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PHYSICAL REVIEW D 101, 115015 (2020)

Boosting vector leptoquark searches with boosted tops

† ‡ Arvind Bhaskar ,1,* Tanumoy Mandal ,2, and Subhadip Mitra 1, 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

(Received 7 April 2020; accepted 21 May 2020; published 15 June 2020)

At the LHC, a TeV-scale leptoquark (LQ) that decays dominantly to a top (t) and a light charged (l ¼ e, μ) would form a resonance system of boosted-tþ high-pT-l. We consider all possible vector LQ models within the Buchmüller-Rückl-Wyler classifications with the desired decay. We propose simple phenomenological Lagrangians that are suitable for bottom-up/experimental studies and, at the same time, can cover the relevant parameter spaces of these models. In this simplified framework, we study the pair and single production channels of vector LQs at the LHC. Interestingly, we find that, like the pair production, the cross sections of some single production processes also depend on the parameter κ that appears in the -vector LQ coupling. We adopt a search strategy of selecting events with at least one boosted hadronic and exactly two high-pT of the same flavor and opposite sign. This combines events from the pair and single production processes and, therefore, can enhance the discovery potential beyond that of the pair-production-only searches. For 5σ discovery we find that vector LQs can be probed up to 2.55 TeV for 100% branching ratio in the tl decay mode and Oð1Þ new couplings at the 14 TeV LHC with 3 ab−1 of integrated luminosity.

DOI: 10.1103/PhysRevD.101.115015

I. INTRODUCTION the RD-RD plane by the HFLAV Group puts the anomalies away from the corresponding SM predictions [10–13] by a In the recent past, several experimental collaborations combined significance of ∼3.1σ. The LHCb Collaboration have reported some hints of lepton flavor universality has also observed downward deviations of about 2.5σ violation in the heavy decays. Collectively, these [14–18] from the SM predictions [19,20] in the flavor- point toward the existence of some physics beyond the changing neutral current transition b → sμμ measured in (SM) as the SM gauge interactions are terms of the R ðÞ observables. Similarly, an excess of about flavor-blind. Intriguingly, these seem to be quite tenacious K ∼2σ was found in another observable, R ψ [21]. In addition, and have created a lot of excitement in the physics J= ∼3 5σ community. Initially, the BABAR Collaboration found two a long-standing discrepancy of about . exists in the significant anomalies in the flavor-changing charged cur- anomalous magnetic moment measurement [22]. rent decays of the via the b → cτν transition. They It is known that TeV-scale leptoquarks (LQs) are good candidates to address the flavor anomalies. Moreover, their reported the anomalies in terms of excesses in the R ðÞ D phenomenology has been explored in various other con- observables defined as the ratios of branching ratios (BRs) – to reduce some systematic and hadronic uncertainties [1,2]. texts as well [23 77]. LQs are color-triplet [either scalars (sLQs) or vectors (vLQs)] predicted by many Since then, the excesses have survived the later measure- – ments by the LHCb [3–5] and Belle [6–9] collaborations. beyond-the-SM theories [78 82]. They have fractional The statistical average of these two observables obtained in electric charges and carry both lepton and numbers. In general, a LQ can couple to a quark and a lepton of either the same or different generations. The flavor anomalies suggest that LQs couple more strongly to the third- *[email protected] † [email protected] generation than the other two. Cross-generational ‡ [email protected] couplings of LQs could generate flavor-changing neutral currents; those involving the first and second generations Published by the American Physical Society under the terms of are tightly constrained. However, bounds are relatively the Creative Commons Attribution 4.0 International license. weaker when a of the third generation is involved. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, The search for LQs is an important research program at and DOI. Funded by SCOAP3. the LHC. Usually, the LHC searches are done for LQs that

2470-0010=2020=101(11)=115015(15) 115015-1 Published by the American Physical Society BHASKAR, MANDAL, and MITRA PHYS. REV. D 101, 115015 (2020) couple to and leptons of the same generation and are strategy as the one we proposed for the sLQs [89].We labeled accordingly. For example, pair production of a identify our signal by selecting at least one boosted scalar LQ that decays to a top quark and a lepton (or a hadronic top and exactly two high-pT leptons and use and a tau lepton or ), i.e., a third- the highest-pT top (if there is more than one top) and one of generation LQ, has been extensively analyzed by both the selected leptons to reconstruct a heavy system, i.e., the the ATLAS [83,84] and CMS collaborations [85,86]. LQ. As we have demonstrated before [89,96–98], such a Altogether, the current bound on the third-generation LQ selection strategy combines pair and single production is roughly about a TeV (this, of course, depends on various events and increases the LHC reach. Although pair pro- assumptions and we refer the reader to the actual papers for duction is suitable for probing the low-mass region, single details). However, the flavor-motivated LQ models with production takes over when the LQ becomes heavy. sizable cross-generational couplings would have exotic Compared to the sLQs, the pair production cross sections signatures and require different search strategies. Of late, for vLQs are relatively bigger and hence the current mass the nonstandard decay modes of LQs have started to gain limits obtained for pair production are generally higher for attention; the CMS Collaboration published their first the vLQs than for the sLQs. In the case of vLQs, the results on the pair production searches of LQs in the importance of single production becomes visible for ttμμ channel [87]. Based on the 13 TeV data, they relatively higher mass compared to sLQs. We shall see performed a prospect study for the pair production of that the discovery prospects of the vLQs at the HL-LHC are sLQs in the ttμμ channel at the high-luminosity LHC significantly improved if the new couplings controlling (HL-LHC) [88]. single production are of order unity. In Ref. [89], we investigated the HL-LHC prospects of Before we proceed further, we note that since this paper sLQs that couple dominantly to the top quark in some is a follow-up to Ref. [89], we shall frequently refer to that detail. There, we focused on charge 1=3 and 5=3 sLQs that paper and omit some details that are common while decay to a top quark and a charged lepton. Even though we ensuring that our presentation is self-contained. The rest considered only third-generation quarks, interestingly, we of the paper is organized as follows. In Sec. II we describe found that in some scenarios single production can improve 1 the vLQ models and introduce simplified models suitable their prospects significantly. In this paper, we present a for experimental analysis. In Sec. III we discuss the LHC similar follow-up study for vLQs. Here, too, we concentrate phenomenology and illustrate our search strategy, and then on a specific subset of possible vLQs that dominantly we present our estimations in Sec. IV. Finally, we sum- couple with a top quark and can decay to a top quark and a marize and conclude in Sec. V. light charged lepton (e or μ) with a substantial BR. Since an analysis of the pair production of vLQs that decay to a top quark and a neutrino at the LHC is available in Ref. [90],in II. VECTOR LEPTOQUARK MODELS this paper we do not analyze this channel again. Instead, we To conserve electromagnetic charge, vLQs that decay to a present a set of simplified models that covers all of the top-lepton pair would have either equal to possibilities of a vLQ decaying to a top quark and any 1=3 or 5=3 (if the lepton is a charged one), or 2=3 (if the lepton. These are suitable for experimental analysis. We lepton is a neutrino). This means that among the vLQs listed also demonstrate how they are related to the known models ˜ in Refs. [91–94], the weak singlets U1 and U1, doublets V2 of vLQs [91–94]. ˜ and V2,andtripletU3 would qualify for our study. Below, Our main motivation for considering this specific type of we display the relevant terms in the interaction Lagrangians, vLQs is to investigate their discovery/exclusion following the notation of Ref. [94]. To avoid decay potential by making use of the boosted top signature constraints, we ignore the operators. coming from the LQ decay. They form an exotic resonance ˜ ˜ (i) U1 3; 1; 5=3 : The electric charge of U1 is 5=3. system with a boosted top and a high-p lepton and provide ¼ð Þ T Hence, it couples exclusively with the right-handed a novel way to search for these models at the LHC. Various leptons: flavor anomalies suggest that cross-generational Yukawa- type LQ couplings with tops and leptons might be large. A RR i μ ˜ j L ⊃ x˜ u¯ γ U1 μl þ H:c:; ð1Þ large coupling makes various single production channels 1 ij R ; R important, especially in the high-mass region. For example, where uR and lR are a SM right-handed up-type the relevance of the process gg → LQ þ tμ was pointed out quark and a charged lepton, respectively, and i; j ¼ in Ref. [95]. In our analysis, we adopt the same search f1; 2; 3g are the generation indices. The color indices are suppressed. For our purpose, we consider 1This is interesting because, when a LQ (or any other particle) only those terms that would connect a vLQ to a mostly couples to the third-generation quarks, we generally third-generation quark and ignore the rest, expect their single production to be ignorable as the bottom (top) quark density in the proton is too small (nonexistent) to play L ⊃ ˜RR ¯ γ ˜ lj any significant role at the LHC. x13jtRð · U1Þ R þ H:c: ð2Þ

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(ii) U1 ¼ð3; 1; 2=3Þ: The necessary interaction terms The terms with the third-generation quarks are for the charge-2=3 U1 can be written as L ⊃ ˜RL ¯C − γ ˜ 1=3 lj γ ˜ −2=3 νj x23jtRf ð · V2 Þ L þð · V2 Þ LgþH:c: LL ¯ i μ j RR ¯ i μ j L ⊃ x Q γ U1 μL þ x d γ U1 μl þ H:c:; 1 ij L ; L 1 ij R ; R ð10Þ ð3Þ (v) U3 ¼ð3; 3; 2=3Þ: The necessary interaction terms where QL, LL, and dR are the SM left-handed quark for the triplet U3 are doublet, lepton doublet, and a down-type right- 3 L ⊃ LL ¯ i;aγμ τk k ab j;b handed quark, respectively. The i ¼ terms can x3 ijQL ð U3;μÞ LL þ H:c:; ð11Þ be written explicitly as where τk denotes the Pauli matrices. This can be L ⊃ LL ¯ γ νj ¯ γ lj x13jftLð · U1Þ L þ bLð · U1Þ Lg expanded as j RR ¯ γ l 2 3 2 3 þ x13jbRð · U1Þ R þ H:c: ð4Þ L ⊃− LL ¯ i γμ = lj V LLU ¯ i γμ = νj x3 ijdL Uμ L þð x3 ÞijuL Uμ L pffiffiffi 3¯ 2 5 6 2 LLU ¯ i γμ −1=3νj (iii) V2 ¼ð ; ; = Þ:ForV2, the Lagrangian is as þ ðx3 ÞijdL Uμ L follows: pffiffiffi 2 V LL ¯ i γμ 5=3lj þ ð x3 ÞijuL Uμ L þ H:c: ð12Þ L ⊃ xRL d¯ CiγμVa ϵabLjb 2 ij R 2;μ L The terms for the third-generation quarks can be LR ¯ Ci;aγμϵab b lj written explicitly as þ x2 ijQL V2;μ R þ H:c: ð5Þ

L ⊃ LL −¯ γ 2=3 lj ¯ γ 2=3 νj The superscript C denotes charge conjugation. Ex- x33jf bLð · U3 Þ L þ tLð · U3 Þ L pffiffiffi pffiffiffi panding the Lagrangian, we get 2¯ γ −1=3 νj 2¯ γ 5=3 lj þ bLð · U3 Þ L þ tLð · U3 Þ Lg L ⊃− RLU ¯ Ciγμ 1=3νj RL ¯ Ciγμ 4=3lj þ H:c: ð13Þ ðx2 ÞijdR V2;μ L þ x2 ijdR V2;μ L VT LR ¯ Ciγμ 1=3lj þð x2 ÞijuL V2;μ R − LR ¯ Ciγμ 4=3lj A. Simplified model and benchmark scenarios x2 ijdL V2;μ R þ H:c:; ð6Þ The above models can be simplified into the following where U and V represent the Pontecorvo-Maki- phenomenological Lagrangians: Nakagawa-Sakata neutrino mixing matrix and the ffiffiffiffiffi ffiffiffiffiffi L ⊃ Λ pη ¯C γ χ l pη ¯C γ χ l Cabibbo-Kobayashi-Maskawa (CKM) quark mixing lf RtLð · 1Þ R þ LtRð · 1Þ Lg U matrix, respectively. We assume to be unity, as the ¯ C þ Λνb ðγ · χ1Þν þ H:c:; ð14Þ LHC is blind to the flavor of the . Similarly, R L ffiffiffiffiffi ffiffiffiffiffi since the small off-diagonal terms of the CKM L ⊃ Λ¯ ϵ pη ¯ γ χ l pη ¯ γ χ l matrix play a negligible role at the LHC, we assume lf R RbRð · 2Þ R þ LbLð · 2Þ Lg ¯ ¯ a diagonal CKM matrix for simplicity. Hence, the þ ΛνtLðγ · χ2ÞνL þ H:c:; ð15Þ terms relevant for our analysis are ffiffiffiffiffi ffiffiffiffiffi ˜ p ¯ p ¯ L ⊃ Λlf ηRtRðγ · χ5ÞlR þ ηLtLðγ · χ5ÞlLgþH:c:; 1 3 4 3 L ⊃−xRL b¯ C γ · V = νj − γ · V = lj 23j Rfð 2 Þ L ð 2 Þ Lg ð16Þ LR ¯C γ 1=3 − ¯ C γ 4=3 lj þ x23jftLð · V2 Þ bLð · V2 Þg R þ H:c: where we have suppressed the lepton generation index. ð7Þ We denote a generic charge n=3 vLQ by χn. Here, ηL η 1 − η ˜ ¯ ˜ and R ¼ L are the charged lepton chirality fractions (iv) V2 3; 2; −1=6 :ForV2, the Lagrangian becomes ¼ð Þ [89,97]. In Eq. (15), we have introduced a sign term ϵR ¼ 1 to incorporate a possible relative sign between the left- L ⊃ ˜RL ¯ Ciγμ ˜ b ϵab j;a x2 ijuR V2;μ LL þ H:c: ð8Þ handed and right-handed terms [see Eq. (7)]. We shall consider only real couplings in our analysis for simplicity. Expanding it, we get As we did for the sLQs [89], here we identify some benchmark scenarios with the simplified models (see L ⊃−˜RL ¯ Ciγμ ˜ 1=3lj ˜RL ¯ Ciγμ ˜ −2=3νj Table I). Each scenario corresponds to one of the realizable x2 ijuR V2;μ L þðx2 UÞijuR V2;μ L models described above [see Eqs. (1)–(13)]. Here, we have þ H:c: ð9Þ ignored any possible mixing among the vLQs. The BR for a

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TABLE I. Summary of the nine benchmark scenarios considered. The branching ratio for a χ to decay to a top quark, β, is fixed for all 1=3 models [Eqs. (1)–(13)], except for U1 in the LCSS scenario ðβ ≤ 50%Þ and V2 in the RLCSS/OS scenarios where 0 ≤ β < 100% (for β ¼ 100%, these two scenarios become the same as the RC scenario). The exceptional scenarios are marked by an asterisk. Here, λ is a generic free coupling parameter. For simplicity, we have chosen only this one coupling to control all of the nonzero new couplings in every benchmark. This essentially means also choosing β to be 50% in the exceptional scenarios.

Simplified models [Eqs. (14)–(16)] LQ models [Eqs. (1)–(13)] Benchmark Possible Type Nonzero couplings Charged lepton Type Nonzero coupling Decay Branching ratios(s) scenario charge(s) of LQ equal to λ chirality fraction of LQ equal to λ mode(s) fβ; 1 − βg 1 3 χ Λ η 1 ˜ 1=3 ˜RL l LC = 1 l L ¼ V2 x23j t ¯ −2 3 † RL 2=3 χ2 Λ — ˜ = x˜ tν 100% 0 ν ðV2 Þ ð ffiffiffi23jÞ f ; g 5 3 p 5=3 χ5 Λ˜ η 1 = 2 LL tl l L ¼ U3 x33j 2 3 χ Λ¯ Λ¯ η 1 LL ν l 50% 50% LCSS* = 2 l ¼ ν L ¼ U1 x13j ft ;b gf; g Λ¯ −Λ¯ 2=3 − LL LCOS l ¼ ν U3 x33j 1 3 χ Λ η 1 1=3 LR l 100% 0 RC = 1 l R ¼ V2 x23j t f ; g 5 3 χ Λ˜ ˜ ˜RR = 5 l U1 x13j 1 3 χ Λ Λ η 1 1=3 LR − RL l ν 50% 50% RLCSS* = 1 l ¼ ν R ¼ V2 x23j ¼ x23j ft ;b gf; g Λ −Λ 1=3 LR RL RLCOS* l ¼ ν V2 x23j ¼ x23j

χ to decay to a top quark, β, is fixed in all models single production cross section as there is no [Eqs. (1)–(13)], except for two cases that we shall describe interference among the contributing diagrams. shortly. For simplicity, we choose only one free coupling λ (3) The right coupling (RC) scenario, where a LQ couples parametrizing the nonzero new couplings in every bench- only to right-handed charged leptons, is exclusive to mark scenario. (See the fourth and seventh columns of χ1 and χ5. Like the LC scenario, here we have β 1=3 Table I. By doing this, we are essentially also choosing to β ¼ 100%. In this case a χ1 behaves as a V2 with be 50% in the free β scenarios.) Λ LR χ ˜ Λ˜ RR l ¼ x23j and a 5 behaves as a U1 with l ¼ x13j. (1) In the left coupling (LC) scenario, a χ can directly (4) Unlike the sLQ ϕ1 (see Ref. [89]), the χ1 type vLQs couple with left-handed leptons. We set λ equal to Λl 1=3 ˜ ¯ (if it is V2 ) can decay to both tl and bν pairs, (for χ1), Λl (for χ5), or Λν (for χ2) and put all other provided Λl and Λν are both nonzero. We design couplings to zero. For χ1 and χ5 we set η 1. Here, L ¼ two scenarios, namely, right (lepton) left (neutrino) χ ˜ 1=3 Λ ˜RL χ 1 represents a V2 with l ¼ x23j, 5 represents a couplings with the same sign (RLCSS) where 5 3 pffiffiffi = Λ˜ 2 LL χ χ ≡ 1=3 Λ Λ LR RL U3 with ¼ x33j, and 2 represents an anti- 1 V2 with l ¼ ν ¼ x23j ¼ x23j, and right ˜ −2=3 Λ¯ ˜RL χ χ V2 with ν ¼ðx23jÞ . In this scenario, a 1 or 5 (lepton) left (neutrino) couplings with opposite signs 1=3 decays to tl pairs and a χ2 decays to tν pairs all of (RLCOS) where χ1 ≡ V2 with Λl ¼ −Λν ¼ LR RL β the time. x23j ¼ x23j. In these two scenarios, can be any- 2=3 (2) If a χ2 is of U1 or U3 type, it can also decay to a bl thing between 0 and 100% as both involve two χ LR RL pair. Hence, it is possible that a 2 couples with left- independent couplings [x23 and x23 ; see Eq. (7)]. χ → ν β j j handed leptons but the BR for the decay 2 t ð Þ However, we consider only β ¼ 50% for these is 50%. Such possibilities are captured in the left benchmarks. We introduce these two benchmarks couplings with the same sign (LCSS) or the left for completeness, though for our purpose these two couplings with opposite signs (LCOS) scenarios. are equivalent. As there is no interference contribu- The difference between these two comes from the tion sensitive to this sign flip, all of the production χ l χ ν different relative signs between the 2b and 2t processes would have the same cross sections in χ couplings. In LCSS, the 2 behaves as a U1 with both scenarios. Λ¯ Λ¯ LL l ¼ ν ¼ x13j, whereas in LCOS it behaves as a Before we move on, we note that the kinetic terms for a 2=3 ¯ ¯ LL U3 with Λl ¼ −Λν ¼ −x33 . It is important to vector leptoquark contains a free parameter, usually j κ note that in the U1 case, it is possible to have β < denoted as [94], 50% RR if we consider a nonzero x13j. This can be seen 1 from Eq. (4). Unlike the sLQ case [89], the LCSS † μν 2 † μ † a aμν L ⊃− χμνχ þ Mχχμχ − ig κχμT χνG ; ð17Þ and LCOS scenarios for the vLQ yield the same 2 s

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(a) (b) (c) (d)

FIG. 1. Representative Feynman diagrams for the LQ production at the LHC. Panels (a) and (b) show pair production processes and panels (c) and (d) show single production processes. where χμν stands for the field-strength tensor of χ. This choice of κ. The pair production would lead to the parameter κ can change pairs and (interestingly) some following final states: single production cross sections through the modification 8 9 of the χχg vertex.2 We take two benchmark cases with < χ1χ1 → ðtlÞðtlÞ=ðtlÞðbνÞ=ðbνÞðbνÞ = κ ¼ 0 and κ ¼ 1 in our analysis. → χ χ → ν ν ν l l l pp : 2 2 ðt Þðt Þ=ðt Þðb Þ=ðb Þðb Þ ;: ð18Þ χ5χ5 → ðtlÞðtlÞ III. LHC PHENOMENOLOGY AND SEARCH STRATEGY Here, as we did for the sLQs [89], we ignore those channels We keep our computational setup the same as before with no top quark and consider only symmetric channels, i.e., both of the vLQs decay to the same final state. [89]. We use FeynRules [99] to create the UFO [100] model files for the Lagrangians in Eqs. (14)–(16). Both the signal Constraining ourselves to such channels will restrict the possible SM backgrounds and make our signal easier to and background events are generated in MADGRAPH5 [101] detect. It is generally believed that the symmetric modes at the leading order (LO). We include higher-order cor- 3 rections to the background processes with QCD K factors have good discovery prospects [108]. With these consid- l l χ wherever available. For VLQs, higher-order K factors for erations, we are now left with only the ðt Þðt Þ (for 1 or χ ν ν χ signal processes are not yet known. We use NNPDF2.3LO 5) and ðt Þðt Þ (for 2) channels. [102] parton distribution functions with default dynamical With similar consideration for the single production renormalization and factorization scales to generate events processes, where a LQ is produced in association with a in MADGRAPH5, and then pass them through PYTHIA6 [103] lepton and either a jet or a top quark, the possible final for showering and hadronization. Detector effects are states are given as simulated using DELPHES3 [104] with the default CMS   χ1tl → ðtlÞtl card. Fat jets are reconstructed from DELPHES tower objects pp → ; ð19Þ using the Cambridge-Achen [105] clustering algorithm χ1lj → ðtlÞlj (with R ¼ 1.5)inFASTJET [106]. We reconstruct hadronic   χ2tν → ðtνÞtν tops from fat jets with HEPTOPTAGGER [107] with default pp → ; ð20Þ parameters except for the top-mass window which we relax χ2νj → ðtνÞνj a little to 80 GeV from the default 50 GeV to keep more   χ5tl → ðtlÞtl signal events. pp → : ð21Þ χ5lj → ðtlÞlj A. Production at the LHC In Fig. 1 we show some representative Feynman diagrams The vLQs would be produced resonantly at the LHC of the pair and single productions of vLQs. through the pair and single production channels. The In Fig. 2 we show the parton-level cross sections of dominant pair production diagrams are free of the new different production processes of χ1 [Figs. 2(a)–2(b)], χ2 couplings and depend only on the universal strong coupling [Figs. 2(c)–2(d)], and χ5 [Figs. 2(e)–2(f)] as functions of (there are diagrams with t-channel lepton exchange that their masses. The single production cross sections scale involve new couplings [see Fig. 1(b)], but their contribution as λ2. Here they are computed for different benchmark to the total pair production cross section is small [97]); hence, the process is mostly model independent up to a 3The asymmetric modes (where the two LQs decay differently) have not been used for LQ searches so far. For some LQ models, 2Similar modifications are also possible for other gauge bosons asymmetric channels could provide a better reach than symmetric [92,93]. However, we ignore direct electroweak χ − V couplings channels and, therefore, require a separate dedicated analysis in our analysis. [109].

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(a) (b)

(c) (d)

(e) (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 λ 1 14 TeV LHC as functions of Mχn . The single production cross sections are computed for a benchmark coupling ¼ (see Table I). Here, l stands for either an or a muon and the j in the single production processes includes all of the light jets as well as b jets. j 20 Their cross sections are generated with a cut on the transverse momentum of the jet, pT > GeV.

115015-6 BOOSTING VECTOR LEPTOQUARK SEARCHES WITH … PHYS. REV. D 101, 115015 (2020) scenarios with a reference value λ ¼ 1. We see that in the TABLE II. Total cross sections without any cut for SM back- LC scenario with κ ¼ 0, the single production cross section ground processes considered in our analysis. The higher-order σðpp → χ1ljÞ overtakes the pair production cross section QCD cross sections are taken from the literature and are shown in at about 1.8 TeV, while σðpp → χ1tlÞ always remains the last column. We use these cross sections to compute the K smaller. For κ ¼ 1, the pair production cross section factors, which multiply the LO cross sections to include higher- order effects. increases, moving the crossover point with σðpp → χ1ljÞ to about 2.6 TeV. Interestingly, we find that σðpp → Background processes σ (pb) QCD Order χ1tlÞ depends on the choice of κ despite being a single V þ jets [110,111] Z þ jets 6.33 × 104 NNLO production process as it contains the κ-dependent χ1χ1g Wþ jets 1.95 × 105 NLO vertex. In the RC scenario, σðpp → χ1ljÞ is reduced by almost 2 orders of magnitude compared to that in the LC VV þ jets [112] WW þ jets 124.31 NLO scenario. This happens because in the RC scenario, a χ1 WZ þ jets 51.82 NLO couples to a right-handed top that comes from another left- ZZ þ jets 17.72 NLO handed top generated in the charged-current interaction Single t [113] tW 83.1 N2LO 2 through a chirality flip. If the Λν coupling alone is turned tb 248.0 N LO 2 on, the cross section for the pp → χ1lj process is tj 12.35 N LO – negligible [see Figs. 2(a) 2(b)]. (Note, however, that a tt [114] tt þ jets 988.57 N3LO nonzero Λν can still affect the BRs. For example, we can consider RLCSS and RLCOS scenarios where the BRs for ttV [115] ttZ 1.045 NLO þ NNLL ttW 0.653 NLO þ NNLL the χ1 → tl and χ1 → bν modes are 50% each.) Now, because of the small contribution from the Λν-dependent diagrams and the fact that there is no interference in both detailed discussion on the possible SM background proc- the RLCSS and RLCOS scenarios, the pp → χ1lj process esses; here, we present the gist of our discussions found would have the same cross section as in the RC scenario. there. The dominant SM background processes for our For χ2, pair production pp → χ2χ2 always dominates over desired signal can arise from processes with two leptons single production pp → χ2tν up to a mass of 3 TeV with and significant cross sections at the LHC. The top-like fat λ ¼ 1 coupling for both κ ¼ 0 and κ ¼ 1. In this case, we jet can appear from either an actual top quark decaying obtain a tt plus large =E signature, which was analyzed in T hadronically or a bunch of QCD/non-QCD jets mimicking Ref. [90]. The χ5 vLQ is similar to the χ1 and yields similar its signature. We find that pp → Z þ jets and pp → tt þ signatures at the . jets processes contribute significantly to the background. The distinctive feature of our signal is the presence of The single top, diboson, and ttV (V ¼ W, Z) production boosted top quarks and high-p charged leptons. In sym- T processes are subdominant. There are SM processes with metric modes, we have at least one top quark in the final state large cross sections, e.g., pp → W þ jets → lν þ jets that for single production while the pair production gives rise to can in principle act as backgrounds because of a jet two top quarks. In both cases, we have two high-p charged T mimicking a lepton. However, we found that these proc- leptons. Therefore, as already indicated in the Introduction, esses actually contribute negligibly, thanks to a very small we combine events from both pair and single productions by misidentification efficiency. demanding at least one top jet (a hadronically decaying top In Table II we list the relevant SM processes and their quark forming a fat jet) and exactly two high-p same- T higher-order cross sections. We consider these backgrounds flavor-opposite-sign (SFOS) leptons in the final state to after adjusting with appropriate K factors to include higher- enhance the signal sensitivity. Note that the same final state order effects. Although the bare cross sections (i.e., without can arise from both pair and single production processes. For any cut) of some background processes are seemingly example, the tltl state can come from both pp → χ1 5χ1 5 ; ; huge, we control them by applying strong selection cuts. and pp → χ1 5tl processes (see Fig. 1). This can lead to ; These cuts are designed in such a way that they would double counting the contribution of some diagrams while drastically reduce the background without harming the generating signal events. One can avoid this by ensuring that χ χ† signal much since our signal possesses specific kinematic both and are not on-shell simultaneously in any single features that are very different from the backgrounds. production event [97]. However, some backgrounds are so big at the beginning (e.g., Z þ jets) that in order to save computation time and B. Backgrounds and selection have better statistics, we apply the following strong cuts at Since the topology of the vLQ signal is identical to that the generation level: l 250 of the sLQ signal [i.e., at least one (hadronic) top fat jet (1) pTð 1Þ > GeV. l l 115 and exactly two high-pT SFOS leptons], our background (2) Invariant mass Mð 1; 2Þ > GeV (Z-mass veto). l μ analysis essentially remains the same as before [89]. Here i denotes the ith pT-ordered lepton (e= ). After Therefore, we refer the reader to the earlier paper for a generating events with the above generation-level cuts, we

115015-7 BHASKAR, MANDAL, and MITRA PHYS. REV. D 101, 115015 (2020) apply the following final selection criteria sequentially on (3) C3:MaxðMðl1;tÞ OR Mðl2;tÞÞ > 0.8 × the signal and background events at the analysis level: MinðMχ; 1750Þ GeV. (1) C1: (a) Minimum one top jet (obtained from HEPTOP- 135 IV. DISCOVERY POTENTIAL TAGGER) with pTðthÞ > GeV. l (b) Exactly two SFOS leptons with pTð 1Þ > We use the following formula to estimate the signal 400 l 200 GeV and pTð 2Þ > GeV and pseu- significance Z: η l 2 5 dorapidity j ð Þj < . .Fore, we consider the sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi barrel–end cap cut on η between 1.37   NS þ NB and 1.52. Z ¼ 2ðNS þ NBÞ ln − 2NS; ð22Þ (c) Invariant mass of the lepton pair Mðl1; l2Þ > NB 120 GeV (Z veto). (d) The missing energy =ET < 200 GeV. where the number of signal and background events (2) C2: The scalar sum of the transverse pT of all visible surviving the final selection cuts (as listed in the previous 1 2 1750 objects, ST > . ×MinðMχ; Þ GeV. section) are denoted by NS and NB, respectively. In Fig. 3

(a) (b)

(c) (d)

FIG. 3. Expected significance Z in units of σ for observing the χ1 (a) [κ ¼ 0], (b) [κ ¼ 1] and χ5 (c) [κ ¼ 0], (d) [κ ¼ 1] signals over the SM backgrounds. They are plotted as functions of their masses for 3 ab−1 of integrated luminosity at the 14 TeV HL-LHC for different coupling scenarios in the electron mode. We use the combined pair and single productions for the signals in the LC and RC scenarios. We also show the pair production significance for 50% and 100% BRs in the χ → tl decay mode. We have considered λ ¼ 1 when computing the signals.

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

Limit on Mχ (TeV) κ ¼ 0 κ ¼ 1

χ1 χ5 χ1 χ5 Combined Pair Combined Pair Combined Pair Combined Pair Significance Z LC50 LC RC50 RC BR ¼ 0.5 BR ¼ 1 LC RC BR ¼ 1 LC50 LC RC50 RC BR ¼ 0.5 BR ¼ 1 LC RC BR ¼ 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 2.36 3 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 2.47 2 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

(a) (b)

(c) (d)

FIG. 4. The 5σ discovery reaches in the λ − Mχ planes for χ1 with (a) κ ¼ 0 and (b) κ ¼ 1 and for χ5 with (c) κ ¼ 0 and (d) κ ¼ 1. −1 These plots show the smallest λ needed to observe χ1 and χ5 signals with 5σ significance for a range of Mχ with 3 ab of integrated luminosity. The pair-production-only regions for 50% and 100% BRs in the χ → tl decay mode are shown with shades of green. Since the pair production is insensitive to λ, a small coupling is sufficient to attain 5σ significance within the green regions.

115015-9 BHASKAR, MANDAL, and MITRA PHYS. REV. D 101, 115015 (2020) we show the expected significance as a function of vLQ other decay modes of χ1 (which play no role in our masses. As discussed earlier, the choice of κ affects the pair analysis beyond modifying the BR). Hence, we and some single productions. In Figs. 3(a) and 3(b) we show these plots to give some estimates of how present Z for χ1 with κ ¼ 0 and κ ¼ 1, respectively. the significance would vary with the BR. Similarly, Figs. 3(c) and 3(d) are for χ5. These curves (iii) For comparison, we also show the expected signifi- are obtained for the 14 TeV LHC with 3 ab−1 of integrated cance obtained with only the pair production events luminosity. We have used λ ¼ 1 to estimate the significance for the 50% and 100% BR cases. For instance, for for the combined signal (i.e., the pair and single production 100% BR in the χ1 → tl mode, the HL-LHC −1 events together). We note the following points: (3 ab ) discovery mass reach (i.e., Z ¼ 5σ) with (i) The LC100 (RC100) curves for χ1 and the LC (RC) only pair production is about 2.05 (2.35) TeV for curves for χ5 represent the significances in the LC κ ¼ 0 (κ ¼ 1). (RC) scenario where the BR of the χ1 → tl decay (iv) When the LC coupling is unity, the discovery reach is 100%. goes up to 2.35(2.50) TeVonce the single production (ii) For χ1, the LC50 and RC50 curves represent the processes are included. However, in the RC scenario cases where the BR of χ1 → tl decay mode is 50%. the improvement is minor. This happens because Although they are not realized in the LC and RC σðpp → χ1ljÞ is larger in the LC scenario than that scenarios, such a situation is possible if there are in the RC scenario.

(a) (b)

(c) (d)

FIG. 5. The 2σ exclusion limits in the λ − Mχ planes for χ1 with (a) κ ¼ 0 and (b) κ ¼ 1 and for χ5 with (c) κ ¼ 0 and (d) κ ¼ 1. These plots show the smallest λ that can be excluded by the HL-LHC with 3 ab−1 of integrated luminosity. The pair-production-only regions for 50% and 100% BRs in the χ → tl decay mode are shown with green shades.

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(v) Unlike the scalar case, there is no interference On the other hand, the single production processes produce among the different signal diagrams, and hence final states with at least one boosted top quark and two high- the signal significances in the RLCSS or RLCOS pT leptons. We observed two interesting points about single benchmarks are the same as that in the RC scenario. production. 1) Despite considering vLQ couplings with only (vi) In Figs. 3(c) and 3(d) we observe that the maximum third-generation quarks, we saw that the single production reach for χ5 comes from the combined LC scenario. cross sections are not necessarily very small, provided, of The values are 2.35 and 2.50 TeV for κ ¼ 0 and course, the new couplings controlling them are not negli- κ ¼ 1, respectively. There is a suppression in the RC gible. 2) Like the pair production, some single production channel for a similar reason as for χ1,aχ5 LQ also processes can also depend on the parameter κ that appears in couples to a right chiral top. the gluon-vector LQ coupling. In some scenarios, for order- In Table III we collect all of the numbers for Z ¼ 2σ, 3σ, one new coupling(s), the single production would control the and 5σ. LHC reach in the high-mass region. Since we can parametrize the combined signal cross We adopted a search strategy of selecting events with at section for any Mχ as least one boosted hadronic top quark and exactly two high- p leptons of the same flavor and opposite sign. This σ ≈ σ λ2σ λ 1 T signal pairðMχÞþ singleð ¼ ;MχÞ; ð23Þ combines events from the pair and single productions and, therefore, enhances the discovery reach by about 300 GeV the combined signal cross section increases with λ for any from the usual pair production searches at the LHC. Our fixed Mχ. By recasting the figures shown in Fig. 3, which results show that charge 1=3 and 5=3 vector LQs can be are for λ ¼ 1, we can obtain the reach in the λ − Mχ plane, probed up to 2.35 (2.50) TeV for 100% branching ratio in as we show in Figs. 4 and 5. We show the 5σ discovery the tl decay mode for κ ¼ 0 (κ ¼ 1) and order-one new curves in Fig. 4, while the 2σ exclusion curves are couplings at the 14 TeV LHC with 3 ab−1 of integrated displayed in Fig. 5. These plots show the lowest value luminosity with 5σ significance. Alternately, in the absence of λ required to observe the vLQ signal for a varying Mχ of their discoveries, they can be excluded up to 2.65 with 5σ confidence level for discovery. For the exclusion (2.75) TeV at the 95% confidence limit. Since the single plots, all points above the curves can be excluded at the production cross sections scale as λ2, we also showed how 95% confidence level at the HL-LHC. the discovery/exclusion reach would vary with λ within its perturbative domain. V. SUMMARY AND CONCLUSIONS Comparing with the results in Ref. [89], we saw that in Usually, in the direct LQ searches, it is assumed that LQs general it may be possible for the LHC to discover/exclude only couple to quarks and leptons of the same generation. heavier vLQs than sLQs for comparable parameters. For λ 1 5σ χ Collider signatures of TeV-scale LQs with large cross- example, for ¼ the discovery reach for 5 goes up to κ 0 generational couplings, motivated by the persistent flavor 2.35 TeV ( ¼ ) in the LC scenario. This is higher than the anomalies, are completely different than what is considered 1.75 TeV reach in the LC scenario for ϕ5 (or even 1.95 TeV in the usual LQ searches at the LHC. It is then important to in the RC scenario). Similar observations can be made for explore these possibilities in detail. In a previous paper other LQs/scenarios too. Of course, in the case of vLQs, the [89], we investigated the HL-LHC prospects of all scalar additional parameter κ can enhance the reaches even more; LQ models within the Buchmüller-Rückl-Wyler classifica- for χ5 in the LC scenario, it increases to 2.5 TeV. There is − l tions [91] that would produce boosted-tþ high-pT no such parameter in the case of sLQs; in this regard, the signatures at the LHC. In this follow-up paper, we inves- sLQ pair production process is more model independent tigated the case for the vector LQs with the same signature. (i.e., QCD driven) than that for vLQs. Also, for some sLQs The vLQs that decay to a top quark can have three possible the relative signs between new physics couplings are electric charges: 1=3, 2=3, and 5=3. Among these, our important as they affect the single production cross sections primary focus was on the charge 1=3, 5=3 vLQs that through interference among different signal diagrams. This can decay to a top quark and an electron or a muon, as a happens for ϕ1 whose single production cross sections in unique top-lepton resonance system would appear from the the LCSS and LCOS scenarios differ significantly. decays of these LQs. However, there is no such interference for vLQs; for In this paper, we introduced some simple phenomeno- example, the χ1 single production cross section is the same logical Lagrangians. These simple models can cover the in the RLCSS and RLCOS scenarios. Of course, for both relevant parameter spaces of the full models described in sLQs as well as vLQs, single production processes do play Refs. [91,94]. In this simplified framework, we studied the an important role in determining the LHC discovery/ pair and single production channels of vector LQs at the exclusion reaches even though we considered only third- LHC. Pair production of the vLQs produces final states with generation quarks coupling with the LQs. It would be two boosted top quarks and two high-pT leptons and interesting to investigate ways to distinguish sLQs and determines the LHC discovery reach in the low-mass region. vLQs with such similar signatures at the LHC. Finally, we

115015-11 BHASKAR, MANDAL, and MITRA PHYS. REV. D 101, 115015 (2020) point out that in these two papers we have presented ACKNOWLEDGMENTS simplified models for all possible LQs that couple with the A. B. and S. M. acknowledge financial support from the top quark and leptons. These simplified modes are suitable Science and Engineering Research Board (SERB), DST, for bottom-up/experimental studies and can be easily India under Grant No. ECR/2017/000517. mapped to the full models.

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