Next-to-Leading Order QCD Corrections to $\Lambda_b \to p $ Form Factors from Light-Cone Sum Rules

Abstract

In this study, we compute the radiative corrections to the $\Lambda_b \to p$ transition form factors at next-to-leading logarithmic accuracy, employing the framework of QCD light-cone sum rules with the light-cone distribution amplitudes of the $\Lambda_b$ baryon. The factorization formulae of the vacuum-to-$\Lambda_b$ correlation function, constructed from the interpolating current for the proton, are derived at leading power in $m_p / m_{\Lambda_b}$, using the method of regions. With our specific choice of interpolating current, only the twist-4 distribution amplitude of the $\Lambda_b$ baryon contributes to the form factors. Numerically, we find that the next-to-leading order QCD perturbative corrections reduce the tree-level form factors to approximately 65$\%$ of their original value, with the next-to-leading-order jet function providing the dominant contribution. In the large-energy limit ($E_p \to \infty$), the form factors exhibit a clear $1/E_p^3$ scaling, consistent with the expected power-counting behavior. By applying the $z$-series parameterization to perform a combined fit of the form factors from our results and available lattice QCD simulations, we further investigate the decay rate of $\Lambda_b \to p \ell^- \bar{\nu}_{\ell}$ and extract the CKM matrix element $|V_{ub}| = (3.33\pm 0.43 ) \times 10^{-3}$.