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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 Mobiusdomain 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 thefactorization method for the non-factorizable contribution.

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