JHEP06(2021)080 − TeV (1 7 -data. . O ∗ 1 the mass Springer > K,K 1 May 12, 2021 May 26, 2021 June 11, 2021 R V : : March 29, 2021 : = 1 : M κ . The mass limits 1 , − Revised Accepted ab Published Received TeV, and 20 9 . 1 representations in the -anomalies are observed at the > 3 ∗ V 1 V TeV and K,K M R b Published for SISSA by https://doi.org/10.1007/JHEP06(2021)080 = 100 TeV, s or triplet 9 [email protected] . √ by the LHCb Collaboration can be explained , 1 1 V ∗ -collisions beyond the LHC-energies are needed. > 1 pp can be up to 3 TeV (2.1 TeV) at the HL-LHC and K,K V in the parameter space connected to 1 R M V 3 singlet V L and Ivan Nišandžić and a 1 are similar or higher, depending on flavor. While there is the SU(2) V 3 V ) we obtain . 3 = 1 κ 2103.12724 Dennis Loose The Authors. a c , we extract improved limits for the leptoquark masses: for gauge boson- Beyond Standard Model, Heavy Quark Physics

Evidence for electron-muon universality violation that has been revealed in , jµ [email protected] transitions in the observables and s`` TeV range. We explore the sensitivity of the high luminosity LHC (HL-LHC) and future bµ E-mail: [email protected] Fakultät Physik, TU Dortmund, Otto-Hahn-Str. 4, D-44221 Dortmund, Germany Institut Rudjer Bošković, DivisionBijenička of 54, Theoretical Physics, HR-10000 Zagreb, Croatia → b a Open Access Article funded by SCOAP Keywords: ArXiv ePrint: up to 15 TeV (19.9 TeV)and at reach the for FCC-hh with theexciting triplet possibility that leptoquarksLHC, addressing to the fully cover the parameter space to type leptoquarks ( for leptoquarks decaying predominantly accordingquark flavor to structure, hierarchical, respectively. flipped Futureof and sensitivity democratic existing projections based ATLAS on andreach extrapolations CMS for searches pair are (single) worked production out. of We find that for with spin-1 leptoquarks in 10) proton-proton colliders to We consider pair production andflavor benchmarks. single production Reinterpreting a in recent association ATLAS with search for muons scalar in leptoquarks different decaying Abstract: b Gudrun Hiller, Flavorful leptoquarks at the LHC and beyond: spin 1 JHEP06(2021)080 . . 3 = σ σ → 4 5 . B 2 lower than LHCb(2021) K R 25)% ] with the central − 4 [ (15 K R currents, thus contributing s` transitions. Recent measurements - and ], cf. recent tests in baryonic decay 5 s`` b` 15 12 → b , each with statistical significance up to 7 – 1 – ] from the SM expectation. Naive combination 3 ] probe electron-muon universality violating new 4 = 1 V 1 19 [ ∗ ∗ K ] but with reduced uncertainty, namely: K and R 2 -decays. One important cross check is to look for lepton R 1 4 = B V ] returned values that are both about 7 K 9 3 and deviation [ 14 , R 2 σ K production 1 R . 1 3 V to ], which intriguingly point in the same direction as the ones in 6 ]. [ 3 1 measurements shows a deviation from the standard model above 3 18 V 10 ∗ – 7 K pK`` R , revealing a → 041 044 b and . . involves a heavy leptoquark that couples to — a suppression of dimuon modes relative to dielectron ones — although with lesser 0 -decay observables Λ ∗ +0 − K B `` An interesting class of models that can naturally accommodate the measured values of ) 3.3 Single and3.4 pair production cross Resonant production sections 3.5 Sensitivity projections for future colliders 2.1 The vector2.2 leptoquarks Three flavor benchmarks 3.1 Leptoquark3.2 production and decay Current mass bounds ) colliders [ R ∗ ( 846 K,K . pp significance. The anomalies also suggestNP to particles undertake direct at searches the for( the Large corresponding Hadron Collider (LHC) and future high-energyR proton-proton Even more precise measurementsaddition, are correlations therefore with mandatory other toactually violated observables clarify in are these semileptonic to anomalies.universality be breaking In expected in if othermode lepton rare universality decay is channelsK [ the lepton-universality limit Very recently, the LHCb Collaborationvalue presented equal a to their new previous update result0 of [ of 1 Introduction The physics (NP) in flavor changingby neutral the current LHCb Collaboration [ A Comparing 4 Conclusions 3 Collider phenomenology Contents 1 Introduction 2 Model setup JHEP06(2021)080 ] - ]. ], at L 53 14 21 and , (1.1) 5 = 1 -quark 3) b angular / ∗ SU(2) 2 K , X 1 , divided by sµµ , , but matters b` (3 λ → 1 1 , see refs. [ ] for other recent V 2 b 27 – . GeV 2 24 ) , that is, the 6) ∗ , -singlet that the data point to a K 1 TeV L . , consistent with constrain the leptoquark’s R ]; see [ (1 13 ii) ), as is taken into account in ∗ (37 . / 0 , K 23 2 , 1.1 SU(2) ± and R ) 23) -bin . also deserve precise experimental 24 2 22 0 . 84 K q . 0 ± -quarks and leptons, ), but also determine the leptoquark TeV R and b 1 see ± we introduce the relevant interaction = 0 − . In a two-dimensional fit with both left- and 1 1.1 K ( (40 2 → 6) K R / which also suggest NP in b ] in the 5 /R 3 2 − ∗ [ ' − , , and to K 2 ∗ proportional to the strange over the ) reads ] for a review on leptoquark phenomenology. , R s` ∗ se fits, K – 2 – . As in our previous works we assume that the λ λ (3 1.1 b` ) are muons. This choice is pragmatic, as both 28 3 s R 2 ≡ , be S V ` as /λ ∗ λ 1.1 → 2 s` K V V − b λ X M M ] ∗ sµ 5 this indeed requires the leptoquark to couple differently ]. Specifically, λ 15 i) ]. bµ ] can provide such an input to leptoquark couplings [ – λ ). This is obvious for single production, which feeds on the 20 18 that further input is required to extract values of the individual , ], since the flavor patterns dictate the signature from leptoquark 11 1.1 , , and two spin-1 multiplets, the 5 17 ] combined with 19 [ iii) 3) 4 [ / 1 3) or vector leptoquarks K , , and introduce three flavor scenarios for the relative size of the cou- / 3 3 2 R 6) , , V / ¯ 3 3 1 ( , , 3 2 , (3 S and One verifies that ] on the scalar leptoquark 3 (3 1 V 2 transitions at tree-level, with masses at scales of up to a few tens of TeV. Three 1 ˜ 16 S V s`` ) is consistent with the global , which indicates the possibility of a small admixture from right-handed currents. These could stem σ → This paper is organized as follows: in section To quantitatively study the sensitivity to leptoquarks at the LHC and beyond, the In this paper we focus on the collider signatures of spin-1 (vector) leptoquarks, as a 1.1 3 Current data results in the ratio [ It is possible that both muon- and electron channels are affected by contributions of opposite sign [ . b 1 2 1 terms for ∼ from scalar right-handed currents the right-hand side of eq. ( with inverted hierarchy, and aleptons democratic and one. quarks Note are that requiredrecent flavor leptoquark to non-diagonal searches explain in couplings the pair to production anomaliessingle at ( ATLAS and [ pair production searches and [ corresponding parton distribution functions (pdfs)also for in pair the production proton, [ seedecay. figure Flavor symmetriesimplying [ hierarchical pattern with mass. To explore more general settings we employ in addition a flipped benchmark pattern, to ( distributions. We stress thattreatment dielectron in decays the future [ leptoquark couplings to bottom-only and their to product strange quarks as have in to ( be given individually, not sequel to [ dominant lepton species involvedlepton in species ( could couplepresently to not NP excluded. and However, choosing sizeable muons couplings over of electrons leptoquarks as the to main electrons contributors are collider mass scale, and leptoquark couplings, and therefore,the the couplings mass. are The sufficientlycan latter not small. only can discover be In leptoquarkscouplings in consistent general, and with reach mass. given ( of sufficient the energy, LHC a if collider study where we included for details. to muons than to electrons, that is, lepton nonuniversality, suitable representations aretriplet singled scalar out usingthe both triplet coupling to strange quarks andthe leptons square of the leptoquark mass to JHEP06(2021)080 , L 3) / (2.1) (2.2) (2.3) (2.5) 2 , 3 SU(2) , µ ) can be 3 (3 / 5 3 3 2.2 V V L ` or µ γ 3) L / ¯ u 2 , in terms of its 1 ¯ QL , 3 ., λ c V -colliders. Going beyond 2 . (3 1 √ pp V + h ., + we discuss single-, pair- and , c µ . 1 µ 3 3 V   , / 3 are denoted by  1 3 + h / / 5 3 −      3 E µ 2 3 3 3 and their interactions with standard V µ V V ~ V V bτ sτ dτ 2 3 L · λ λ λ − ¯ ν V √ Dγ  µ and . In the appendix we give an approximate 3 γ bµ sµ dµ ¯ / 1 DE 4 L ~σL λ λ single production cross sections. λ 1 3 V ¯ we discuss predictive flavor patterns in the and λ d µ / − 3 3 3 2 1 be se de 3 V + ¯ V ¯ – 3 – QL V V λ λ Qγ for λ V 2.2 2 λ L 2      ¯ µ √ QL ¯ h.c. (2.4) QL and √ λ   = and ¯ λ 1  Qγ anomalies. + + = V 1 ) µ ¯ ¯ = ∗ µ QL QL 3 V ( 3 to leptons and quarks are 3 3 λ ~ λ / V / K 2 1  · ,V 3 2 3 V R V . In section ~σ V int = ) and the flavor benchmarks. We work out present mass lim- L L L 1 ν ` µ 1.1 2.1 ,V µ leptoquark, here the projections are based on extrapolations of γ γ int L 3 L ¯ ¯ u L d S 3 anomalies. ¯ ¯ V QL ) QL ∗ λ λ ( K − + R = ] of the 3 16 ,V denotes the Pauli matrices. After expanding the triplet int L ~σ We start by recalling the new interaction terms that need to be added to the SM in the mass-basis of the down-type quarks and the charged leptons. The elements of the coupling matrix where the superscriptswritten denote as: the electric charges, the Lagrangian in eq. ( while they read for where components provides the resolution of the Lagrangian. The couplings of model particles in section context of the 2.1 The vector leptoquarks We assume that one of the leptoquark representations, either analytical argument for comparing 2 Model setup We briefly review the vector leptoquarks resonant production mechanisms inbottom the quarks final-state based channels on involving ( its muons, and strange- determine or thethe sensitivity study at [ theexisting HL-LHC LHC and searches. future We conclude in section plings to second and third quark generations. In section JHEP06(2021)080 , µν and 3.1 (2.6) (2.7) B 1 imply ν V 1 2 V − µ renormal- a µν † in a Yang- transitions 1 10 µ G V ν 3 D − Y s`` ~ V κ = 1 3 · Y − κ → a ig 10 b T µ − † ∼ 3 mixing constraints on ~ V a µν κ s sµ s G ¯ λ B ν , 1 ig – bµ non-unitary. Several models s , outside of the search range V is a gauge boson also include µν λ on the masses of the a − B ]. The bound from the loop- 1 ~ ¯ T W QL  V µ 54 · † λ † 1  ) µ ν 40 TeV 3 3 κV contribute at 1-loop, combined with are irrelevant for the present study. ~ V 20 TeV ~ V s ). It is apparent that an additional throughout the paper, see section 3 ν , × ig 1 µν D 1.1 µ V B −  and † 3 · = 1 are the three-component vectors in spin-1  ~ V ). This feature is not generic across possible † ν ( 3 κ ) have been proposed in the literature. For a ~ and V µ µν W ] can be accommodated with the combination 2.1 1 1 µ κ ~ 3 – 4 – W V V [ 2 µν 45 TeV D , ν and g on leptoquark production. 3 ∗ W D − ~ V leptoquark in the context of the K − κ ( † ]. ]). Other renormalizable couplings of the leptoquark 1 ν R = 0  1 µν V ν 53 with the standard model gauge bosons follow from the V 3 κ – B 30 µ , ~ 3 V ν , and ]. More recent analysis of 3 µ V D 2 ~ V 29 31 ] and , / 14 D · 4 − [  ab µ † 13 · † δ and ) 3 K ν ν ~ V 1 3 1 points to a mass scale around R . In addition to the terms with covariant derivatives ~ V V Y V mass difference, to which denote the generators of QCD in the fundamental representation, 1 L µ ) = κ µ s b a Y D ∼ ¯ D B T ( T  ig a – ν s sµ 1 T SU(2) − − λ V B mixing turns out to be dependent on the specific completion of the vector ]. These symmetries determine the ratio between the leptoquark couplings depends on the ultraviolet completion of the model, e.g. µ bµ tr( = , exist (see e.g. [ suggest even lower upper mass limits ref. [ s λ D κ 13 3 κ ¯ ∗ B  ,V – quarks. We employ these constructions when defining flavor benchmark pattern. s − kin s K,K B L = R , impose upper bounds of around 1 ∗ ,V We assume that only couplings to quark and lepton doublets are present and hence The interactions of - and leptoquarks, respectively [ b kin K,K 3 L In addition, the R V NP in induced For instance, of any presently plannedlower collider, leptoquark whereas mass, in weaker reach couplings ofpattern the of LHC. Flavor standard symmetries, model which masses explainmechanisms the and [ observed mixings, do provideto naturally requisite suppression 2.2 Three flavorThe benchmarks measured values of of couplings and theconstraint on leptoquark the leptoquark’s mass parameter space given with in regards to ( collider searches is required. Pati-Salam model. Some of thenew vector-like proposed fermions models which render in the which couplingthat matrix can accommodate suchselection a of references choice studying for the we refer the reader to refs. [ We choose the benchmarkfor values a brief discussion of the impact of neglect couplings to singlet fermionsUV in eq. completions ( and requires some model building, e.g. it does not hold in the minimal izable, gauge invariant interactionsthe with coupling the gluon fieldbilinear strength to tensor, weak parametrized boson by The field value strengths of Mills case in which the vector leptoquark is the gauge boson of a non-abelian gauge group. respectively. Here, normalized to representation of kinetic terms and JHEP06(2021)080 ] ]. = 20 57 ) sµµ (2.9) (2.8) ] and (2.11) (2.10) → 14 Belle ( ) implies b couplings, ] based on µ/e D 1.1 16 bµ R λ ] 56 and sµ λ conversion or rare kaon : 1 e - which is safely satisfied by . 2 µ  2 is of the order of the Wolfen- ) : 2 TeV . . , 0 4 5 TeV /           ∼ 4 V . ∗ ∗ ∗ ∗  . . .  M 2 2 (5 3 1 1    / . 1 ∗ ∗ 0 0 0 ∗ ∗ 0 0 0 ] that corresponds to our models [ . The measured value [ 0           ) . λ 55 ∼ 0 0 3 , λ λ . 1 2 V Deν – 5 – ∼ ∼ b` λ ], where we assume that the hierarchies found in /M TeV → ¯ ¯ | factor in the ratio between QL QL : 13 ” arise only through higher order corrections within λ λ solution [ ∗ sµ 14 B ∗ / λ ( s` (1) 10 V B λ bµ O / λ M ) : and other muon specific observables. Our scenarios also | −C ∗ ]. The parametric suppression of the individual quark gener- = d` , the central value on the right handed side of eq. ( 9 λ Dµν 3 13 C K,K The first texture we consider is the same as in ref. [ R → and 3 B As a second scenario, we consider the inverted form of the previous ( eV on the scale of effective operator relevant for our present setup [ / 1 ). Furthermore, the constraints from perturbative unitarity place an upper 80 T ≡ B implies the limit 1.1 ). µ/e D R 1.1 texture, that is: taken within These additional flavorin model ( uncertainties dominate over the experimental ones the models from ref. [ ations is preserved by Cabibbo-Kobayashi-Maskawaare (CKM) reconstructed rotations. inclusively As at neutrinos sector do collider not experiments affect flavor such observables. rotationsAllowing for in an the additional lepton where we assume contributions to theenough first quark to generation not to violate be any suppresseddecays. strongly existing Entries bounds marked from with data “ on between the different quark generations,stein where parameter, i.e. the sine of the Cabibbo angle. Specifically, we employ flavor models discussed inthe ref. standard model [ masses andThis mixings is are the also case in present simple inwhich flavor the induces models leptoquark based the couplings. on hierarchies the Froggatt-Nielsen-Mechanism [ In the following we consider three benchmark scenarios with coupling textures that 995(22)(39) . Flipped scenario. Hierarchical scenario. 0 our relation ( bound of about couple the vector leptoquark predominantly to the second lepton generation. scalar leptoquarks. Adata comprehensive sharply fit supports to the availableshows leptonic consistency and with semileptonic induce lepton universality violationthe in ratio the charged current semileptonic B decays within leptoquark model into a renormalizable theory at high energies, contrary to models with JHEP06(2021)080 - ) → c`ν b 2.12 (2.12) (2.13) → ), ( b , which is qµ 2.11 ” correspond λ ∗ 2 ), ( 10 and the dominant 2.9 ∼ ) imply κ qτ 1.1 ” in ( λ ∗ -suppressed. An effect of ’s. As a study in concrete, . ) τ qµ ], however, more general set- ) points to a NP contribution TeV /λ 21 1.1 . qτ 23 λ /      · V ∗ ∗ 2 factor and eq. ( ) M 1 1 π as in the hierarchical scenario given in 0 0 0 ∗ ∗ . (4 (1) 0      0 / λ transitions as the hierarchical pattern while O 0 λ (1 λ − . Note that ( . ` O , which evades dominant constraints from ) ∼ – 6 – ∗ 1 + ( V D s` ¯ QL TeV R λ → 70 b / V M contribute also at tree level to charged current 3 S observables Lastly, we consider a texture where the couplings to the second ]. In particular . and . The measurements of the single- or pair-production cross section, cτν  58 , ] is beyond the scope of this work, we also do not consider links with 3 sµ , 1 → 44 λ 13 V – b 32 ). and , observables. bµ 13 2.10 , λ cτν 12 Taking into account the aforementioned quarks at order and third quark generation are of equal size: enhancing the single production crossWe section obtain due the to larger sameeq. pdf coupling ( of range the for strange quark. Note that this pattern has ain weaker the foundation interaction in basis flavor the models, CKM and rotations if can it induce is contributions introduced to first generation This yields the same effect in → Leptoquarks We stress that flavor models which isolate a single species of leptons are straightforward Each scenario contains four parameters, the mass, the parameter on third generation lepton couplings, has received interest as a possible resolution of the b ¯ ν -tagging would be necessary for such an analysis. the same order ofabout magnitude ten in percent, the wouldunsupported charged by therefore flavor current require models and as substantial pointsfull in hierarchy to flavor strong the models couplings [ neutral to the current, which is decays [ sν anomalies in the to a loop-induced processlevel in charged the currents standard model, would hence naturally a be corresponding NP effect in tree to obtain using techniquestings from can neutrino arise and model are building viable,would too. [ open Allowing up for significant further entriesbranching “ leptoquark ratios decay modes in and thetherefore search to signal channels, the which channels most would favorable studied reduce situation here. for an observation Negligible in entries the “ muon channel. couplings the corresponding branching fractionsstruction and of the resonance the width,b mass together peak, with would the recon- suffice to determine all four parameters. Note that Democratic scenario. JHEP06(2021)080 . , 1 κ − (3.1) 27 TeV = 3 ab L . . We consider colliders: pair 3.5 3.3 pp 3 3 , , † 1 1 V V 3 (LHC run 3), , 1 V 3 , `, ν 1 ` (e) (h) V -collisions and decays of lep- 14 TeV pp ¯ : ` q 3 , s 1 V ¯ q q √ κ (b) colliders in section ¯ ν , pp 3 3 , , † 1 1 V V , t 3 3 we also briefly discuss resonant produc- , , † 1 1 + V V q g colliders by extrapolating current limits on 3 vector leptoquarks. The dots indicate additional , 1 bµ 3.4 3 V κ κ pp V κ (g) ) can be distinguished experimentally by differ- (d) – 7 – → . We work out bounds on the masses of vector . The structure of the final state signatures of all 3 / and g g 1 2.12 1 ] with target integrated luminosities of 3.1 +2 1 V 8 g g 3 ), ( V , ` 1 V 2.11 q (a) ), ( 3 3 3 3 , , , , † † 1 1 1 1 V V V V κ κ 2.9 (FCC-hh) [ q g (f) (c) ), and cross sections for future , respectively. In section 1 − ¯ q q g g 3.2 100 TeV 20 ab ), the dominant leptoquark decay modes are 2.9 . Leading order Feynman diagrams for single production, (a) and (b), pair production, (c) - and ] (section 1 22 − The flavor scenarios ( three classes of processes is determined by the flavor structureent of patterns the of leptoquark couplings. thescenario final ( states in two-body decays of the leptoquarks. In the hierarchical 3.1 Leptoquark productionWe and consider decay three dominantproduction, mechanisms single production of in association leptoquark withby a production quark-lepton lepton fusion, at and shown resonant-production induced in figure three setups corresponding to(HE-LHC), and center-of-mass energies 15 ab tion. We analyze thecross mass sections reach to of higher future center-of-mass energies and luminosities in section In this section wetoquarks. study vector Basics leptoquark areleptoquarks production given in in using section availableLAS search [ results for pair-production of leptoquarks from AT- (g), and resonant production, (h),contributions of the stemming from theNotice coupling the with crossed the versions of gluon diagram field (g), strength which tensor are proportional not to shown3 explicitly. Collider phenomenology Figure 1 JHEP06(2021)080 L for ) a (3.2) (3.3) (3.4) κ 2.12 SU(2) . 2 and in the benchmark 1 3 / 2 3 V 2 4 / / ¯ ν c ) . Approximate branching + 2 eV collider. | . The cross sections exhibit cµ ¯ ( Q` + 2 1 2 4 1 λ 14 T ¯ / / / ν s leptoquarks are related by 3 ]. The shapes vary mildly with the = 3 TeV / ) are given in tables B ∼ | ) ¯ ¯ ¯ ν , ν , ν , 3 1 , 29 +2 + 1 V 2 0 0 4 1 , t , c , c ) all of the above modes arise and final V , , / / ¯ 2.12 ν sµ tµ M t ( + + + + + ) leptoquarks in the benchmark scenarios from 2 1 ¯ ¯ ν , ν , 3 ), ( / ¯ ν 2.12 bµ tµ b / sµ s sµ cµ 1 0 1 1 0 b and +5 3 – 8 – → → → → → → → + 2 1 4 1 2.11 V / / 3 3 3 ( 3 3 3 3 , see also [ / / / / / / / bµ 1 0 0 1 1 1 3 1 1 ), ( / − +5 +2 − +2 − +2 +5 1 3 3 3 1 3 3 3 − V V V 2.9 V V V V 3 leptoquark and the triplet component or V 1 = 14 TeV V 0 ) the leading signatures involve charm and strange quarks s final states of the √ ¯ ν t 2.11 and democratic flipped hierarchical . + 2.2 bµ hierarchical flipped democratic we show the pair- and single production cross sections as functions of in the vicinity of 2 κ . . Branching fractions of the . Branching fractions of the 2.2 In figure In the flipped scenario ( ratios for the benchmark patterns ( the example of theminima HL-LHC for variation of the leptoquark mass in a range suitable for a for the triplet.states In with the both democratic lightmild scenario and hierarchy heavy ( between quarks the are twosize relevant. couplings of We which recall the can that have different we a final allow strong state in impact ( branching on the ratios relative as for the singlet and for the triplet. The symmetry such that their branching fractions are approximately equal. for the singlet and Table 2 section scenarios from section Table 1 JHEP06(2021)080 = 0 colli- κ 13 TeV for the p , due to - p -channel. for )-channel. ) = 1 κ 3 TeV . . 1 bµ , bµ qµ , qµ 13 TeV ( and final states nearly = 1 > -channels (bottom ) 0(1) TeV ) κ . 1 . For the democratic 2 V ] for pair production = 0 1 M 22 κ sµ, sµ cµ, cµ ], for and ( ( 3 for 59 leptoquarks using the limits ). Such final states appear in ). Previously derived collider of data from 3 3 - and V 2 ) - and 1 V -channel, since the corresponding ) ( ) − -leptoquark model. For both the 7(1) TeV quarks are approximately equal and 3 . fb 3 1 model by the strange quark, and by 8(1) TeV / channel [ and 1 -pairs, see Tab . S s 2 V 1 1 − 1 bµ, bµ ∓ 1 1 µ V ( V 1480 GeV sµ qµ, qµ bµ, bµ 3 139 3 µb V ( ( / . For the single production cross section we / ( 2 and +2 ± 1 1 and -, V V 0 κ ) − → → b - and pp pp in the . For the hierarchical scenario we use the limits bµ = 3 TeV – 9 – 1 1 − 1 − bµ, bµ V 1470 GeV ( 5(1) TeV . M 7 TeV 2 1 . − 1 triplet leptoquark and > = 139 fb L 3 1 − V L 6 5 − − M

10 10

(plots to the left) — the comparison to the theoretical cross ) of the single- (red, solid) and pair production cross section (green, pb σ/ SU(2) 3 = 14 TeV 2.6 -channel while for the flipped scenario we use the ( s ) , and √ τb bµ , bµ ( in the latter channel is played in our . We fix . The bound in the democratic scenario is obtained from the 1 -dependence ( q 3 V κ V , respectively. The bounds are the same for both of these scenarios because the . ]. Mass limits for scalar leptoquarks decaying dominantly to top and electron 23 = 1 κ We now spell out the obtained limits for the We evaluate the current mass limits for the coincide in the region ofcase large of democratic leptoquark scenario masses. and Thesmaller read individual limits branching are fractions somewhat into weakerscenario, for in which the the leptoquark couplingsboth to of the above mentioned limits apply, we used channels determines the mass limits. hierarchical and the flippedand scenarios the limitscurrent are experimental limits for the cross sections to obtained in the The role of charm for The limits on theplot) cross are section shown in insections the figure for leptoquark pair production and subsequent decay in corresponding final-state dominant decays to on the cross sectionsof found scalar in leptoquarks. theLHC This ATLAS run search Collaboration with was a search luminosity performed [ of using the data collected in the search for pair-produced scalarsions leptoquarks [ with (muon), obtained from thisdecays search, of are scalar (vector) bounds on vector leptoquarks from pair production searches are employ the hierarchical scenario. Analogousand results flavor are benchmarks. obtained for other choices of the parameters 3.2 Current mass bounds Leptoquark-based explanations of the deviations found in B-physics motivated the recent Figure 2 dashed) for JHEP06(2021)080 . ]. ]. 3 . pb 7 0 22 61 with − , − . The 3 state is 2 60 V ] in the = 3 / κ 62 ] used the 2 1 ) = 10 V 3 50 / 4 , respectively. − 3 . , see table S 4 TeV for 3 1 = 1 / in the hierarchical / 4 1 4 . 3 κ ∼ 3 -pair contributing to (plots to the right). 1 S 3 V ) / 3 , which corresponds to > + , which lowers the cross → and +5 with flipped and leptoquark typically turn 1 2) 2 3 cµ V , / and V 1 1 -channel exchange [ 2 1 pp 3 t V V M ( / 1 → = 0 − 5 σ V ( ' 3 − κ / 3 ) 5 ∈ V 3 V , where the role of the bµ for κ ( is found in the case of hierarchical B → channel by factor 3 V ) 3 structure of a leptoquark representation. / 2 1 L 0(1) TeV , as shown in figure V . 0(1) TeV ( κ TeV, we have . 2 bµ, bµ B 2 ( SU(2) – 10 – . In the flipped scenario, the respective limits are of data, while the authors of ref. [ and leptoquark in the hierarchical scenario the limit is 3 = 14 and / 1 , and equal to one for 3 2 s 3 − 3 pb. However, within e.g. the hierarchical scenario in V . V , while 7 √ 0 fb . This is due to the 1 ] corresponding to the same center-of-mass energy and − − 63 36 ' 10 ]. This is not surprising, given that the vector leptoquark 7(1) TeV · = . ) 7(1) TeV 9 1 . 16 κ . bµ 1 : with 1 3(1) TeV TeV and . ]. However, we note that the pattern of the branching fractions V → ]. 2 . ) = 6 44 3 ) 3 61 with large branching fractions / = 3 / 4 3 2 ) TeV for and S − 13 TeV 6 1 ( LQ . V B 1 qµ, qµ 3 M ( / cµ, cµ > ( studied in ref. [ +2 3 1 , 3 1 V ] performed the recast of the ATLAS collaboration measurement [ 0(1) TeV V S . 2 → M 61 , ) we have mass is obtained in the democratic scenario and reads pp ( 44 1 2.9 σ We find that the cross sections for pair production of the Constraints on the parameter space of leptoquark models can also be obtained from The mass limits depend on the value of In the case of the model with the V Yukawa couplings to the fermions, and the For example, for and eq. ( section of the vector pair-production in the involves three helicity states.specific lepton-quark channels, Thus, taken to forthe be corresponding given equal search values for limits the ofpreviously scalar for noted the and the in branching the ref. scalar vector [ fractionsinto turn leptoquark, the in out final weaker, the state lepton-quark in pairs accord is with guided what by the was details of the flavor structure of the model does not receive constraintscollected at in present. the This future situation [ could change as more data is out several times largerleptoquark than those for any specific weak-isospin component of the scalar For our present setup,refs. [ the correspondingdimuon di-muon channel channel at isresult relevant. by the The CMS collaboration authorsluminosity. [ of The results of these studies imply that the parameter space relevant for our the The corresponding weakest boundscenario, given in above. the case of Drell-Yan processes, to which the leptoquarks contribute via Note that the crossthe sections weakest have bound a onscenario, minimum the within mass.democratic These flavor are structure. the Note, however, same that for the absolute minimum for the bound on the final states corresponding final state has beenThis included channel in becomes the the search leading by one thescenario in ATLAS as Collaboration the well, determination [ resulting of the in bound for the democratic than the one for the same as for the casenow of played by the triplet component stronger: experimental limit is currently somewhat more strict in the most of the explored mass range JHEP06(2021)080 µq = 0 , 2 2 2 in the ]. Top κ µb 1 1 3 − − 22 V = 13 TeV = 13 TeV 1 = 139 fb = 139 fb 1 1 1 s s − √ L √ L as the function of = 13 TeV 3 = 139 fb s ,V √ L in the hierarchical and 1 0 κ 0 0 κ κ V 3 V 1 1 1 − − − 2 2 2 − − − 5 0 5 0 0 5 0 0 5 0 5 5 ......

1 1 2 2

2 1 1 2 1 1 2 2

1 3 3 , 1 V V V TeV / M TeV / M TeV / M denotes quarks lighter than the charm quark, The 0 0 . . q 3 3 1 – 11 – 1 1 − − − in the democratic scenario, and bottom row: = 0 = 1 -pair production, assuming dominant decays to = 0 = 1 = 0 = 1 1 3 κ κ 5 κ κ κ κ . V 2 = 13 TeV ,V = 139 fb = 13 TeV = 13 TeV 1 s 5 5 = 139 fb = 139 fb . . s s V √ L 2 2 √ √ L L 0 . 2 TeV TeV TeV / 0 0 / . . / 3 3 , 2 2 1 1 V V V M M M 5 . 5 5 1 (dashed). Right: mass bounds for the leptoquarks . . 1 1 ). The boundary of the excluded region is represented by the band whose width = 1 2.6 ( κ κ 0 0 0 . . . . Sensitivity and mass bounds from reinterpretation of a current ATLAS search [ 1 1 1 in the hierarchical and flipped flavor scenarios, which equals 4 5 6 1 2 3 4 5 6 3 4 5 6 1 2 3 1 2 − − − − − − − − − − − − − − − − − − in purple, blue and black, respectively; 1

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V pb σ/ pb σ/ pb σ/ µc parameter results from the pdf- and scale uncertainties. row: democratic flavor scenarios, middle row: flipped scenario. Left:and sensitivity to green bands indicate the(solid) theory and prediction including the pdf- and scale uncertainties, for Figure 3 JHEP06(2021)080 , - 1 ], ∗ V sµ for 67 λ [ 4 K,K . Since R 1 at parton ` 3 LHAPDF / in figure in association 2 1 1 V , as functions of V = 0 1 → κ . qg = 1) quarks in the final state, κ . In this case, the implementations of the . ] for several cross-checks. b 4 V ). We note that there are also 70 M , = 0 ( are displayed by hatched bands. κ 69 [ 2.13 = 1 ), ( κ Feynrules -quarks which amounts to the branching 2.10 b final states that were not taken into account Feyncalc ) . As an exception to this, the large contribution – 12 – 1 q` , q` ) for large values of ( ] output of the leptoquark models that we implemented . The results for 2.10 3 65 V becomes noticeable for the large-mass region within the [ implementations with the corresponding implementations 1 for UFO 5 ]. The pdf-, and scale uncertainties are evaluated using Feynrules 66 ] with the [ 64 [ ) for flipped flavor hierarchy, forces the large values for the coupling , and in figure . Assuming the narrow width approximation, we multiply the corresponding for each of the three flavor scenarios. 1 ]. We used the software package 1.1 V ¯ 2 Q` 68 / λ 1 models are attached to this paper as supplementary material. We checked the (c)-(g) are well separated by appropriate kinematic cuts. ). The band widths originate from eqs. ( Feynrules 3 1 Madgraph V 1.1 The magnitude of the single production cross section induced by Pair production is predominantly induced by the QCD-initiated processes and is es- For the evaluation of the cross sections and the corresponding uncertainty bands we For each flavor scenario we assume that the parameters of the leptoquark model satisfy coupling production cross sections by thethere corresponding are branching fractions no givenwe available in added single table the production contributionsfraction searches involving jets involving and reaching the borders ofthis the plot perturbativity. can This be as understood well from as ( the larger uncertainty band in level is directly proportional to the square of the magnitude of the corresponding flavor sentially independent of the flavor structure.into various The final latter state determines channels, the seeof branching table fractions diagram (e) shownflipped in scenario, figure see thecondition last ( plot of the second row in figure and consistency of our from ref. [ used using symmetrized and combined in quadrature. Our eq. ( non-resonant diagrams contributing to in our numerical analysis, assumingfigure that the contributions of the resonant diagrams shown the leptoquark mass. The resultsthe are case displayed of by the redThe bands leading-order using cross sectionsrepresented for by the pair solid production (hatched) and light subsequent green resonant bands for decays are We evaluate the leading orderwith cross a sections muon, for represented by the the single resonant production diagrams of (a) and (b) in figure 3.3 Single and pair production cross sections JHEP06(2021)080 ] 22 2.2 . -band ∗ 3 K,K 1 25 25 25 R − 20 20 20 for details. The = 20 ab ] and ATLAS [ L 15 15 15 25 TeV 3.5 / 1 V ) = 1 ∗ FCC-hh M 10 10 10 ( = 1 κ K κ R 5 5 5 = 100 TeV, s , derived from the ) √ ∓ µ ) for the democratic scenario. Light ) 8 8 8 1 j − ± µ 2.13 6 6 6 Single production for in association with Pair production for Sensitivity (single production) → = 15 ab ( L 3 TeV / / are shown in a dashed/hatched form together 1 2 V 4 4 4 ± 1 M HE-LHC V for the hierarchical and democratic scenarios and = 1 ) → = 27 TeV, 2 2 2 κ – 13 – ) s = 0 ∗ ( √ pp = 0 κ K ( -collisions in the flavor scenarios introduced in section κ bµ, bµ R σ ( pp 4 4 4 1 ) + − ∓ µ ) b = 3 ab 3 3 3 (–) L . The solid dark red and the dark green curves depict the projected ± TeV / µ 1 V = 0 M HL-LHC → Sensitivity (pair production) Single production for Pair production for in association with 2 2 2 ( κ 3 / = 14 TeV, 2 s ± 1 √ 1 1 1 V 7 3 5 7 1 3 5 1 3 5 7 1 − − − − − − − − − − − − →

10 10 10 10 10 10 10 10 10 10 10 10

pb σ/ pb σ/ pb σ/

-leptoquark production in

pp

1 ( Flipped Democratic Hierarchical V ) for hierarchical and flipped scenarios, and eq. ( σ . for the flipped scenario. The error bands for pair production are evaluated by combining ]. The dotted segments for the large masses represent the smooth continuation above the 2.10 ) 79 qµ, qµ dot-dashed segments ofvariation the of extrapolated the luminosities curves betweenref. for the [ initial the and low thefinal target masses extrapolated values, required following points the additional towardslimit. prescription the smooth in Neither higher of masses these with segments play the a constant role values in of determining the the cross-section mass reaches shown in table ( the pdf-, and scalewith uncertainties. the Results solid curves for for experimental sensitivity for singlethese extrapolations, and we pair usedcollaborations, production, the for respectively. results the of As single- the the and measurements starting pair by the curves production, CMS for respectively, [ see section Figure 4 (rows) for different futuresection collider for experiments (columns).in eq. ( Red bands:green: single pair production production with cross final states JHEP06(2021)080 , ) for 71 2.2 ) 2.10 cµ, cµ ( 1 25 25 25 − 20 20 20 ]. These results = 20 ab -band in eq. ( 73 L ∗ 15 15 15 TeV / 3 V ) K,K = 1 ∗ FCC-hh M 10 10 10 ( = 1 κ R K κ R 5 5 5 = 100 TeV, s √ 8 8 8 1 − . Next-to-leading-order QCD and 1 6 6 6 Single production for in association with Pair production for Sensitivity (single production) = 15 ab L TeV , derived from the / 3 3 V 4 4 4 V ) for the democratic scenario. Light green: pair M HE-LHC 2.13 for the details. = 27 TeV, 2 2 2 – 14 – ) s = 0 ∗ ( √ 3.5 = 0 κ K -collisions in the flavor scenarios introduced in section κ R pp 4 4 4 1 − for the hierarchical and democratic scenarios and ) = 3 ab 3 3 3 and section L TeV bµ, bµ / 4 ( 3 induced by the triplet ], see diagram (h) in figure V ) M HL-LHC Sensitivity (pair production) Single production for Pair production for in association with 2 2 2 74 j − µ = 14 TeV, s + √ µ 1 1 1 7 3 5 7 1 3 5 1 3 5 7 1 → − − − − − − − − − − − −

10 10 10 10 10 10 10 10 10 10 10 10

pb σ/ pb σ/ pb σ/ collisions [ pp

]. -leptoquark production in

(

3 Flipped Democratic Hierarchical σ V 75 pp . ] were recently followed by the determination of the lepton pdfs in ref. [ 72 opened up the possibilityfusion to in consider resonantQED leptoquark corrections production to from theavailable lepton-quark [ resonant production of scalar leptoquarks have recently become the flipped scenario. Thescale error uncertainties, bands see for figure pair production are evaluated by combining the pdf-, and 3.4 Resonant production Determinations of the photon distribution function inside the proton introduced in refs. [ Figure 5 (rows) for differentsection future for collider experimentsfor (columns). hierarchical and flipped Red scenarios,production bands: and with eq. final single ( states production cross JHEP06(2021)080 ], 78 with 1 in the V 3 / ), we give 1 → − 3 ) s V 2.12 + ), ( b ( µ 2.11 0 . ), ( 5 collider. The results are 3 2.9 / 5 pp 2 . 4 ± 1 V 0 = 14 TeV . )-plane to the right of the thick → 4 s s ]. The resulting cross sections are pp HL-LHC √ √ , 5 = 14 TeV . 76 1 [ 3 V s M √ TeV ( 0 ] pdf set that includes the leptonic pdfs. . / 3 1 V 73 ]. The method assumes that the exclusion [ M at a 5 anomalies, and the corresponding backgrounds, . 1 2 – 15 – 79 ∗ , V ManeParse 78 0 . D,D 2 R Hierarchical Flipped Democratic ) coupling set to one. -channel resonances, for which it was initially used [ s 5 sµ ]. . ( 1 77 bµ 0 . 1 5 7 3 ) at the HL-LHC. The solid (dash-dotted) grey line indicates the reso- − − −

10 10 10

σ/ pb TeV. The regions of the 2.12 using the package 10 ), ( ∼ 2.11 we compare the cross sections of the resonant- and single production for 7 ), ( ). ] for more details. We expect the method to be less suitable for the case of lep- the resonant cross section for 2.9 . Resonant leptoquark production cross section from lepton-quark fusion for the flavor 6 2.4 79 Mathematica , 78 We note in passing the absence of the triplet leptoquark component In figure To illustrate the expected range within the flavor scenarios ( LUXlep-NNPDF31_nlo_as_0118_luxqed -masses up to 1 extrapolation method followinglimits refs. are [ determined byre-scaling the of numbers the of background processes backgroundsee with events the [ and corresponding involves parton the luminositytoquarks functions, appropriate than for e.g., the case of see eq. ( 3.5 Sensitivity projections forIn future order colliders to estimatenarios, the we mass extrapolate reach existing of bounds the future from colliders single- for and the pair flavor production benchmark using sce- the limit V blue lines result inThe resonant current cross level section of the being leptonenergy larger pdf-uncertainties scales. than does not the allow one for for extrapolations single to higher production. resonant production — its coupling to the fermion sector exclusively involves neutrinos, larger than those ofwould pair- be and desirable to single look for production collidercollider due signatures signatures of to motivated this by process. lesser the phase-space Resonantwere vector suppression. recently leptoquark discussed It in ref. [ in figure obtained by convolution of thethe leading order partonic crossNote section for that the chargeset conjugated process in is also included in the results. We parse the pdf Figure 6 scenarios ( nant cross section with only the JHEP06(2021)080 , 1 = − , in = 0 s 1 pair 3 (3) 5 (6) κ √ V ]. For . The 15 (18) . 1 4 76 0) V [ . -channel, ) = 139 fb = 1 — — 7 (14 κ . L 11 democratic bµ , bµ in figure ( 7) 1 . 8) 4) . . V with ManeParse in parentheses, for the 1 (2 5 (6 9 (22 . . . 3 flipped 2 5 V -tagging is required for quark is not tagged and 19 b Mass reach for b 13 TeV for details. 5 5 . A . — 4 17 3 ] at ]. 22 hierarchical 79 pair ). In the flipped and democratic scenarios 2 (3) 5 (5) 13 (15) . We find good agreement with the similar 2.13 colliders turn out to be rather small, below 5 7) . = 0 ), ( — — , for both pair- and single production channels. κ (10 – 16 – ], parsed using the package 3 democratic 2.10 81 the theoretical predictions for single production in 27 TeV [ 5) . 5 6) . 3) we compare the expectations for the single production . and pair production, at different future colliders for and ]. The latter paper presents the limits on the resonant (2 8 4 (5 7 (20 and . . flipped 4 25 -channel were used for the flipped scenario, where the role 4 17 [ 2.2 ) Mass reach for is given in figure 1 reaches are the same, see appendix − 3 14 TeV 1 3 V 7 . fb . V — ] for the evaluation of the extrapolations. As a cross-check, we use 2 , 15 qµ , qµ 1 6 ( . 80 V hierarchical 1 ] for earlier searches. We use the leading order set of pdfs provided by − = 19 3 is given separately in parentheses, if different from the reach in ab 15 20 ]. 26 / , L 3 L 82 V 24 NNPDF23_lo_as_0130_qed TeV 14 27 100 s/ . For single production we provide the mass reaches corresponding to the upper limit of final states. Our extrapolations assume that the final √ . Mass reach in TeV for vector leptoquark single production in the hierarchical, flipped and run with = 1 is played by the strange quark. As can be seen from figures We provide a list of possible mass reaches at future colliders for the leptoquark The extrapolations of the limits for the single- and pair production cross sections are For the extrapolations of the limits on cross sections for pair production we use the As the starting point for our approximation for the future sensitivity projections for κ µµj Up to date analysis of the future sensitivity for the pair production of scalar leptoquarks were recently 3 q Collider FCC-hh HL-LHC HE-LHC association with muons at the projected sensitivity. In figure presented in ref. [ comparison for the case of extrapolations for the case of single-production in ref. [ each of the three flavorThe scenarios, reach in for table the hierarchical and democratic scenarioswhile we extrapolate the the limits limits for in the of the compared to the corresponding theoretical resonant cross sections for search performed by thesee ATLAS also Collaboration refs. in [ ref.MSTW Collaboration [ [ the pdf-set cross sections of thethe single productionis of the counted leptoquarks asdistinguishing in a between association light the with flavor jet, scenarios,of muons however, and the in hierarchical could we and lead stress democratic to once flavor improved scenarios. limits again in that the case however, it should provide thelimits on correct the estimate corresponding of cross the sections. order of magnitude forsingle the production, collider we employ8 the TeV limits obtained by the CMS Collaboration in the democratic scenarios from section and the cross section bandas resulting well from as eqs. forhierarchical ( pair scenario the production we show the increased mass reaches for Table 3 JHEP06(2021)080 ) s √ , V M

(

pb σ/ , since the ∗ 4 5 6 7 8 9 10 2 3 − − − − − − − − − K,K 10 10 10 10 10 10 10 10 10 R 20 . Notice that the cross 8 are restricted by the low ) collisions. Pair production is 15 p - p d, s, b ( TeV / depending on the center-of-mass energy 1 10 V . 1 Flipped M V = 0 Pair production κ 5 – 17 – 20 . All plots are for 15 ) 3 / 2 − -tagging would be important in order to confirm the connection 1 b TeV V / 3 1 10 / V would point to a leptoquark that is unrelated to M 8 +2 Democratic 1 Hierarchical V denotes the center-of-mass energy of the → 5 TeV) the resonant leptoquark production cross section is larger than the single s ). In the regions to the right of the red lines the single leptoquark production cross pp we compare the cross sections for single- and pair production in the 10 ( √ -anomalies. 7 σ ∗ ∼ 2.13 1

V . Single leptoquark production cross section for ), ( 80 60 40 20 80 60 40 20 K,K

100 100

TeV s/ TeV s/ √ √ R M 2.10 In figure Observation of a single production signal with a cross section that is much larger than , and the leptoquark mass. For each scenario we use the central value of the allowed ranges from s turn out larger than thoseon of the right the of pair the production solidsections red — of lines the in the corresponding the regions single firstcase three are production of plots located a of vary the signal significantly figure discovery, withto the the different flavor scenarios. In plane, where instrumental for the discovery orTeV. the For exclusion large of masses vector and leptoquarks scattering in energies, the region the of cross a sections few of the single production those shown in figure simultaneous leptoquark couplings toenergy flavor-changing-neutral all current (FCNC) three observables, flavors such as kaon decays. cross sections for thespan flavor up scenarios to and two different orders future of collider magnitude. experiments; the values eqs. ( section is larger than the(up pair to production cross section.production In one, the see regions text.cross to the section In right the of the plot blue to lines the lower right we show in addition the pair production Figure 7 √ JHEP06(2021)080 ] ] ] ]. 4 at for 22 23 21 ∗ TeV ) 6 ∓ . µ 1 K,K 3 / R 2 -term are > ± 25 κ 1 3 V V 1 − M → 20 pp = 100 TeV ( = 20 ab s σ FCC-hh √ L . 15 TeV = 0 / -decays has yet to be con- 1 V b κ M ), or without the 10 = 1 ). Here we study the vector lepto- Hierarchical Flipped Democratic Sensitivity (single production) 5 κ 1.1 , and higher otherwise. Analogous lim- 3 . 0 − 0 . 8 4 = 1 1 κ − − – 18 – 7 5 . 3 = 14 TeV = 27 TeV = 15 ab = 3 ab s s 6 L HL-LHC √ L HE-LHC √ 0 . TeV for 3 4 . 5 ) at different future colliders, for 1 induce sufficiently large contributions explaining ), with dominant coupling to third generation quarks, a TeV TeV 5 . / / 2 3 1 1 > V V 2.9 V 2.12 4 M M 1 V 0 ), ( . 2 M , neglecting mass splitting within the multiplet, as and . 3 3 1 V 2.11 V 5 3.2 . 1 2 ), ( ), with dominant coupling to second generation quarks, and a democratic 2.9 0 . 1 1 . Limits for gauge-type leptoquarks ( 3 5 7 1 3 5 7 1 3 ], with coupling over mass ratio fixed ( − − − − − − − − 2.11 .

10 10 10 10 10 10 10 10

0 pb pb σ/ σ/ 14 − ). Reinterpreting a recent ATLAS search for pair-produced scalar leptoquarks [ . Comparison of the single leptoquark production cross sections = 2.12 We work out single- and pair production cross sections in three quark flavor bench- κ one ( we obtain the mass limit its can be derived for for stronger, see section neutrino masses and mixingWe result stress that in dedicated leptoquark searches for couplingsare leptoquarks to decaying well-motivated to a and leptons single complementary, other however, lepton than beyond muons species the [ [ scope of thismarks: work. a hierarchicalflipped one one ( ( tree-level [ quark reach at the LHC andsignatures beyond targeting from this leptoquarks parameter with space. couplings Specifically,and to we to second analyze and muons. third generation Thepresently quark no reason doublets, necessity why to this consider simplified couplings framework to is electrons, and sensible flavor is symmetries two-fold: explaining there is dependence alike.for While the the breakdown recent offirmed lepton evidence by universality reported in experiments by rare andinformative semileptonic the directions in in LHCb other the Collaboration observables,representations leptoquarks’ taking only [ parameter the space: data among at the face spin 1 value leptoquark provides the benchmarks ( 4 Conclusions Leptoquarks are flavorful — a feature that allows for rich phenomenology and model- Figure 8 JHEP06(2021)080 , 5 triplet. and 4 L ] searches. 22 , and improve SU(2) 2 is similar in single . 3 , the HE-LHC with is 3 TeV (HL-LHC), 8 V 1 1 − V ab ]. Allowing for significant 3 ] and ATLAS [ is shown in figures 14 -anomalies would strengthen 1 25 ∗ − in the flipped and democratic ab 1 K,K V R 20 TeV and ) are simplified and in general lepton , as illustrated in figure | = 14 κ | 2.12 s √ ), ( – 19 – , the maximal reach for 2.11 ), ( = 1 κ 2.9 production ), and could distinguish flavor patterns. Besides being strik- 1 TeV (FCC-hh). The reach for the triplet . For 1.1 V 9 are larger than the ones of . 3 3 19 to V 3 for the HL-LHC. A full study of efficiencies also at future machines is and the FCC-hh with 100 TeV and V 6 1 − ab 15 in the patterns would open up further search channels, and reduces leptoquark ] is beyond the scope of this work. ) 13 ∗ . Single production is, however, valuable on its own as it is sensitive to the flavor ( 7 We conclude that leptoquark searches at the LHC are very well motivated by flavor Recent works suggest to study resonant production from lepton-quark fusion at the Note also that the patterns ( The future reach at the HL-LHC, with TeV (HE-LHC) and 5 . A Comparing The cross sectionsscenario, of due to theHere contributions we from give analytical the arguments additional forof the components single approximate in production. relations the between In the the cross hierarchical sections flavor scenario the dominant contribution is from I.N. acknowledges support providedthe by framework the of the Alexander ResearchMinistry von Group of Humboldt Linkage Education Foundation Programme and funded within Research. by the German Federal mass from couplings, as ining ( signals from beyondthe the flavor standard puzzle. model, this would allow to makeAcknowledgments progress towards models [ physics, although covering thequires full higher mass energies. range Thethe supported actual case confirmation presently for of by the a rare corresponding processes machine. re- Observing leptoquarks directly would disentangle flavor violating signatures can arise inentries leptoquark decays, e.g., [ branching ratios in the signalin channels studied single here. production, Note and that quadraticsuch this in as rescaling pair effect quark production, is but linear flavor leaves hierarchies the of qualitative features, our analysis intact. A study in concrete, full flavor LHC via lepton pdfs.as shown Similar in to figure singlebeyond production the the scope cross of section this is work. sensitive to flavor, the mass reach. Results arePair based production on extrapolations has of larger CMSsuppression [ cross kicks sections in due andfigure to single the production strong takes interactionpatterns over, until in as the phase demonstrated new space physics quantitativelylargest sector. in cross The sections, flipped followed pattern by with the subject hierarchical to one, the larger see pdf also gives figure 27 TeV and and summarized in table 5 production and the hierarchical pattern, andbecome generically larger larger for otherwise. larger All value cross sections of the parameter JHEP06(2021)080 . ) ) , ) ' '  V ) ) and jµµ ) jµµ + − Phys. , and (A.1) (A.2) jµµ ) (2020) µ 5 , s, M → − . cµ 3 (2015) → jµµ / 2 µ → 08 √ 05 2 3 3 ( pp → / pp V 02 2 3 pp → 1 ( / ( decays V 5 ) Phys. Rev. D 3 → − , JHEP V pp + ` JHEP ( ( ) → , µ  , + sg 1 ) JHEP 1 + B ) ` ( Flipped V ) Flipped V , µ + + σ pp ) arXiv:2103.11769 σ − ( b, s /σ K , µ 5 ( ) s`` cµ σ decays 3 decays ). Using the different b, s for values of processes / . → ( ' − 5 3 → − → → 3 ` . Numerical results from s 5 Democratic ` V jµµ 5 ) with signature . b 2.3 ) + ) = V 3 3 + σ + → 2 / / ` 3 − V ` B → 2 5 3 → 0 3 3 V − µ → b ∗ jµµ / V 3 V 2 ( / ( ]. 3 K cg pp 2 pK s, M ) which makes the cross section 3 V B ( → B ( ( ) ) V σ √ → → ( − B − 3.2 pp 0 ) 0 b µ µ ( → SPIRE )+ 3 − 3 B Λ results in 3 / / + . In the flipped scenario holds IN µ Flipped V 2 5 3 3 ) 3 pp − σ ][ / ( V V sµ − 2 µ 3 3 σ ) Flipped µ V V 3 → → + σ → ]. / 3 2 3 / → jµ sg cg 2 are included in figure V 3 ( ( is an isospin factor ( ]. V ) – 20 – σ σ bg → ( 2 ( SPIRE ( − → 3 B + + σ µ IN 2) / )  from the triplet ( , we find 3 5 3 / ][ − √ 3 SPIRE bg 2 5 ( ]. V 3 / µ ( IN 2 ]. 3 V 3 σ / ) = 2 ][ V → 2 , for relevant ranges of arXiv:1903.09252 3 and ), which permits any use, distribution and reproduction in 5 → [ V . 1 cg Diagnosing lepton-nonuniversality in SPIRE 1 jµµ SPIRE cg IN → ( More model-independent analysis of ) = 4 IN → ][ σ − sg , whereas an explicit evaluation results the ratio to be ][ ( µ ) Test of lepton universality with Test of lepton universality in beauty-quark decays Search for lepton-universality violation in Test of lepton universality with ) one. 3 pp σ , where the / (  ) 2 hep-ph/0310219 3 − CC-BY 4.0 3.1 jµµ stem from adding the CP-conjugate of the process. Assuming that the [ V µ 2 3 (2019) 191801 ) = 2 This article is distributed under the terms of the Creative Commons / → 5 → 3 arXiv:1705.05802 V 3 pp [ 122 jµµ Democratic V ( sg ]. σ ( → → σ arXiv:1411.4773 arXiv:1912.08139 pp cg ( [ [ (2004) 074020 ( SPIRE σ 1 IN 2 [ 055 040 Rev. Lett. (2017) 055 69 Democratic V In order to estimate the cross section of singly produced G. Hiller and M. Schmaltz, LHCb collaboration, LHCb collaboration, LHCb collaboration, LHCb collaboration, G. Hiller and F. Krüger, σ 3 2) Flipped V 5 [5] [6] [2] [3] [4] [1] . -quarks which involves only the √ σ any medium, provided the original author(s) and source are credited. References dropping for larger masses to the explicit evaluations of Open Access. Attribution License ( Assuming 2 An explicit numerical evaluation revealsto the be ratio decreasing forin larger the leptoquark range mass, of and interest within for the 4 present and paper. For the democratic scenario we find where the factor of pdfs for the strange and charm( quarks are roughly the same, onebranching obtains ratios given in tables equal to the singlet ( in the flipped andinclude democratic the scenarios, contribution we from use b JHEP06(2021)080 , ] , , ]. , (2017) (2020) (2015) 96 10 SPIRE Phys. Rev. TeV with the Erratum IN 115 Phys. Lett. B , , ]. Phys. Rev. D [ ) [ , 0 − , ( ` + JHEP ]. = 13 ` s`` , ∗ s SPIRE arXiv:1509.03744 √ K → puzzles [ IN . Physics and detector b ) 1 Phys. Rev. D ][ ∗ SPIRE → B decay anomalies ( , IN D (2019) 1109 B & R ][ ICFA Beam Dyn. Newslett. (2019) 123C01 , Phys. Rev. Lett. 228 , and ]. 2019 K (2016) 032004 ]. R ]. ]. 93 ]. SPIRE IN ]. ]. physics beyond the Standard Model PTEP [ SPIRE arXiv:2010.02098 , [ SPIRE IN ]. SPIRE s`` SPIRE arXiv:1408.1627 IN ][ ]. IN [ IN SPIRE SPIRE → ][ [ ][ Eur. Phys. J. ST IN IN b ]. , SPIRE ][ ][ 4 beyond the Standard Model – 21 – Phys. Rev. D IN (2019) 755 SPIRE ∗ Clues for flavor from rare lepton and quark decays Leptoquark flavor patterns collisions with the ATLAS detector Leptoquark pair production in hadronic interactions , (2021) 313 ][ IN ]. ]. K Flavorful leptoquarks at hadron colliders Effective field theory approach to SPIRE pp R ][ 228 TeV 81 IN ]. (1979) 277 Hierarchy of quark masses, Cabibbo angles and and future (2014) 054014 and SPIRE SPIRE TeV with third generation couplings = 8 K IN IN s K 147 90 R SPIRE τν ][ ][ hep-ph/9610408 √ arXiv:1808.10567 R ) = 13 IN ∗ [ arXiv:1612.05014 ( Vector leptoquark resolution of The Belle II physics book s ][ [ ]. Search for pair production of scalar leptoquarks decaying into first- or Search for pairs of scalar leptoquarks decaying into quarks and D √ arXiv:1503.01084 arXiv:1609.08895 Lepton-flavor-dependent angular analysis of [ [ Search for pair production of first and second generation leptoquarks in HE-LHC: the High-Energy Large Hadron Collider. Future Circular FCC-hh: the hadron collider. Future Circular Collider conceptual design → arXiv:1801.09399 CEPC-SPPC preliminary conceptual design report. B Eur. Phys. J. C HE-LHC overview, parameters and challenges [ SPIRE Eur. Phys. J. ST arXiv:1511.06024 , , IN (1997) 137 [ 3 Phys. Rev. D Nucl. Phys. B and , , 76 ν (2020) 029201] [ (2015) 072 (2016) 027 collaboration, (2017) 111801 ν ) collaboration, collaboration, ]. arXiv:1506.02661 arXiv:1704.05444 ∗ ( collaboration, 06 12 [ [ collaboration, collaboration, collaboration, K 118 2020 arXiv:2006.05872 (2016) 270 [ (2018) 075004 (2017) 138 [ → SPIRE IN ATLAS second-generation leptons and top quarksATLAS detector in proton-proton collisions at CMS proton-proton collisions at [ JHEP ATLAS electrons or muons in 112 Z. Phys. C CP-violation 97 Belle Lett. Belle-II ibid. B 181801 755 JHEP 035003 FCC report volume opportunities IHEP-CEPC-DR-2015-01, (2015) [ 72 FCC Collider conceptual design report volume F. Zimmermann, M. Ahmad et al., J. Blümlein, E. Boos and A. Kryukov, C.D. Froggatt and H.B. Nielsen, I. de Medeiros Varzielas and G. Hiller, L. Calibbi, A. Crivellin and T. Ota, G. Hiller, D. Loose and I. Nišandžić, G. Hiller, D. Loose and K. Schönwald, G. Hiller and I. Nisandzic, G. Hiller and M. Schmaltz, S. Fajfer and N. 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