Lepton flavor non-universality in $b\to s{\ell }^{+}{\ell }^{-}$ processes

Abstract

We explore a scenario of New Physics entering the description of $B\to K^{(\ast )}\mu \mu$ decay through couplings to the operators ${\mathcal{O}}_{9,10}^{\prime }$, satisfying $C_9^{\prime }=-C_{10}^{\prime }$. From the current data on $\mathcal{B}(B_s\to \mu \mu )$ and $\mathcal{B}(B\to K\mu \mu {)}_{[15,22]{\mathrm{GeV}}^2}$, we obtain constraints on $\mathrm{Re}{C}_{10}^{\prime }$ and $\mathrm{Im}{C}_{10}^{\prime }$ which we then assume to be lepton specific, and find $R_K=\mathcal{B}(B\to K\mu \mu )/\mathcal{B}(B\to Kee{)}_{[1,6]{\mathrm{GeV}}^2}=0.88(8)$, consistent with recent value measured at LHCb. A specific realization of this scenario is the one with a scalar leptoquark state $\Delta$, in which $C_{10}^{\prime }$ is related to the mass of $\Delta$ and its Yukawa couplings. We then show that this scenario does not make any significant impact on $B_s-{\overline{B}}_s$ mixing amplitude nor to $\mathcal{B}(B\to K\nu \bar{\nu })$. Instead, it can modify $R_{K^{\ast }}=\mathcal{B}(B\to K^{\ast }\mu \mu )/\mathcal{B}(B\to K^{\ast }ee{)}_{[1,6]{\mathrm{GeV}}^2}$, which will soon be experimentally measured and we find it to be $R_{K^{\ast }}=1.11(8)$, while $R_{K^{\ast }}/R_K=1.27(19)$. A similar ratio of forward-backward asymmetries also becomes lower than in the Standard Model.

Comments: 13 pages, 3 figures, further typos corrected