Explanation of B to K^((*)) ell^+ ell^- and muon g-2, and implications at the LHC

More than $3\sigma$ deviations from the standard model are observed in the angular observable $P'_5$ of $B\to K^* \mu^+ \mu^-$ and muon $g-2$. To resolve these anomalies, we extend the standard model by adding two leptoquarks. It is found that the signal strength of the diphoton Higgs decay can exhibit a significant deviation from unity and is within the data errors. Although $\ell_i \to \ell_j \gamma$ puts severe bounds on some couplings, it is found that the excesses of $P'_5$ and muon $g-2$ can still be explained and can be accommodated to the measurement of $B_s\to \mu^+ \mu^-$ in this model. In addition, the leptoquark effects can also explain the LHCb measurement of $R_K = BR(B^+ \to K^+ \mu^+\mu^-)/BR(B^+ \to K^+ e^+e^-)=0.745^{+0.090}_{-0.074} \pm 0.036$, which shows a $2.6\sigma$ deviation from the standard model prediction.