Simultaneous explanation of the R K and R D * $$ {R}_{D^{\left(*\right)}} $$ puzzles: a model analysis

R K and $$ {R}_{D^{\left(*\right)}} $$ 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 $$ {R}_{D^{\left(*\right)}} $$ puzzles. There are two UV completions that can give rise to the effective Lagrangian: (i) V B: 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 V B contributes to $$ {B}_s^0\hbox{-} {\overline{B}}_s^0 $$ mixing and τ → 3μ, while U 1 does not. We show that, when constraints from these processes are taken into account, the V B model is just barely viable. It predicts $$ \mathrm{\mathcal{B}}\left({\tau}^{-}\to {\mu}^{-}{\mu}^{+}{\mu}^{-}\right)\simeq 2.1\times {10}^{-8} $$ . This is measurable at Belle II and LHCb, and therefore constitutes a smoking-gun signal of V B. For U 1, there are several observables that may point to this model. Perhaps the most interesting is the lepton-flavor-violating decay Y(3S) → μτ, which has previously been overlooked in the literature. U 1 predicts $$ {\left.\mathrm{\mathcal{B}}\left(\varUpsilon (3S)\to \mu \tau \right)\right|}_{\max }=8.0\times 1{0}^{-7} $$ . Thus, if a large value of $$ \mathrm{\mathcal{B}}\left(\varUpsilon (3S)\to \mu \tau \right) $$ is observed — and this should be measurable at Belle II — the U 1 model would be indicated.

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