PHYSICAL REVIEW D 101, 115017 (2020) Scalar leptoquark pair production at hadron colliders † ‡ Christoph Borschensky ,1,* Benjamin Fuks ,2,3, Anna Kulesza,4, and Daniel Schwartländer4,§ 1Institute for Theoretical Physics, University of Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany 2Sorbonne Universit´e, CNRS, Laboratoire de Physique Th´eorique et Hautes Énergies, LPTHE, F-75005 Paris, France 3Institut Universitaire de France, 103 boulevard Saint-Michel, 75005 Paris, France 4Institute for Theoretical Physics, WWU Münster, D-48149 Münster, Germany (Received 4 March 2020; accepted 2 June 2020; published 16 June 2020) We revisit scalar leptoquark pair production at hadron colliders. Apart from QCD contributions, we include the lepton t-channel exchange diagrams relevant in the light of the recent B-flavor anomalies. We evaluate all contributions at next-to-leading order in QCD and resum, in the threshold regime, soft-gluon radiation at next-to-next-to-leading-logarithmic accuracy. All corrections are found equally relevant. Our predictions consist of the most precise leptoquark cross section calculations available to date and are necessary for the best exploitation of leptoquark LHC searches. DOI: 10.1103/PhysRevD.101.115017 I. INTRODUCTION accuracy in the strong coupling αs [11–15], sometimes also supplemented by logarithmic threshold corrections [9,10], Many extensions of the Standard Model (SM) predict the are used. Thus the predictions include contributions at existence of scalar leptoquarks [1–8], i.e., scalar bosons Oðα2Þ and Oðα3Þ, or possibly of higher order in α , but are coupling to a quark and a lepton simultaneously. Evidence s s s independent of y [34,35]. Bearing in mind the B-anomalies for their existence is consequently vastly searched for at the and ðg − 2Þ motivation, the limits may thus be incorrectly LHC. However, none of the recent ATLAS [9,10] and CMS μ estimated. [11–15] analyses find any hint for these leptoquarks, so that In this paper, we perform for the first time a full NLO-QCD their mass is now constrained to be larger than 1–1.5 TeV. cross section calculation for scalar leptoquark pair produc- Recently, scalar leptoquarks have gained significant interest tion at hadron colliders, in which we include both the QCD as they may provide an explanation [16–22] for the B-meson – and t-channel contributions. Hadronic production of heavy anomalies [23 30] and address [31] the discrepancy between systems, which is the case considered here, inevitably probes theoretical predictions [32] and experimental measurements partonic center-of-mass energies close to the production [33] of the anomalous magnetic moment of the muon threshold given by twice the leptoquark mass m . In this ðg − 2Þ LQ μ. In this context, favored scenarios generally feature limit, radiative corrections are dominated by soft-gluon large lepton-quark-leptoquark Yukawa couplings y. emissions, manifesting themselves as large logarithmic terms The most stringent bounds originating from LHC direct that must be consistently resummed to all orders [36–39].We searches for leptoquark pair production and decay are report here threshold-resummed results at next-to-next-to- extracted by assuming that leptoquarks are solely produced leading-logarithmic (NNLL) accuracy and showcase pre- via strong interactions. In other words, non-QCD diagrams 2 dictions obtained by matching them to our new NLO results. involving lepton t-channel exchanges of Oðy Þ are In the following, we first present the considered theoretical neglected. In the associated limit setting procedure, signal framework and provide brief technical computational details. cross sections evaluated at next-to-leading-order (NLO) We then show an illustrative selection of results that under- lines how all considered corrections affect the results in *[email protected] comparable and significant ways. Our predictions, which are † [email protected] the most precise to date, are hence required to derive limits ‡ [email protected] consistently, in particular when assessing the influence of the § [email protected] leptoquark Yukawa couplings. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. II. THEORETICAL FRAMEWORK Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, We focus on a simplified model in which the SM is and DOI. Funded by SCOAP3. supplemented by several species of scalar leptoquarks 2470-0010=2020=101(11)=115017(7) 115017-1 Published by the American Physical Society CHRISTOPH BORSCHENSKY et al. PHYS. REV. D 101, 115017 (2020) ˜ ˜ S1, S1, R2, R2 and S3. Inspired by standard naming III. SCALAR LEPTOQUARK PAIR ð3 1Þ PRODUCTION AT THE LHC conventions [40,41], these leptoquarks lie in the ; −1=3, ð3 1Þ ð3 2Þ ð3 2Þ ð3 3Þ ; −4=3, ; 7=6, ; 1=6 and ; −1=3 representations We present selected predictions for scalar leptoquark pair of the SM gauge group respectively, and we target their production at the 13 TeV LHC for the three most commonly Yukawa interactions involving exactly one lepton and discussed types of scalar leptoquarks in the context of the ð2Þ quark. The latter are collected in the Lagrangian: flavor anomalies: the SU L singlet state S1 (denoted by ð−1=3Þ S1 due to its electric charge of −1=3),doublet state R2 and L ¼ yRR ¯ c l † þ yLLð ¯ c Þ † þ y˜RR ¯ c l ˜ † the triplet state S3. More specifically, in the last two cases, we int 1 uR RS1 1 QL ·LL S1 1 dR RS1 consider the pair production of the R2 mass eigenstate of LR † RL RL ¯ ˜ ð5 3Þ þ y e¯ Q R þ y u¯ ðL · R2Þþy˜ d ðL ·R2Þ = 2 R L 2 2 R L 2 R L electric charge of 5=3 (denoted by R2 ) andthe one of the S3 þ yLLð ¯ c σ Þð kÞ† þ ð Þ mass eigenstate of electric charge of −4=3 (denoted by 3 QL · kLL S3 H:c: 1 ð−4=3Þ S3 ). In all our calculations, we treat the leptoquark mass m as a free parameter and assume the Cabibbo-Kobayashi- In this expression, all flavor indices are suppressed for LQ σ Maskawa matrix (CKM) matrix to be diagonal. While the clarity, k stands for the Pauli matrices and the dot for the determination of a scenario compatiblewith flavor constraints invariant product of two fields lying in the (anti)funda- and Z-pole observables is desirable [56],thisgoesbeyondthe ð2Þ mental representation of SU . The QL and LL spinors scope of this study. We consider instead benchmarks moti- denote the SM weak doublets of left-handed quarks and vated by Ref. [21]. The values of the Yukawa couplings found l leptons, and uR, dR and R are the corresponding weak in this study were obtained in a fit to low-energy observables singlets. Moreover, the y=y˜ couplings are 3 × 3 matrices in and did not involve constraints from direct searches for the flavor space, the first index of any element yij=y˜ij leptoquarks at the LHC. Given that the description of lepton referring to the quark generation and the second one to the flavor university-violating observables involves both lepto- lepton generation in the gauge basis. quark couplings and masses, optimally one should aim at a The calculations reported in this work concern scalar global fit based on direct and indirect constraints, in which case the calculations presented in this work will play a crucial leptoquark pair production and include fixed order con- à tributions at leading order (LO) and NLO in QCD. In role. For S1S1 production, we adopt a minimal flavor ansatz ðyLLÞ ¼ −0 15 contrast with previous work [34,35,42,43], we not only for the leptoquark Yukawa couplings, 1 22 . and LL LL à 2 3 ðy Þ ¼ 3 with all other y elements set to 0. For R2R consider the QCD components at OðαsÞ and Oðαs Þ,but 1 32 1 2 also include the t-channel lepton exchange contributions at production, we similarly consider as the only nonvanishing RL Oð 4Þ Oð 4α Þ Oð 2α Þ Oð 2α2Þ coupling ðy2 Þ22 ¼ 1.5, a value still allowed by direct y and y s as well as the y s and y s à interference of the t-channel diagrams with the QCD ones. exclusion bounds [21], while for S3S3 production, we adopt ðyLLÞ ¼ −ðyLLÞ The full NLO-accurate predictions are collectively coined 3 22 3 32, keeping the actual coupling value free “NLO w=t-channel” in the following, in contrast to the pure and setting all other couplings to 0. QCD ones that we refer to as the “NLO-QCD” predictions. Our results are obtained by convoluting the partonic The NLO w=t-channel cross sections are then additively results with two different sets of parton distribution functions (PDFs), NNPDF3.1 [57] and CT18 [58]. Unless stated matched with the resummed NNLL soft-gluon contribu- otherwise, NLO sets are employed for NLO-QCD and tions, resulting in cross section predictions at NLO þ NLO w=t-channel predictions, while NNLO sets are used w=t-channel NNLL accuracy. Threshold resummation is for NLO þ NNLL calculations. We set the renormalization performed in Mellin space (see e.g., [39]) and involves (μR) and factorization (μF) scales equal to a common value one-loop matching coefficients [44]. μ ¼ μR ¼ μF. The central scale choice μ ¼ μ0 is fixed to To ensure the correctness of the results, we perform the μ ¼ μ 0 mLQ, and scale uncertainties are estimated by varying calculations in two independent ways: We first implement by a factor of 2 up and down. the above model into FeynRules [45], which we jointly use In Fig.