The semi-leptonic form factors of $\Lambda_{b}\to\Lambda_{c}$ and $\Xi_{b}\to\Xi_{c}$ in QCD sum rules

TL;DR

This paper calculates the semi-leptonic form factors for $to$ transitions using QCD sum rules, considering contributions up to dimension-5, and compares results with lattice QCD, achieving consistent findings.

Contribution

First to provide full leading order form factors for $to$ transitions in QCD sum rules with comprehensive consideration of higher-dimensional contributions.

Findings

Form factors are consistent with lattice QCD within errors.

Uncertainties of about 20% are introduced due to Borel region issues.

Higher accuracy achieved in pole residue calculations.

Abstract

In this work, the full leading order results of the form factors for $\Xi_{b}\to\Xi_{c}$ and $\Lambda_{b}\to\Lambda_{c}$ are obtained in QCD sum rules. Contributions from up to dim-5 have been considered. For completeness, we also study the two-point correlation function to obtain the pole residues of $\Xi_{Q}$ and $\Lambda_{Q}$, and higher accuracy is achieved. For the three-point correlation function, since stable Borel regions can not be found, about $20\%$ uncertainties are introduced for the form factors of $\Xi_{b}\to\Xi_{c}$ and $\Lambda_{b}\to\Lambda_{c}$. Our results for the form factors are consistent with those of the Lattice QCD within errors.