The role of long distance contribution to the $B\to K^{(\ast)} \ell^+ \ell^-$ in the Standard Model

Abstract

We investigate rare semileptonic $B \to K^\ast\ell^+\ell^-$ by looking at the long distance contributions. Our analysis is limited to the very small values of physical accessible range of invariant mass of the leptonic couple $q^2$. We show that the light quarks loop has to be accounted for, along with the charming penguin contribution, in order to accurately compute the $q^2$-spectrum in the Standard Model. Such a long distance contribution may also play a role in the analysis of the lepton flavour universality violation in this process.