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

TL;DR

This paper advances the precision of heavy-to-light baryonic form factors by computing next-to-leading-log QCD corrections to Λ_b → p transitions within a heavy-hadron light-cone sum-rule framework. Using a leading-power Λ_b current and the twist-4 Λ_b LCDA, the authors derive factorization formulas, perform a complete NLO analysis via the method of regions to obtain hard and jet functions, and resum large logarithms at NLL accuracy. The numerical analysis shows a substantial radiative suppression of the tree-level form factors (about a 35% reduction), with the jet function driving most of the correction, and confirms the expected 1/E_p^3 scaling in the large-recoil region. By fitting the LCSR results to lattice QCD data using a z-series parameterization, they extract |V_{ub}| = (3.33 ± 0.43) × 10^{-3} and provide phenomenological predictions for Λ_b → p semileptonic decays, including partial widths and angular observables, while acknowledging the remaining theoretical uncertainties from higher-twist effects and non-factorizable corrections.

Abstract

In this study, we compute the radiative corrections to the $Λ_b \to p$ 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 $Λ_b$ baryon. The factorization formulae of the vacuum-to-$Λ_b$ correlation function, constructed from the interpolating current for the proton, are derived at leading power in $m_p / m_{Λ_b}$, using the method of regions. With our specific choice of interpolating current, only the twist-4 distribution amplitude of the $Λ_b$ 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 $Λ_b \to p \ell^- \barν_{\ell}$ and extract the CKM matrix element $|V_{ub}| = (3.33\pm 0.43 ) \times 10^{-3}$.

Figures (7)

• Figure 1: Diagrammatical representation of the correlation function $\Pi_{\mu,a}(n\cdot p',\bar{n} \cdot p')$ at tree level, where the red internal line indicates the hard-collinear propagator of the up quark, $q$ represents the transfer momentum caused by the weak transition vertex, and $p'$ represents the proton caused by the local interpolating current operator.
• Figure 2: Diagrammatical representation of the correlation function $\Pi_{\mu,a}(n\cdot p',\bar{n} \cdot p')$ at one loop.
• Figure 3: The momentum-transfer dependence of the $\Lambda_b \to p$ form factors compute from LCSR with the fitted values of $\omega_0$ parameters presented in Eq. \ref{['omphi1']}and Eq. \ref{['omphi2']} for three different models of $\psi_4(\omega,\mu)$. Solid , dashed and dot dashed curves correspond to the sum rule predictions with the $\Lambda_b$-baryon LCDA $\psi^{\rm I}_4(\omega,\mu)$,$\psi^{\rm II}_4(\omega,\mu)$ and $\psi^{\rm III}_4(\omega,\mu)$
• Figure 4: Dependence of $f^T_{\Lambda_b \to p} (0)$ on the threshold parameter (left), on the Borel parameter(middle), and on the factorization scale (right). Solid , dashed and dot dashed curves correspond to the sum rule predictions with $M^2=1.5 \rm GeV^2$, $M^2=2 \rm GeV^2$, $M^2=2.5\rm GeV^2$ (left) and $s_0=1.42 \rm GeV^2$, $s_0=1.52 \rm GeV^2$, $s_0=1.62 \rm GeV^2$(middle). The label "LL" , "NLO" and "NLL" (right) represent the sum rule predictions at LL, NLO and NLL accuracy. All the other input parameters are fixed at their central values with the $\Lambda_b$-baryon LCDA $\phi^I_4 (\omega,\mu)$.
• Figure 5: Compared with the predictions at LL and NLL accuracy, the contribution to the sum rules of $f^T_{\Lambda_b \to p} (q^2)$ from the NLO hard and the NLO jet function (left panel) and the momentum transfer dependence of the ratio $[f^T_{\Lambda_b \to p} (q^2)]_{NLL} / [f^T_{\Lambda_b \to p} (q^2)]_{LL}$ with theory uncertainty from varying the renormalization and the factorization scales(right panel).