Combined explanations of B-physics anomalies, $$(g-2)_{e, \mu }$$ and neutrino masses by scalar leptoquarks

Eur. Phys. J. C (2022) 82:959 https://doi.org/10.1140/epjc/s10052-022-10920-x Regular Article - Theoretical Physics Combined explanations of B-physics anomalies, (g − 2)e,μ and neutrino masses by scalar leptoquarks Shao-Long Chen1,2,a , Wen-wen Jiang1,b , Ze-Kun Liu1,c 1 Key Laboratory of Quark and Lepton Physics (MoE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China 2 Center for High Energy Physics, Peking University, Beijing 100871, China Received: 10 August 2022 / Accepted: 13 October 2022 © The Author(s) 2022 Abstract We extend the contents of the standard model (SM) by introducing TeV-scale scalar leptoquarks to generate neutrino masses and explain some current observed deviations from the SM predictions, including the anomalous magnetic moments of charged leptons (electron and muon) and B-physics anomalies (R K (∗) and R D (∗) ). The model consists of SU(2) L singlet leptoquark S1 ∼ (3̄, 1, 1/3), doublet leptoquark R̃2 ∼ (3, 2, 1/6) and triplet leptoquark S3 ∼ (3̄, 3, 1/3). We combine the constraints arising from the low-energy lepton flavor violation, meson decay and mixing observables. We perform a detailed phenomenological analysis and identify the minimized texture of leptoquark Yukawa matrices to accommodate a unified explanation of the anomalies and neutrino oscillation data. 1 Introduction The neutrino oscillation experiments have firmly established that neutrinos are massive and have non-trivial mixing between different generations [1–4]. The experiments also indicate that the neutrino masses are much smaller than that of charged fermions, which suggests that neutrinos may have specific sources of mass generation. In the recent decades, a plethora of models have been proposed to explain the neutrino mass and the natural way is the so called seesaw mechanism [5]. Type-I seasaw model [6–10] provides neutrino masses at the tree-level by extending the particle content of the SM with three SU(2) L -singlet right-handed neutrino fields, while type-II [10–12] and type-III [13] models introduce SU(2) L -triplet scalar and SU(2) L -triplet fermions, a e-mail: b e-mail: c e-mail: (corresponding author) 0123456789().: V,-vol respectively. Beyond tree level, the tiny neutrino masses could radiatively originate from loop levels [14–18]. Extending the SM to include the source of the origin of neutrino mass and mixing brings new physics, especially to the flavor sector. The intensity frontier precision measurements may pin down the possible connections between neutrino physics and flavor physics. Such as the anomalous magnetic moments of electron and muon, there are long-standing discrepancies between the theoretical predictions and measured values [19–41]. The anomalies also include the ratios R K (∗) and R D (∗) in B-decays, pointing towards the lepton flavor universality violation, measured by BaBar [42,43], Belle [44–46] and LHCb [47–51] collaborations. In this work, we propose a model with scalar leptoquarks to provide a common explanation of neutrino mass and these flavor anomalies. Leptoquarks (LQs) have been introduced in many new physics models beyond the SM and are very popular to explain B-physics anomalies with one or more leptoquark states [52–54]. The unified solution to both R K (∗) and R D (∗) anomalies seems rule out single scalar leptoquark models [55]. Among the scalar leptoquarks, triplet S3 ∼ (3̄, 3, 1/3) can accommodate the R K (∗) anomalies, while the R D (∗) anomalies can be resolved by introducing either a singlet S1 ∼ (3̄, 1, 1/3) or a doublet R2 ∼ (3, 2, 7/6) leptoquark. The double leptoquarks models were proposed to explain both R K (∗) and R D (∗) anomalies, involving S1 and S3 combination [56–61] or R2 and S3 combination [62–64]. Extending with leptoquarks will give contribution to the anomalous magnetic moment of charged lepton at one-loop level and the no-chiral scalar leptoquarks S1 or R2 , which have both leftchiral and right-chiral couplings, can provide good explanations to the aμ and ae deviations [65,66] simultaneously. The mixing between different type leptoquarks can also generate non-trivial Majorana neutrino mass terms at one-loop level. The minimal model to generate neutrino mass by the scalar leptoquark mixing requires a pair of leptoquarks and 123 959 Page 2 of 18 Eur. Phys. J. C the possible combinations are S1 − R̃2 (3, 2, 1/6), S3 − R̃2 and S3 − R2 [67–71]. Motivated by the leptoquark abundant phenomenologies, we attempt to extend the SM contents by scalar leptoquarks to generate neutrino mass and explain the flavor anomalies mentioned above. This paper is organized as follow: In Sect. 2, we briefly introduce the model set-up and the neutrino mass generation mechanism. In Sect. 3, we show how to explain the flavor anomalies in the model, including R K (∗) , R D (∗) , aμ and ae . We discuss the observables constraints on the leptoquark couplings in Sect. 4 and then we perform a detailed analysis of model parameter space and identify two benchmark points in Sect. 5 and we conclude in the final section. 2 The model and neutrino mass generation 2.1 The model In addition to the SM fields, we introduce three scalar leptoquarks, including an SU(2) L singlet S1 ∼ (3̄, 1, 1/3), a doublet R̃2 ∼ (3, 2, 1/6) and a triplet S3 ∼ (3̄, 3, 1/3). The scalar leptoquarks are denoted as 1/3 2/3 S1 (3̄, 1, 1/3) = S1 , −1/3 T R̃2 (3, 2, 1/6) = ( R̃2 , R̃2  √ 4/3  1/3 S3 2 S3 i i S3 (3̄, 3, 1/3) = τ S3 = √ −2/3 , 1/3 2 S3 −S3 ) , (1) are the Pauli matrices and we where τ i (i = 1, 2, 3) √ √define 4/3 −2/3 = (S31 − iS32 )/ 2, S3 = (S31 + iS32 )/ 2 and S3 1/3 S3 = S33 . The corresponding Yukawa terms that describe the interactions between leptoquarks and fermions are given by ij j ij + − where Q and L denote the SU(2) L doublet left-handed quarks and leptons, u R , d R and e R denote the SU(2) L singlet righthanded up-type quarks, down-type quarks and charged leptons, respectively. All fields in Eq. (2) are represented in the flavor basis. For phenomenological analysis, it is more convenient that we re-parametrize the couplings in the fermion mass basis. The Yukawa coupling terms are then rewritten in the mass basis of fermions as the following form, ij j 1/3 + (V T y1L )i j d LiC ν L S1 ij j 1/3 + y2L d Ri ν L R̃2 ij j 2/3 − y2L d Ri e L R̃2 123 j ij j 1/3 −1/3 j 1/3 + (V T y3L )i j d LiC ν L S3 ij j −2/3 2y3L u iC L ν L S3 ij j 1/3 + y3L u iC L e L S3 + h.c., + λ3 Tr(S3† S3† )Tr(S3 S3 ) + λ H 1 H † H S1† S1   1 + λ H 2 H † H R̃2† R̃2 + λ H 3 H † H Tr S3† S3 2  + λ13 H † S3† H S1 + μ1 R̃2† H S1∗  + μ2 R̃2† S3† H + h.c. , (3) (4) where H is the SM Higgs doublet. More general interactions of leptoquarks and SM Higgs can be found in Ref. [72]. After the spontaneous electroweak symmetry breaking, the Higgs field H √ acquires a vacuum expecting value (VEV) with H  = v/ 2, v = 246 GeV. The physical scalar particles include one electric neutral Hig (...truncated)