Test of factorization for the long-distance effects from charmonium on $B\to K\ell^+\ell^-$

Abstract

We report on a calculation of the charmonium contribution to the decay $B \rightarrow K\ell^+\ell^-$ using lattice simulations with 2+1 flavors of Mobius domain wall fermions. We focus on the region of $q^2$ below the $J/\psi$ resonance and test the factorization approximation to estimate the amplitude. We show a possible discrepancy between the lattice calculation and the factorization method for the non-factorizable contribution.