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

A preprint version of the article is available at arXiv.


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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Bhattacharya, B., Datta, A., Guévin, JP. et al. Simultaneous explanation of the R K and \( {R}_{D^{\left(*\right)}} \) puzzles: a model analysis. J. High Energ. Phys. 2017, 15 (2017).

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