The $\hat{I}{›}_b\to \hat{I}›$ transition form factors in perturbative QCD approach

Abstract

In this work, we investigate the $\hat{I}{›}_b\to \hat{I}›$ transition form factors in the perturbative QCD (PQCD) approach, incorporating higher-twist light-cone distribution amplitudes (LCDAs). The resulted form factors show that higher-twist LCDAs are dominant numerically. By combining our PQCD predictions at low-$q^2$ with lattice QCD results at high-$q^2$, $z$-series expansion fits are performed to parametrize the form factors over the full kinematic range. We also provide the prediction for physical observables in the rare decay $\hat{I}{›}_b\to \hat{I}›\hat{I}{¼}^{+}\hat{I}{¼}^{-}$, including the differential branching fraction, dilepton longitudinal polarization fraction, and forward-backward asymmetries (lepton-side, hadron-side, and combined lepton-hadron). Our obtained form factors are consistent with those in other theoretical methods within the uncertainties.