Explaining the R_K and R_{K^*} anomalies

Abstract

Recent LHCb results on R_{K^*}, the ratio of the branching fractions of B rightarrow K^* mu ^+ mu ^- to that of B rightarrow K^* e^+ e^-, for the dilepton invariant mass bins q^2 equiv m_{ell ell }^2 = [0.045–1.1] GeV^2 and [1.1–6] GeV^2 show approximately 2.5 sigma deviations from the corresponding Standard Model prediction in each of the bins. This, when combined with the measurement of R_K , (q^2=[1-6], mathrm GeV^2), a similar ratio for the decay to a pseudo-scalar meson, highly suggests lepton non-universal new physics in semi-leptonic B meson decays. In this work, we perform a model independent analysis of these potential new physics signals and identify the operators that do the best job in satisfying all these measurements. We show that heavy new physics, giving rise to q^2 independent local 4-Fermi operators of scalar, pseudo-scalar, vector or axial-vector type, is unable to explain all the three measurements simultaneously, in particular R_{K^*} in the bin [0.045–1.1], within their experimental 1sigma regions. We point out the possibility to explain R_{K^*} in the low bin by an additional light (lesssim , 20 , {mathrm{MeV}}) vector boson with appropriate coupling strengths to (bar{b} , s) and (bar{e} , e).