Analysis of the semileptonic decays $Λ_b\toΛ_cl\barν_l$ and $Ξ_b\toΞ_cl\barν_l$ in QCD sum rules

TL;DR

This paper computes the electroweak transition form factors for the semileptonic decays $\Lambda_b\to\Lambda_c$ and $\Xi_b\to\Xi_c$ using three-point QCD sum rules, including all couplings of the interpolating currents to both ground and excited baryons and truncating the OPE at dimension $8$. The resulting form factors, obtained from double Borel transforms and quark-hadron duality, enable predictions of decay widths and branching ratios for $l=e,\mu,\tau$, as well as lepton-universality ratios $R_{\Lambda_c}$ and $R_{\Xi_c}$ and helicity observables $A_{FB}$ and $\alpha$. The authors find branching ratios for $\Lambda_b\to\Lambda_c l\bar\nu_l$ in agreement with experimental data and other approaches, and provide $\Xi_b\to\Xi_c l\bar\nu_l$ predictions that can guide future measurements. Their analysis highlights the importance of including higher-dimension condensates and all parity-coupled interpolating-current contributions to achieve reliable form factors and decay predictions in heavy-baryon systems.

Abstract

In this article, the electroweak transition form factors of $Λ_b\toΛ_c$ and $Ξ_b\toΞ_c$ are analyzed within the framework of three-point QCD sum rules. In phenomenological side, all possible couplings of interpolating current to hadronic states are considered. In QCD side, the perturbative part and the contributions of vacuum condensates up to dimension 8 are also included. With the estimated form factors, we study the decay widths and branching ratios of semileptonic decays $Λ_b\toΛ_cl\barν_l$ and $Ξ_b\toΞ_cl\barν_l$ ($l=e,μ$ and $τ$). Our results for the branching ratios of $Λ_b\toΛ_cl\barν_l$ are comparable with experimental data and the results from other collaborations. In addition, our prediction for the branching ratio of $Ξ_b\toΞ_cl\barν_l$ can provide a valuable reference for future experimental measurements.

Figures (8)

• Figure 1: The Feynman diagram of semi-leptonic decay processes $\Lambda_b[\Xi_b]\to \Lambda_c[\Xi_b]l\bar{\nu}_{l}$.
• Figure 2: The Feynman diagrams for the perturbative part and vacuum condensate terms, where the blue, red and black solid lines denote the $b$, $c$ and $u$ quark lines, respectively. The green solid lines denote the $d$ and $s$ quark lines for $\Lambda_b\to\Lambda_c$ and $\Xi_b\to\Xi_c$ transition, respectively. The black loop lines are the gluon lines.
• Figure 3: The pole contributions (a, c) and the contributions of perturbative term and different vacuum condensates (b, d) of form factors $F_3$ and $G_3$ for $\Lambda_b\to\Lambda_c$ transition. The grey bounds are Borel platform.
• Figure 4: The pole contributions (a, c) and the contributions of perturbative term and different vacuum condensates (b, d) of form factors $F_3$ and $G_3$ for $\Xi_b\to\Xi_c$ transition. The grey bounds are Borel platform.
• Figure 5: The fitting results of vector (a-c) and axial vector (d-f) form factors for $\Lambda_b\to\Lambda_c$ transition.