New physics in $$\text {b} \rightarrow \text {s}$$ transitions in the MF331 model

Eur. Phys. J. C (2022) 82:966 https://doi.org/10.1140/epjc/s10052-022-10916-7 Regular Article - Theoretical Physics New physics in b → s transitions in the MF331 model N. T. Duy1,2,a , P. N. Thu2,3 , D. T. Huong1,b 1 Institute of Physics, VAST, 10 Dao Tan, Ba Dinh, Hanoi, Vietnam 2 Graduate University of Science and Technology, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam 3 Faculty of Natural Sciences and Technology Tay Bac University, Quyet Tam Ward, Son La, Son La, Vietnam Received: 9 May 2022 / Accepted: 13 October 2022 © The Author(s) 2022 Abstract There are two sources that help to explain the RK , RK∗ anomalies in the MF331 model. The first is non-LFUV couplings of the new neutral gauge boson Z with leptons,   gZ (e) = gZ (μ, τ ), which causes the RK , RK∗ anomalies via  Z -penguin diagrams involving newly charged gauge bosons X± μ , and exotic U-quarks. The second is the contribution from the box diagram only for the first generation of leptons. We show that the penguin diagrams can not explain RK , RK∗ anomalies, and that the box diagram is required. The experimental constraints for RK and RK∗ result in new particle mass degeneracy. The contributions of NP to the branching ratios Br(Bs → μ+ μ− ), Br(b → sγ ) predict results that agree with the experimental limits in the allowed region of the NP scale. 1 Introduction In recent years, the LHCb has provided observations that show a conflict between the standard model (SM) predictions and the experimental results. The results of the angular analysis of the decay B0 → K0∗ μ+ μ− and measurements of the branching fraction of several b → sl+ l− [1– 10] are in tension with those of SM. Some of these tensions can be explained by the involvement of hadronic uncertainties arising from the different long-distance effects [11–15], while the rest are explained by NP signs [16–20]. Lepton flavor universality violating (LFUV) observables, such as the ratios of branching fractions involving both b → sμ+ μ− and b → se+ e− transitions, are also intriguing to theorists. The LHCb and Belle collaborations measured [21–24] the Br B+ →K+ μ+ μ− ratio RK ≡ Br( B+ →K+ e+ e− ) in the low dilepton invariant ( )   mass-squared range 1.0 ≤ q2 ≤ 6.0 GeV2 . The LHCb has a e-mail: b e-mail: (corresponding author) 0123456789().: V,-vol   reported the latest value of RK [24], RLHCb [1.1, 6] GeV2 = K 0.846+0.042+0.013 −0.039−0.012 , which showed 3.1σ deviation from the SM expectation [25,26] of  1, giving evidence for the violation of lepton universality in these decays. Another ratio was reported by the LHCb [27] and Belle [28], RK∗ ≡ Br(B→K∗ μ+ μ− ) , which is measured in two dilepton invariBr(B→K∗ e+ e− ) ant mass squared regions [27], ⎧ 0.11 2 2 4 0.66 + ⎪ − 0.07 (stat) for 0.045 < q < 1.1 GeV /c , ⎪ ⎪ ⎨ ±0.03 (syst) RLHCb = K∗ 0.11 2 2 4 ⎪ 0.69 + ⎪ − 0.07 (stat) for 1.1 < q < 6.0 GeV /c . ⎪ ⎩ ±0.05 (syst) These ratios have been determined to be 2.1, 2.5 standard deviations below their SM expectations, respectively [25,26,29]. Because the hadronic uncertainties are canceled, the LFUV observables RK and RK∗ are theoretically clean, contrary to observations of the angular and branching fraction of the b → sll decays. As a result, we can certainly infer the presence of NP. These novel metrics have sparked a lot of interest, leading to a slew of model-independent global analyses [30–37]. The majority of these studies revealed that the LFUV observables RK and RK∗ may be explained by using the combination of new contributions of Wilson coefficients (WCs) associated with V and A operators. The NP interpretations of the RK , RK∗ anomalies postulate the existence of a new state with tree-level couplings to muons and quarks, namely Z vector bosons [38–44], scalar leptoquarks [45,46]. For addressing model building, it is reasonable to consider what models naturally lead to the LFUV. Extending the symmetry of SM reveals one of the natural candidates for violating the lepton flavor universality (LFU). In different approaches to extending the SM symmetry, the class of model-based upon the gauge symmetry SU(3)C × SU(3)L × U(1)X (3-3-1) [47–52]is known as an attractive proposal. Because this model explains not only the existence of only three fermions, strong CP conservation, and electric charge 123 966 Page 2 of 15 quantization, but also dark matter, neutrino masses, cosmic inflation, and matter-antimatter asymmetry, all of which are current SM issues. In order to cancel the [SU(3)L ]3 anomaly, the number of fermion triplets must equal that of the antitriplet. Traditionally, the arrangement of the particles is one of the quark families that transforms differently from the remaining quark families, while all lepton families transform identically. According to this arrangement, the models predict the tree-level quark FCNCs coupled to Z , whereas Z boson interacts with a pair of the same flavors and strengths as the three lepton families. It means that this approach predicts the lepton flavor universality (LFU) [53–56]. In contrast with this setup , the quark and lepton arrangements flip over, creating new versions that are called the flipped 3-3-1 (F331) models [57,58]. The FCNCs are coupled to the Z swap from quarks into leptons. Therefore, the F331 models break the LFU at the tree level [59], but quark FCNCs induce it at the one-loop level. It naturally provides solutions for explaining the LFUV measuremens in rare B meson decays. Based on the minimal flipped 3-3-1 (MF331) model [58], a version of the F331 models in which scalar multiplets are reduced to a minimum, we explore the RK , RK∗ anomalies from LFUV including the tree-level and the radiative structure of quark flavor-changing interactions. We are looking for NP parameter space regions that sufficiently repre∗ sent the experimental  data on RK and RK . Furthermore, the Br Bs → μ+ μ− is one of the cleanest observables [60] and there is a minor disagreement with SM prediction [61]. This tension suggests the same direction as the RK∗ fit’s chosen WCs. As a result, we consider whether  the parameter space  for fixing RK∗ and Br Bs → μ+ μ− are compatible. Apart from affecting the above observations, NP can also alter the Br (b → sγ ). Using the parameter space of the above fits, we estimate the role of NP in the Br (b → sγ ). The structure of paper is organized as follows. In Sect. 2, we give a quick summary of the MF331 model. In Sect. 3, we examine all of the NP contributions to the WCs associated decay processes caused by b − s transitions and provide the effective Hamiltonian for these processes. A detailed description of the RK , RK∗ anomalies included in the global fit is given in Sect. 4. In Sects. 5 and 6, we study the NP contributions to the branching ratios of decays, Bs → μ+ μ− , b → sγ , respectively. Finally, we provide our conclusions in Sect. 7. 2 A Summary of the MF331 model 2.1 Paticle content and mass spectrum o (...truncated)