, pair production of a scalar LQ thatdecays to a top quark and a tau lepton (or a bottom quarkand a tau lepton or neutrino), i.e, a third-generation LQ, hasbeen extensively analyzed by both the ATLAS [83, 84] andCMS [85, 86] collaborations. Altogether, the current bound onthe third-generation LQ is roughly about a TeV (this, of course,depends on various assumptions and we refer the reader tothe actual papers for details). However, the flavor-motivatedLQ models with sizable cross-generational couplings wouldhave exotic signatures and require different search strategies.Of late, the nonstandard decay modes of LQs have started togain attention; the CMS Collaboration published their first re-sults on the pair production searches of LQs in the ttµµ chan-nel [87]. Based on the 13 TeV data, they performed a prospectstudy for the pair production of sLQs in the ttµµ channel at thehigh-luminosity LHC (HL-LHC) [88].

In Ref [89], we investigated the HL-LHC prospects of sLQsthat couple dominantly to the top quark in some detail. There,we focused on charge 1/3 and 5/3 sLQs that decay to a topquark and a charged lepton. Even though we considered onlythird-generation quarks, interestingly, we found that in somescenarios single production can improve their prospects signif-icantly.1 In this paper, we present a similar follow-up study forvLQs. Here, too, we concentrate on a specific subset of possiblevLQs that dominantly couple with a top quark and can decay

1 This is interesting because, when a LQ (or any other particle) mostlycouples to the third-generation quarks, we generally expect theirsingle production to be ignorable as the bottom (top) quark densityin the proton is too small (nonexistent) to play any significant roleat the LHC.

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to a top quark and a light charged lepton (e or µ) with a sub-stantial BR. Since an analysis of the pair production of vLQsthat decay to a top quark and a neutrino at the LHC is avail-able in Ref. [90], in this paper we do not analyze this channelagain. Instead, we present a set of simplified models that cov-ers all of the possibilities of a vLQ decaying to a top quark andany lepton. These are suitable for experimental analysis. Wealso demonstrate how they are related to the known models ofvLQs [91–94].

Our main motivation for considering this specific type ofvLQs is to investigate their collider discovery/exclusion poten-tial by making use of the boosted top signature coming fromthe LQ decay. They form an exotic resonance system with aboosted top and a high-pT lepton and provide a novel wayto search for these models at the LHC. Various flavor anoma-lies suggest that cross-generational Yukawa-type LQ couplingswith tops and leptons might be large. A large coupling makesvarious single production channels important, especially in thehigh-mass region. For example, the relevance of the processgg → LQ + tµ was pointed out in Ref. [95]. In our analy-sis, we adopt the same search strategy as the one we proposedfor the sLQs [89]. We identify our signal by selecting at leastone boosted hadronic top and exactly two high-pT leptons anduse the highest-pT top (if there is more than one top) and oneof the selected leptons to reconstruct a heavy system, i.e., theLQ. As we have demonstrated before [89, 96–98], such a selec-tion strategy combines pair and single production events andincreases the LHC reach. Although pair production is suitablefor probing the low-mass region, single production takes overwhen the LQ becomes heavy. Compared to the sLQs, the pairproduction cross sections for vLQs are relatively bigger andhence the current mass limits obtained for pair production aregenerally higher for the vLQs than for the sLQs. In the case ofvLQs, the importance of single production becomes visible forrelatively higher mass compared to sLQs. We shall see that thediscovery prospects of the vLQs at the HL-LHC is significantlyimproved if the new couplings controlling single productionare of order unity.

Before we proceed further, we note that since this paper is afollow-up to Ref. [89], we shall frequently refer to that paperand omit some details that are common while ensuring thatour presentation is self-contained. The rest of the paper is or-ganized as follows. In Sec. II, we describe the vLQ models andintroduce simplified models suitable for experimental analysis.In Sec. III, we discuss the LHC phenomenology and illustrateour search strategy, and then we present our estimations inSec. IV. Finally, we summarize and conclude in Sec. V.

II. VECTOR LEPTOQUARK MODELS

To conserve electromagnetic charge, vLQs that decay to a top-lepton pair would have either electric charge equal to ±1/3 or±5/3 (if the lepton is a charged one) or 2/3 (if lepton is a neu-trino). This means that among the vLQs listed in Refs. [91–94],the weak singlets U1 and U1, doublets V2 and V2 and triplet U3

would qualify for our study. Below, we display the relevantterms in the interaction Lagrangians following the notation ofRef. [94]. To avoid proton decay constraints, we ignore thediquark operators.

� U1 = (3,1,5/3): The electric charge of U1 is 5/3. Hence,it couples exclusively with the right-handed leptons:

L ⊃ xRR1 ij uiRγ

µU1,µ`jR + H.c., (1)

where uR and `R are a SM right-handed up-type quark and acharged lepton, respectively, and i, j = {1, 2, 3} are the gener-ation indices. The color indices are suppressed. For our pur-pose, we consider only those terms that would connect a vLQto a third-generation quark and ignore the rest,

L ⊃ xRR1 3j tR(γ · U1

)`jR + H.c. (2)

� U1 = (3,1,2/3): The necessary interaction terms for thecharge-2/3 U1 can be written as

L ⊃ xLL1 ij QiLγ

µU1,µLjL + xRR1 ij d

iRγ

µU1,µ`jR + H.c., (3)

where QL, LL, and dR are the SM left-handed quark doublet,lepton doublet, and a down-type right-handed quark, respec-tively. The i = 3 terms can be written explicitly as

L ⊃ xLL1 3j

{tL (γ · U1) νjL + bL (γ · U1) `jL

}+ xRR1 3j bR (γ · U1) `jR + H.c. (4)

� V2 = (3,2,5/6): For V2, the Lagrangian is as follows:

L ⊃ xRL2 ij dCiR γµV a2,µε

abLjbL

+ xLR2 ij QCi,aL γµεabV b2,µ`

jR + H.c. (5)

The superscript C denotes charge conjugation. Expanding theLagrangian we get,

L ⊃ −(xRL2 U)ij dCiR γµV

1/32,µ ν

jL + xRL2 ij d

CiR γµV

4/32,µ `

jL

+ (VTxLR2 )ij uCiL γµV

1/32,µ `

jR − xLR2 ij d

CiL γµV

4/32,µ `

jR + H.c.,

(6)

where U and V represent the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) neutrino mixing matrix and the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix, respectively.We assume U to be unity, as the LHC is blind to the flavor ofthe neutrinos. Similarly, since the small off-diagonal terms ofthe CKM matrix play a negligible role at the LHC, we assume adiagonal CKM matrix for simplicity. Hence, the terms relevantfor our analysis are

L ⊃ −xRL2 3j bCR

{(γ · V 1/3

2

)νjL −

(γ · V 4/3

2

)`jL

}+ xLR2 3j

{tCL

(γ · V 1/3

2

)− bCL

(γ · V 4/3

2

)}`jR + H.c. (7)

� V2 = (3,2,−1/6): For V2, the Lagrangian becomes

L ⊃ xRL2 ij uC iR γµV b2,µε

abLj,aL + H.c. (8)

Expanding it, we get

L ⊃ −xRL2 ij uC iR γµV

1/32,µ `

jL + (xRL2 U)ij u

C iR γµV

−2/32,µ νjL

+ H.c. (9)

The terms with the third-generation quarks are

L ⊃ xRL2 3j tCR

{−(γ · V 1/3

2

)`jL +

(γ · V −2/3

2

)νjL

}+ H.c.

(10)

� U3 = (3,3,2/3): The necessary interaction terms for thetriplet U3 are

L ⊃ xLL3 ijQi,aL γµ

(τkUk3,µ

)abLj,bL + H.c., (11)

2

Simplified models [Eqs. (14) – (16)] LQ models [Eqs. (1) – (13)]

Benchmarkscenario

Possiblecharge(s)

Type ofLQ

Nonzerocouplingsequal to λ

Chargedleptonchiralityfraction

Type ofLQ

Nonzerocouplingequal to λ

Decaymode(s)

Branchingratios(s){β, 1− β}

LC1/3 χ1 Λ` ηL = 1 V

1/32 xRL2 3j t`

{100%, 0}2/3 χ2 Λν —(V−2/32

)† (xRL2 3j

)∗tν

5/3 χ5 Λ` ηL = 1 U5/33

√2 xLL3 3j t`

LCSS*2/3 χ2

Λ` = ΛνηL = 1

U1 xLL1 3j {tν, b`} {50%, 50%}LCOS Λ` = −Λν U

2/33 −xLL3 3j

RC1/3 χ1 Λ` ηR = 1

V1/32 xLR2 3j t` {100%, 0}

5/3 χ5 Λ` U1 xRR1 3j

RLCSS*1/3 χ1

Λ` = ΛνηR = 1

V1/32 xLR2 3j = −xRL2 3j {t`, bν} {50%, 50%}

RLCOS* Λ` = −Λν V1/32 xLR2 3j = xRL2 3j

TABLE I. Summary of the nine benchmark scenarios considered. The branching ratio for a χ to decay to a top quark, β is fixedfor all models [Eqs. (1) – (13)], except for U1 in the LCSS scenario (β ≤ 50%) and V 1/3

2 in the RLCSS/OS scenarios where0 ≤ β < 100% (for β = 100%, these two scenarios become the same as the RC scenario). The exceptional scenarios are markedby an asterisk. Here, λ is a generic free coupling parameter. For simplicity, we have chosen only this one coupling to control all ofthe nonzero new couplings in every benchmark. This essentially means also choosing β to be 50% in the exceptional scenarios.

where τk denotes the Pauli matrices. This can be expanded as

L ⊃ −xLL3 ij diLγ

µU2/3µ `jL + (VxLL3 U)ij u

iLγ

µU2/3µ νjL

+√

2(xLL3 U)ij diLγ

µU−1/3µ νjL +

√2(VxLL3 )ij u

iLγ

µU5/3µ `jL

+ H.c. (12)

The terms for the third-generation quarks can be written ex-plicitly as,

L ⊃ xLL3 3j

{− bL

(γ · U2/3

3

)`jL + tL

(γ · U2/3

3

)νjL

+√

2 bL(γ · U−1/3

3

)νjL +

√2 tL

(γ · U5/3

3

)`jL

}+ H.c. (13)

A. Simplified model and benchmark scenarios

The above models can be simplified into the following phe-nomenological Lagrangians:

L ⊃ Λ`

{√ηR t

CL (γ · χ1) `R +

√ηL t

CR (γ · χ1) `L

}+ Λν b

CR (γ · χ1) νL + H.c., (14)

L ⊃ Λ`

{εR√ηR bR (γ · χ2) `R +

√ηL bL (γ · χ2) `L

}+ Λν tL (γ · χ2) νL + H.c., (15)

L ⊃ Λ`

{√ηR tR (γ · χ5) `R +

√ηL tL (γ · χ5) `L

}+ H.c., (16)

where we have suppressed the lepton generation index. Wedenote a generic charge ±n/3 vLQ by χn. Here, ηL andηR = 1−ηL are the charged lepton chirality fractions [89, 97].In Eq. (15), we have introduced a sign term εR = ±1 to in-corporate a possible relative sign between the left-handed andright-handed terms [see Eq. (7)]. We shall consider only realcouplings in our analysis for simplicity.

As we did for the sLQs [89], here too we identify somebenchmark scenarios with the simplified models (see Table I).Each scenario corresponds to one of the realizable models de-scribed above [see Eqs. (1) – (13)]. Here, we have ignoredany possible mixing among the vLQs. The BR for a χ to de-cay to a top quark, β, is fixed in all models [Eqs. (1) – (13)],except for two cases that we shall describe shortly. For sim-plicity, we choose only one free coupling λ parametrizing thenonzero new couplings in every benchmark scenario. (See thefourth and seventh columns of Table. I. By doing this, we areessentially also choosing β to be 50% in the free β scenarios.)

• In the Left Coupling (LC) scenario, a χ can directly cou-ple with left-handed leptons. We set λ equal to Λ` (forχ1), Λ` (for χ5) or Λν (for χ2) and put all other cou-plings to zero. For χ1 and χ5 we set ηL = 1. Here , χ1

represents a V 1/32 with Λ` = xRL2 3j , χ5 represents a U

5/33

with Λ =√

2 xLL3 3j and χ2 represents an anti-V −2/32

with Λν =(xRL2 3j

)∗. In this scenario, a χ1 or χ5 decays

to t` pairs and a χ2 decays to tν pairs all of the time.

• If a χ2 is of U1 or U2/33 type, it can also decay to a b`

pair. Hence, it is possible that a χ2 couples with left-handed leptons but the BR for the decay χ2 → tν (β)is 50%. Such possibilities are captured in the Left Cou-plings with the Same Sign (LCSS) or the Left Couplingswith Opposite Signs (LCOS) scenarios. The differencebetween these two comes from the different relativesigns between the χ2b` and χ2tν couplings. In LCSS,the χ2 behaves as a U1 with Λ` = Λν = xLL1 3j , whereasin LCOS it behaves as a U2/3

3 with Λ` = −Λν = −xLL3 3j .It is important to note that in the U1 case, it is possibleto have β < 50% if we consider a nonzero xRR1 3j . Thiscan be seen from Eq. (4). Unlike the sLQ case [89], theLCSS and LCOS scenarios for the vLQ yield the same sin-gle production cross section as there is no interferenceamong the contributing diagrams.

• The Right Coupling (RC) scenario, where a LQ couplesonly to right-handed charged leptons, is exclusive to χ1

3

g

g

g

χ

χ

(a)

χ

χ

ℓ/ν

q

q

(b)

b

q

W

q′

ℓ

χ

t

(c)

g

g

t

χ

χ

ℓ

t

(d)

FIG. 1. Representative Feynman diagrams for the LQ production at the LHC. Panels (a) and (b) show pair production processesand panels (c) and (d) show single production processes.

and χ5. Like the LC scenario, here we have β = 100%.In this case a χ1 behaves as a V 1/3

2 with Λ` = xLR2 3j anda χ5 behaves as a U1 with Λ` = xRR1 3j .

• Unlike the sLQ φ1 (see Ref. [89]), the χ1 type vLQs (ifit is V 1/3

2 ) can decay to both t` and bν pairs, providedΛ` and Λν are both nonzero. We design two scenar-ios, namely, Right (lepton) Left (neutrino) Couplingswith the Same Sign (RLCSS) where χ1 ≡ V

1/32 with

Λ` = Λν = xLR2 3j = xRL2 3j , and Right (lepton) Left (neu-trino) Couplings with Opposite Signs (RLCOS) whereχ1 ≡ V

1/32 with Λ` = −Λν = xLR2 3j = xRL2 3j . In these

two scenarios, β can be anything between 0 and 100%as both involve two independent couplings [xLR2 3j andxRL2 3j , see Eq. (7)]. However, we consider only β = 50%for these benchmarks. We introduce these two bench-marks for completeness, though for our purpose thesetwo are equivalent. As there is no interference contri-bution sensitive to this sign flip, all of the productionprocesses would have the same cross sections in bothscenarios.

Before we move on, we note that the kinetic terms for a vec-tor leptoquark contains a free parameter, usually denoted asκ [94],

L ⊃ −1

2χ†µνχ

µν +M2χ χ†µχ

µ − igsκ χ†µT aχν Gaµν , (17)

where χµν stands for the field-strength tensor of χ. This pa-rameter κ can change the pair and (interestingly) some singleproduction cross sections through the modification of the χχgvertex.2 We take two benchmark cases with κ = 0 and κ = 1in our analysis.

III. LHC PHENOMENOLOGY & SEARCH STRATEGY

We keep our computational setup the same as before [89].We use FeynRules [99] to create the UFO [100] model filesfor the Lagrangians in Eqs. (14)–(16). Both the signal andbackground events are generated in MadGraph5 [101] at theleading order (LO). We include higher-order corrections to thebackground processes with QCDK factors wherever available.For VLQs, higher-order K factors for signal processes are not

2 Similar modifications are also possible for other gauge bosons [92,93]. However, we ignore direct electroweak χ-V couplings in ouranalysis.

yet known. We use NNPDF2.3LO [102] parton distributionfunctions with default dynamical renormalization and factor-ization scales to generate events inMadGraph5 and then passthem through Pythia6 [103] for showering and hadroniza-tion. Detector effects are simulated using Delphes3 [104]with the default CMS card. Fatj ets are reconstructed fromDelphes tower objects using the Cambridge-Achen [105] clus-tering algorithm (with R = 1.5) in FastJet [106]. We recon-struct hadronic tops from fat jets with HEPTopTagger [107]with default parameters except for the top-mass windowwhichwe relax a little to 80GeV from the default 50GeV to keepmoresignal events.

A. Production at the LHC

The vLQs would be produced resonantly at the LHC throughthe pair and the single production channels. The dominantpair production diagrams are free of the new couplings anddepend only on the universal strong coupling (there are dia-grams with t-channel lepton exchange that involve new cou-plings [see Fig. 1(b)], but their contribution to the total pairproduction cross section is small [97]); hence, the process ismostly model independent up to a choice of κ. The pair pro-duction would lead to the following final states:

pp →

χ1χ1 → (t`)(t`) / (t`)(bν) / (bν)(bν)

χ2χ2 → (tν)(tν) / (tν)(b`) / (b`)(b`)

χ5χ5 → (t`)(t`)

.(18)

Here, as we did for the sLQs [89], we ignore those channelswith no top quark and consider only symmetric channels i.e.,both of the vLQs decay to the same final state. Constrain-ing ourselves to such channels will restrict the possible SMbackgrounds and make our signal easier to detect. It is gen-erally believed that the symmetric modes have good discoveryprospects [108].3 With these considerations, we are now leftwith only the (t`)(t`) (for χ1 or χ5) and (tν)(tν) (for χ2) chan-nels.

With similar consideration for the single production pro-cesses, where a LQ is produced in association with a leptonand either a jet or a top quark, the possible final states are

3 The asymmetric modes (where the two LQs decay differently) havenot been used for LQ searches so far. For some LQmodels, asymmet-ric channels could provide a better reach than symmetric channelsand, therefore, require a separate dedicated analysis [109].

4

10−3

10−2

10−1

100

101

102

103

104

0.5 1 1.5 2 2.5 3

σ(f

b)

Mχ1 (TeV)

χ1χ1(λ → 0)χ1ℓj(LC)χ1ℓj(RC)χ1ℓj(Λν)χ1ℓt(LC)χ1ℓt(RC)

κ = 0

(a)

10−3

10−2

10−1

100

101

102

103

104

105

0.5 1 1.5 2 2.5 3

σ(f

b)

Mχ1 (TeV)

χ1χ1(λ → 0)χ1ℓj(LC)χ1ℓj(RC)χ1ℓj(Λν)χ1ℓt(LC)χ1ℓt(RC)

κ = 1

(b)

10−3

10−2

10−1

100

101

102

103

104

0.5 1 1.5 2 2.5 3

σ(f

b)

Mχ2 (TeV)

χ2χ2(λ → 0)χ2tν(LC)κ = 0

(c)

10−3

10−2

10−1

100

101

102

103

104

105

0.5 1 1.5 2 2.5 3

σ(f

b)

Mχ2 (TeV)

χ2χ2(λ → 0)χ2tν(LC)κ = 1

(d)

10−3

10−2

10−1

100

101

102

103

104

0.5 1 1.5 2 2.5 3

σ(f

b)

Mχ5 (TeV)

χ5χ5(λ → 0)χ5ℓj(LC)χ5ℓj(RC)χ5ℓt(LC)χ5ℓt(RC)

κ = 0

(e)

10−3

10−2

10−1

100

101

102

103

104

105

0.5 1 1.5 2 2.5 3

σ(f

b)

Mχ5 (TeV)

χ5χ5(λ → 0)χ5ℓj(LC)χ5ℓj(RC)χ5ℓt(LC)χ5ℓt(RC)

κ = 1

(f)

FIG. 2. The parton-level cross sections of different production channels of χ1 [(a) and (b)], χ2 [(c) and (d)], and χ5 [(e) and (f)]at the 14 TeV LHC as functions ofMχn . The single production cross sections are computed for a benchmark coupling λ = 1 (seeTable I). Here, ` stands for either an electron or a muon and the j in the single production processes includes all the light jets aswell as b jets. Their cross sections are generated with a cut on the transverse momentum of the jet, pjT > 20 GeV.

5

given as

pp →{χ1t` → (t`)t`

χ1`j → (t`)`j

}, (19)

pp →{χ2tν → (tν)tν

χ2νj → (tν)νj

}, (20)

pp →{χ5t` → (t`)t`

χ5`j → (t`)`j

}. (21)

In Fig. 1 we show some representative Feynman diagrams ofthe pair and single productions of vLQs.

In Fig. 2 we show the parton-level cross sections of differentproduction processes of χ1 [Figs. 2(a)–2(b)], χ2 [Figs. 2(c),–2(d)] and χ5 [Figs. 2(e),–2(f)] as functions of their masses.The single production cross sections scale as λ2. Here theyare computed for a different benchmark scenarios with ref-erence value λ = 1. We see that in the LC scenario withκ = 0, the single production cross section σ(pp→ χ1`j) over-takes the pair production cross section at about 1.8 TeV, whileσ(pp → χ1t`) always remains smaller. For κ = 1, the pairproduction cross section increases, moving the crossover pointwith σ(pp→ χ1`j) to about 2.6 TeV. Interestingly, we find thatσ(pp → χ1t`) depends on the choice of κ despite being a sin-gle production process as it contains the κ-dependent χ1χ1gvertex. In the RC scenario, σ(pp → χ1`j) is reduced by al-most 2 orders of magnitude compared to that in the LC sce-nario. This happens because in the RC scenario, a χ1 couplesto a right-handed top that comes from another left-handed topgenerated in the charged-current interaction through a chiral-ity flip. If the Λν coupling alone is turned on, the cross sectionfor the pp → χ1`j process is negligible [see Figs. 2(a)–2(b)].(Note, however, that a nonzero Λν can still affect the BRs. Forexample, we can consider RLCSS and RLCOS scenarios wherethe BRs for the χ1 → t` and χ1 → bν modes are 50% each.)Now, because of the small contribution from the Λν -dependentdiagrams and the fact that there is no interference in both theRLCSS and RLCOS scenarios, the pp → χ1`j process wouldhave the same cross section as in the RC scenario. For χ2, pairproduction pp → χ2χ2 always dominates over single produc-tion pp→ χ2tν up to a mass of 3 TeV with λ = 1 coupling forboth κ = 0 and κ = 1. In this case, we obtain a tt plus large/ET signature which was analyzed in Ref. [90]. The χ5 vLQ issimilar to the χ1 and yields similar signatures at the colliders.

The distinctive feature of our signal is the presence ofboosted top quarks and high-pT charged leptons. In symmet-ric modes, we have at least one top quark in the final statefor single production while the pair production gives rise totwo top quarks. In both cases, we have two high-pT chargedleptons. Therefore, as already indicated in the Introduction,we combine events from both pair and single productions bydemanding at least one top jet (a hadronically decaying topquark forming a fat jet) and exactly two high-pT same-flavor-opposite-sign (SFOS) leptons in the final state to enhance thesignal sensitivity. Note that the same final state can arise fromboth pair and single productions. For example, the t`t` statecan come from both pp→ χ1,5χ1,5 and pp→ χ1,5t` processes(see Fig. 1). This can lead to double counting the contribu-tion of some diagrams while generating signal events. Onecan avoid this by ensuring that both χ and χ† are not on-shellsimultaneously in any single production event [97].

Background σ QCDprocesses (pb) Order

V+ jets Z+ jets 6.33× 104 NNLO[110, 111] W+ jets 1.95× 105 NLOV V+ jets WW+ jets 124.31 NLO[112] WZ+ jets 51.82 NLO

ZZ+ jets 17.72 NLOSingle t tW 83.1 N2LO[113] tb 248.0 N2LO

tj 12.35 N2LOtt [114] tt+ jets 988.57 N3LO

ttV [115]ttZ 1.045 NLO+NNLLttW 0.653 NLO+NNLL

TABLE II. Total cross sections without any cut for SM back-ground processes considered in our analysis. The higher-orderQCD cross sections are taken from the literature and are shownin the last column. We use these cross sections to computethe K factors which multiply the LO cross sections to includehigher-order effects.

B. Backgrounds and selection

Since the topology of the vLQ signal is identical to that of thesLQ signal [i.e., at least one (hadronic) top fatjet and exactlytwo high-pT SFOS leptons], our background analysis essen-tially remains the same as before [89]. Therefore we refer thereader to the earlier paper for a detailed discussion on the pos-sible SM background processes; here, we present the gist of ourdiscussions found there. The dominant SM background pro-cesses for our desired signal can arise from processes with twoleptons and significant cross sections at the LHC. The top-likefat jet can appear from either an actual top quark decayinghadronically or a bunch of QCD/non-QCD jets mimicking itssignature. We find that pp → Z+jets and pp → tt+jets pro-cesses contribute significantly to the background. The singletop, diboson, and ttV (V = W,Z) production processes aresubdominant. There are SM processes with large cross sec-tions, e.g., pp → W+jets → `ν+jets that can in principle actas backgrounds because of a jet mimicking a lepton. However,we found that these processes actually contribute negligibly,thanks to a very small misidentification efficiency.

In Table II we list the relevant SM processes and their higher-order cross sections. We consider these backgrounds after ad-justing with appropriate K factors to include higher-order ef-fects. Although the bare cross sections (i.e. without any cut)of some background processes are seemingly huge, we con-trol them by applying strong selection cuts. These cuts aredesigned in such a way that they would drastically reduce thebackground without harming the signal much since our sig-nal possesses specific kinematic features that are very differentfrom the backgrounds. However, some backgrounds are so bigat the beginning (e.g., Z+jets) that in order to save compu-tation time and have better statistics, we apply the followingstrong cuts at the generation level:

1. pT(`1) > 250 GeV.

2. Invariant massM(`1, `2) > 115 GeV (Z-mass veto).

Here `i denotes the ith pT-ordered lepton (e/µ). After gener-ating events with the above generation-level cuts, we apply the

6

0

2

4

6

8

10

1.6 1.8 2 2.2 2.4 2.6 2.8 3

Z

Mχ1 (TeV)

pair50pair100

LC50LC100RC50

RC100

κ = 0

(a)

0

2

4

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RC100

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(b)

0

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Z

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pair100LCRC

κ = 0

(c)

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4

6

8

10

1.8 2 2.2 2.4 2.6 2.8 3

Z

Mχ5 (TeV)

pair100LCRC

κ = 1

(d)

FIG. 3. Expected significance Z in units of standard deviation σ for observing the χ1 (a)[κ = 0],(b)[κ = 1] and χ5(c)[κ =0],(d)[κ = 1] signals over the SM backgrounds. They are plotted as functions of their masses for 3 ab−1 of integrated luminosityat the 14 TeV HL-LHC for different coupling scenarios in the electron mode. We use the combined pair and single productionsfor the signals in the LC and RC scenarios. We also show the pair production significance for 50% and 100% BRs in the χ → t`decay mode. We have considered λ = 1 when computing the signals.

Sign

ificanceZ Limit onMχ (TeV)

κ = 0 κ = 1

χ1 χ5 χ1 χ5

Combined Pair Combined Pair Combined Pair Combined PairLC50 LC RC50 RC BR=0.5 BR=1 LC RC BR=1 LC50 LC RC50 RC BR=0.5 BR=1 LC RC BR=1

5 2.10 2.34 1.85 2.10 1.79 2.05 2.36 2.07 2.04 2.26 2.51 2.14 2.40 2.10 2.36 2.52 2.39 2.363 2.25 2.51 1.97 2.22 1.89 2.15 2.52 2.18 2.15 2.40 2.65 2.26 2.51 2.21 2.47 2.66 2.50 2.472 2.39 2.64 2.06 2.31 1.97 2.23 2.66 2.27 2.23 2.52 2.76 2.35 2.59 2.29 2.55 2.78 2.58 2.55

TABLE III. The mass limits corresponding to 5σ (discovery), 3σ and 2σ (exclusion) significances (Z) for observing the (a) χ1 and(b) χ5 signals over the SM backgrounds for 3 ab−1 integrated luminosity at the 14 TeV LHC with combined and pair-production-only signals. Here, LC (RS) stands for LC100 (RC100).

following final selection criteria sequentially on the signal andbackground events at the analysis level:

C1: (a) Minimum one top jet (obtained from HEPTopTag-ger) with pT(th) > 135 GeV.

(b) Exactly two SFOS leptons with pT(`1) > 400 GeV

and pT(`2) > 200 GeV and pseudorapidity |η(`)| < 2.5.For e, we consider the barrel-end cap cut on η between1.37 and 1.52.

(c) Invariant mass of the lepton pair M(`1, `2) > 120GeV (Z veto).

7

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0.5

1

1.5

2

2.5

3

3.5

2 2.2 2.4 2.6 2.8 3

κ = 1

(d)

FIG. 4. The 5σ discovery reaches in the λ-Mχ planes for χ1 with (a) κ = 0 and (b) κ = 1 and for χ5 with (c) κ = 0 and (d)κ = 1. These plots show the smallest λ needed to observe χ1 and χ5 signals with 5σ significance for a range ofMχ with 3 ab−1 ofintegrated luminosity. The pair-production-only regions for 50% and 100% BRs in the χ→ t` decay mode are shown with shadesof green. Since the pair production is insensitive to λ, a small coupling is sufficient to attain 5σ significance within the greenregions.

(d) The missing energy /ET < 200 GeV.

C2: The scalar sum of the transverse pT of all visible objects,ST > 1.2×Min (Mχ, 1750) GeV.

C3: Max(M(`1, t) OR M(`2, t)) > 0.8 × Min (Mχ, 1750)GeV.

IV. DISCOVERY POTENTIAL

We use the following formula to estimate the signal signifi-cance Z:

Z =

√2 (NS +NB) ln

(NS +NBNB

)− 2NS , (22)

where the number of signal and background events survivingthe final selection cuts (as listed in the previous section) aredenoted byNS andNB , respectively. In Fig. 3 we show the ex-pected significance as a function of vLQ masses. As discussedearlier, the choice of κ affects the pair and some single produc-tions. In Figs. 3(a) and 3(b) we present Z for χ1 with κ = 0

and κ = 1, respectively. Similarly, Figs. 3(c) and 3(d) are forχ5. These curves are obtained for the 14 TeV LHC with 3 ab−1

of integrated luminosity. We have used λ = 1 to estimate thesignificance for the combined signal (i.e. the pair and singleproduction events together). We note the following points:

• The LC100 (RC100) curves for χ1 and the LC (RC)curves for χ5 represent the significances in the LC (RC)scenario where the BR of the χ1 → t` decay is 100%.

• For χ1, the LC50 and RC50 curves represent the caseswhere the BR of χ1 → t` decay mode is 50%. Althoughthey are not realized in the LC and RC scenarios, such asituation is possible if there are other decay modes of χ1

(which play no role in our analysis beyondmodifying theBR). Hence, we show these plots to give some estimatesof how the significance would vary with the BR.

• For comparison, we also show the expected significanceobtained with only the pair production events for the50% and 100% BR cases. For instance, for 100% BR inthe χ1 → t`mode, the HL-LHC (3 ab−1) discovery massreach (i.e., Z = 5σ) with only pair production is about

8

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κ = 1

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κ = 0

(c)

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2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3

λ

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comb(LC)comb(RC)

pair(BR=1.0)0

0.5

1

1.5

2

2.5

3

3.5

2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3

κ = 1

(d)

FIG. 5. The 2σ exclusion limits in the λ-Mχ planes for χ1 with (a) κ = 0 and (b) κ = 1 and for χ5 with (c) κ = 0 and(d) κ = 1. These plots show the smallest λ that can be excluded by the HL-LHC with 3 ab−1 of integrated luminosity. Thepair-production-only regions for 50% and 100% BRs in the χ→ t` decay mode are shown with green shades.

2.05 (2.35) TeV for κ = 0 (κ = 1).

• When the LC coupling is unity, the discovery reachgoes up to 2.35 (2.50) TeV once the single produc-tion processes are included. However, in the RC sce-nario the improvement is minor. This happens becauseσ (pp→ χ1`j) is larger in the LC scenario than that inthe RC scenario.

• Unlike the scalar case, there is no interference amongthe different signal diagrams, and hence the signal sig-nificances in the RLCSS or RLCOS benchmarks are thesame as that in the RC scenario.

• In Figs. 3(c) and 3(d) we observe that the maximumreach for χ5 comes from the combined LC scenario. Thevalues are 2.35 and 2.50 TeV for κ = 0 and κ = 1, re-spectively. There is a suppression in the RC channel fora similar reason as for χ1, a χ5 LQ also couples to a rightchiral top.

In Table III we collect all of the numbers for Z = 2σ, 3σ, and5σ.

Since we can parametrize the combined signal cross sectionfor anyMχ as

σsignal ≈ σpair(Mχ) + λ2σsingle(λ = 1,Mχ), (23)

the combined signal cross section increases with λ for any fixedMχ. By recasting the figures shown in Fig. 3, which are for λ =1, we can obtain the reach in the λ-Mχ plane, as we show inFigs. 4 and 5. We show the 5σ discovery curves in Fig. 4 whilethe 2σ exclusion curves are displayed in Fig. 5. These plotsshow the lowest value of λ required to observe the vLQ signalfor a varyingMχ with 5σ confidence level for discovery. For theexclusion plots, all points above the curves can be excluded atthe 95% confidence level at the HL-LHC.

V. SUMMARY AND CONCLUSIONS

Usually, in the direct LQ searches, it is assumed that LQs onlycouple to quarks and leptons of the same generation. Col-lider signatures of TeV-scale LQs with large cross-generationalcouplings, motivated by the persistent flavor anomalies, arecompletely different than what is considered in the usual LQsearches at the LHC. It is then important to explore thesepossibilities in detail. In a previous paper [89], we investi-gated the HL-LHC prospects of all scalar LQ models withinthe Buchmüller-Rückl-Wyler classifications [91] that wouldproduce boosted-t + high-pT-` signatures at the LHC. In this

9

follow-up paper, we investigated the case for the vector LQswith the same signature. The vLQs that decay to a top-quarkcan have three possible electric charges, ±1/3, ±2/3, and±5/3. Among these, our primary focus was on the charge±1/3, ±5/3 vLQs that can decay to a top quark and an elec-tron or a muon as a unique top-lepton resonance system wouldappear from the decays of these LQs.

In this paper, we introduced some simple phenomenologicalLagrangians. These simple models can cover the relevant pa-rameter spaces of the full models described in Refs. [91, 94].In this simplified framework, we studied the pair and singleproduction channels of vector LQs at the LHC. Pair produc-tion of the vLQs produces final states with two boosted topquarks and two high-pT leptons and determines the LHC dis-covery reach in the low-mass region. On the other hand, thesingle production processes produce final states with at leastone boosted top quark and two high-pT leptons. We observedtwo interesting points about single production. 1) Despite con-sidering vLQ couplings with only third-generation quarks, wesee that the single production cross sections are not necessarilyvery small, provided, of course, the new couplings controllingthem are not negligible. 2) Like the pair production, some sin-gle production processes can also depend on the parameter κthat appears in the gluon-vector LQ coupling. In some sce-narios, for order-one new coupling(s), the single productionwould control the LHC reach in the high-mass region.

We adopted a search strategy of selecting events with at leastone boosted hadronic top quark and exactly two high-pT lep-tons of the same flavor and opposite sign. This combines eventsfrom the pair and single productions and, therefore, enhancesthe discovery reach by about 300 GeV from the usual pair pro-duction searches at the LHC. Our results show that charge 1/3and 5/3 vector LQs can be probed up to 2.35 (2.50) TeV for100% branching ratio in the t` decay mode for κ = 0 (κ = 1)and order-one new couplings at the 14 TeV LHC with 3 ab−1

of integrated luminosity with 5σ significance. Alternately, inthe absence of their discoveries, they can be excluded up to2.65 (2.75) TeV at the 95% confidence limit. Since the singleproduction cross sections scale as λ2, we also showed how thediscovery/exclusion reach would vary with λ within its pertur-

bative domain.

Comparing with the results in Ref. [89], we saw that in gen-eral it may be possible for the LHC to discover/exclude heaviervLQs than sLQs for comparable parameters. For example, forλ = 1 the 5σ discovery reach for χ5 goes up to 2.35 TeV (κ = 0)in the LC scenario. This is higher than the 1.75 TeV reach inthe LC scenario for φ5 (or even 1.95 TeV in the RC scenario).Similar observations can be made for other LQs/scenarios too.Of course, in the case of vLQs, the additional parameter κ canenhance the reaches even more: for χ5 in the LC scenario itincreases to 2.5 TeV. There is no such parameter in the case ofsLQs: in this regard, the sLQ pair production process is moremodel independent (i.e. QCD driven) than that for vLQs. Also,for some sLQs, the relative signs between new physics cou-plings are important as they affect the single production crosssections through interference among different signal diagrams.This happens for φ1 whose single production cross sections inthe LCSS and LCOS scenarios differ significantly. However,there is no such interference for vLQs; for example, the χ1 sin-gle production cross section is the same in the RLCSS and RL-COS scenarios. Of course, for both sLQs as well as vLQs, singleproduction processes do play an important role in determiningthe LHC discovery/exclusion reaches even though we consid-ered only third-generation quarks coupling with the LQs. Itwould be interesting to investigate ways to distinguish sLQsand vLQs with such similar signatures at the LHC. Finally, wepoint out that in these two papers we have presented simpli-fied models for all possible LQs that couple with the top quarkand leptons. These simplified modes are suitable for bottom-up/experimental studies and can be easily mapped to the fullmodels.

ACKNOWLEDGMENTS

A. B. and S.M. acknowledge financial support from the Sci-ence and Engineering Research Board (SERB), DST, India un-der grant number ECR/2017/000517.

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