Simultaneous explanation of the RK and RD (*) 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 RK and RD (*) 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) - B-s(0) mixing and t -> 3 mu, 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(t(-) -> mu(-) mu(+) mu(-)) similar or equal to 2.1 Chi 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 gamma(3S) -> mu t, which has previously been overlooked in the literature. U-1 predicts B(gamma(3S)-> mu tau) \ max = 8.0 Chi 10(-7). Thus, if a large value of B(gamma(3S) -> mu tau) is observed - and this should be measurable at Belle II - the U-1 model would be indicated.