Exploring the lepton flavor violating decay modes $b \to s μ^{\pm} τ^{\mp}$ in SMEFT approach

TL;DR

This work analyzes lepton flavor violating decays from the $b \to s \ell_1 \ell_2$ transition within the SMEFT framework, focusing on (pseudo)scalar and axial-vector operators and their impact on exclusive channels $B_{(s)} \to (\phi, K^*, K_2^*) \tau \mu$ and the baryonic mode $\Lambda_b \to \Lambda \tau \mu$. It connects SMEFT Wilson coefficients to low-energy observables, constrains combinations using current upper bounds on $\mathcal{B}(B_s \to \mu\tau)$ and $\mathcal{B}(B \to K \mu\tau)$ with a cutoff $\Lambda_{\rm cut}=1$ TeV, and then predicts the $q^2$-dependent branching fractions, forward-backward asymmetries, and lepton polarization for the LFV channels. The analysis finds sizeable NP effects in several modes, including a zero-crossing in the lepton forward-backward asymmetry for specific combinations (e.g., $\Lambda_b \to \Lambda \tau^+ \mu^-$ and $B \to (K^*, \phi) \tau^+ \mu^-$), with BRs typically in the $10^{-5}$–$10^{-6}$ range, potentially accessible at LHCb and Belle II with future upgrades. The results illustrate how SMEFT-driven LFV signals in both mesonic and baryonic $b$-hadron decays can serve as a complementary probe to anomalous $b \to s \ell\ell$ data and guide experimental searches for NP. Observing these LFV decays would provide clear evidence of physics beyond the Standard Model.

Abstract

We perform an analysis of the consequences of various new physics operators on the lepton flavor violating (LFV) decay modes mediated through $b \to s \ell _1 \ell _2$ transitions. We scrutinize the imprints of the (pseudo)scalar and axial(vector) operators on the exclusive LFV decay channels $ B_{(s)} \rightarrow (φ, K^{*}, K_{2}^{*})\ell_{1}\ell_{2}$ and $Λ_{b}\rightarrow Λ\ell_{1}\ell_{2}$, where $\ell_{1}, \ell_{2}$ represent $μ$ or $τ$. The new physics parameters are constrained by using the upper limits of the branching fractions of the $B \to τμ$ and $B \to K τμ$ processes, assuming the new physics couplings to be real. We then explore the key observables such as the branching fraction, the forward-backward asymmetry, and the longitudinal polarisation fraction of the $B \to (K^*, φ, K_2^*) τ^{\pm} μ^{\mp}$ decays. In addition, we also investigate the impact of the new physics couplings on the baryonic $Λ_b \to Λτ^{\pm} μ^{\mp}$ decay channels mediated by the $b \to s$ quark level transition. With the experimental prospects at LHCb upgrade and Belle II, we also predict the upper limits of the above-discussed observables, which could intrigue the new physics search in these channels.

Figures (4)

• Figure 1: Constraints on the NP couplings obtained from the combined measurement of ${\cal B}(B \to \tau \mu$) and ${\cal B}(B \to K^{+} \tau \mu$), where the red, green and blue regions represent the $1\sigma$, $2\sigma$, and $3\sigma$ contours, while the black star indicating the best-fit value.
• Figure 4: Variation of the branching ratio of $\Lambda_b\to\Lambda \tau^{+} \mu^{-}$ (left), $\Lambda_b\to\Lambda\tau^{-} \mu^{+}$ (right) with the cut-off scale.
• Figure 7: Cut off dependent branching ratio of $B \to K_{2}^{*} \tau^{+} \mu^{-}$ (left) and $B \to K_{2}^{*} \tau^{-} \mu^{+}$ (right).
• Figure 12: Cutoff dependent branching ratio of $B \to K^{*}\tau \mu$ (left) and $B \to \phi \tau \mu$ (right).