The $\Lambda_{b} \to \Lambda$ transition form factors in perturbative QCD approach

TL;DR

This paper calculates the $ ext{Lambda}_b o ext{Lambda}$ transition form factors using perturbative QCD, incorporating higher-twist effects, and combines these with lattice QCD to predict observables in rare baryon decays.

Contribution

It introduces a comprehensive PQCD calculation of the form factors including higher-twist LCDAs and combines them with lattice QCD data for full-range parametrization.

Findings

Higher-twist LCDAs are numerically dominant.

Form factors are consistent with other theoretical approaches.

Predictions for decay observables match experimental data within uncertainties.

Abstract

In this work, we investigate the $\Lambda_b \to \Lambda$ 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 $\Lambda_b \to \Lambda \mu^+ \mu^-$, 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.