Simultaneous Explanation of the $R_K$ and $R_{D^{(*)}}$ Puzzles: a Model Analysis

TL;DR

This paper analyzes two new physics models, vector boson and leptoquark, to explain B-decay anomalies, assessing their viability and predicting measurable signals at Belle II and LHCb.

Contribution

It provides a detailed individual examination of the vector boson and leptoquark models, including their constraints and distinctive experimental signatures.

Findings

VB model is barely viable due to mixing and decay constraints.

VB predicts tau to 3 mu decay at a measurable rate.

U1 model predicts a potentially observable Upsilon to mu tau decay.

Abstract

$R_K$ and $R_{D^{(*)}}$ are two $B$-decay measurements that presently exhibit discrepancies with the SM. Recently, using an effective field theory approach, it was demonstrated that a new-physics model can simultaneously explain both the $R_K$ and $R_{D^{(*)}}$ puzzles. There are two UV completions that can give rise to the effective Lagrangian: (i) $VB$: a vector boson that transforms as an $SU(2)_L$ triplet, as in the SM, (ii) $U_1$: an $SU(2)_L$-singlet vector leptoquark. In this paper, we examine these models individually. A key point is that $VB$ contributes to $B^0_s$-${\bar B}^0_s$ mixing and $\tau \to 3\mu$, while $U_1$ does not. We show that, when constraints from these processes are taken into account, the $VB$ model is just barely viable. It predicts ${\cal B} (\tau^-\to\mu^-\mu^+\mu^-) \simeq 2.1 \times 10^{-8}$. This is measurable at Belle II and LHCb, and therefore constitutes a smoking-gun signal of $VB$. For $U_1$, there are several observables that may point to this model. Perhaps the most interesting is the lepton-flavor-violating decay $\Upsilon(3S) \to \mu \tau$, which has previously been overlooked in the literature. $U_1$ predicts ${\cal B}(\Upsilon(3S) \to \mu \tau)|_{\rm max} = 8.0 \times 10^{-7}$. Thus, if a large value of ${\cal B}(\Upsilon(3S) \to \mu \tau)$ is observed -- and this should be measurable at Belle II -- the $U_1$ model would be indicated.