Heavy quark symmetry of $\Lambda_b^0$ decays in quark models

TL;DR

This paper investigates heavy quark symmetry in $ ext{Lambda}_b^0$ decays using two quark models, calculating decay parameters, branching fractions, and comparing with experimental and lattice QCD results, highlighting the effects of gluon corrections.

Contribution

It provides a detailed analysis of $ ext{Lambda}_b^0$ decays within the homogeneous bag model and light-front quark model, including first-order corrections and the impact of gluon effects, with predictions consistent with data.

Findings

Branching fractions agree with experimental and lattice QCD results.

Hard gluon corrections reduce branching fractions by about 10%.

Models provide predictive decay parameters constrained by heavy quark symmetry.

Abstract

We study the heavy quark symmetry with the homogeneous bag model (HBM) and light-front quark model (LFQM) based on the decays of $\Lambda_b^0\to\Lambda_c^+\ell^-\overline{\nu}_\ell~(\ell=e,\mu,\tau)$. In particular, we calculate various parameters in the heavy quark expansions, including the Isgur-Wise functions and their first order corrections. The parameters in the HBM are fitted from the mass spectra, while the ones in the LFQM are tightly constrained by the heavy quark symmetry, granting the predictive power of our results. We explicitly obtain that ${\cal B}(\Lambda_b^0\to\Lambda_c^+e^-\overline{\nu}_e)=(5.69\pm 0.58, 5.35\pm 0.50)$, ${\cal B}(\Lambda_b^0\to\Lambda_c^+\mu^-\overline{\nu}_\mu)=(5.67\pm 0.58 $, $5.33\pm 0.49)$, and $\Gamma(\Lambda_b^0\to\Lambda_c^+\tau^-\overline{\nu}_\tau)/\Gamma(\Lambda_b^0\to\Lambda_c^+\mu^-\overline{\nu}_\mu)=(0.3243\pm 0.0126$, $ 0.3506\pm 0.0046)$ for the numerical values of (HBM, LFQM). Our results of the branching fractions in both models agree well with the experimental data and lattice QCD calculations. In addition, we find that the hard gluon corrections decrease the branching fractions around $10\%$.