Simultaneous explanation of the R K and R D * R_D(*) puzzles: a model analysis

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) 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 Bₛ⁰- B̄ₛ⁰ 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 B(τ⁻→ μ⁻μ⁺μ⁻) 2.1× 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 .B( (3S)→ μ τ )|ₘₐₓ=8.0× 10⁻⁷ . Thus, if a large value of B( (3S)→ μ τ ) is observed — and this should be measurable at Belle II — the U 1 model would be indicated.