New light mediators for the $R_K$ and $R_{K^{\ast }}$ puzzles

Abstract

The measurements of $R_K$ and $R_K^{\ast }$ provide hints for the violation of lepton universality. However, it is generally difficult to explain the $R_{K^{\ast }}$ measurement in the low $q^2$ range, $0.045\le q^2\le 1.1$ GeV${}^2$. Light mediators offer a solution by making the Wilson coefficients $q^2$ dependent. We check if new lepton nonuniversal interactions mediated by a scalar ($S$) or vector particle ($Z^{\prime }$) of mass between $10-200$ MeV can reproduce the data. We find that a 25 MeV $Z^{\prime }$ with a $q^2$-dependent $b-s$ coupling and that couples to the electron but not the muon can explain all three anomalies in conjunction with other measurements. A similar 25 MeV $S$ provides a good fit to all relevant data except $R_{K^{\ast }}$ in the low $q^2$ bin. A 25 MeV $Z^{\prime }$ with a $q^2$-dependent $b-s$ coupling and that couples to the muon but not the electron provides a good fit to the combination of the $R_K$ and $R_{K^{\ast }}$ data, but does not fit $R_{K^{\ast }}$ in the low $q^2$ bin well.

Comments: 8 pages, 3 tables. Expanded version