Magnetic-dipole corrections to $R_K$ and $R_{K^{\ast }}$ in the Standard Model and Dark Photon scenarios

Abstract

In this work we evaluate the long-distance QED contributions, induced by the magnetic-dipole corrections to the final charged leptons, on the $B$ meson decay widths $B\to (K,K^{\ast }){\ell }^{+}{\ell }^{-}$ and ratios $R_{K,K^{\ast }}=\Gamma (B\to (K,K^{\ast }){\mu }^{+}{\mu }^{-})/\Gamma (B\to (K,K^{\ast })e^{+}{e}^{-})$, as well as on $R_{K,K^{\ast }}^{\tau }$ (with $\mu$ replaced by the $\tau$ lepton). QED long-distance contributions induced by the Coulomb potential corrections (Fermi-Sommerfeld factors) were also included. Corresponding corrections to the inclusive decay widths of $B\to X_s{\ell }^{+}{\ell }^{-}$, with $\ell =e,\mu ,\tau$, are also analyzed for completeness. The magnetic-dipole corrections, which are manifestly Lepton Flavor Universality violating and gauge-invariant, are expected to be particularly enhanced in $R_{K^{\ast }}$ for the dilepton mass region close to the threshold. However, we find that the largest contribution of all these corrections to the $R_{K,K^{\ast }}$ observables do not exceed a few per mille effect, thus reinforcing the validity of previous estimates about the leading QED corrections to $R_{K,K^{\ast }}$. Finally, viable new physics contributions to $R_{K,K^{\ast }}$ induced by the exchange of a massless dark-photon via magnetic-dipole interactions, which provide the leading contribution to the corresponding $B\to (K,K^{\ast }){\ell }^{+}{\ell }^{-}$ amplitudes in this scenario, are analyzed in light of the present $R_{K,K^{\ast }}$ anomalies.

arXiv comment48 pages, 11 figures, new results and references added, same as JHEP published version

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