To understand the rare decay $B_s\to\pi^+\pi^-\ell^+\ell^-$

Abstract

Motivated by the LHCb measurement, we analyze the $B_s\to \pi^+\pi^-\ell^+\ell^-$ decay in the kinematics region where the pion pairs have invariant mass in the range $0.5$-$1.3$ GeV and muon pairs do not originate from a resonance. The scalar $\pi^+\pi^-$ form factor induced by the strange $\bar ss$ current is predicted by the unitarized approach rooted in the chiral perturbation theory. Using the two-hadron light-cone distribution amplitude, we then can derive the $B_s\to \pi^+\pi^-$ transition form factor in the light-cone sum rules approach. Merging these quantities, we present our results for differential decay width which can generally agree with the experimental data. More accurate measurements at the LHC and KEKB in future are helpful to validate our formalism and determine the inputs in this approach.