$\Lambda_b \rightarrow \Lambda_c^{\ast}$ at $1\,/\,m_c^2$ heavy quark order

TL;DR

This paper calculates the form factors for $to cst$ transitions within HQET including second-order $1/m_c^2$ corrections, incorporating various current contributions, and compares results with lattice QCD, advancing the theoretical understanding of these decays.

Contribution

It provides a comprehensive HQET-based calculation of $to cst$ form factors at order $1/m_c^2$, including tensor contributions, and compares with lattice QCD results.

Findings

Form factors agree well with lattice QCD results.

Inclusion of $1/m_c^2$ corrections improves theoretical predictions.

Comprehensive parametrization of matrix elements in HQET.

Abstract

We systematically compute the $\Lambda_b(p, s_b) \to \Lambda_c(2595)^+$ and $\Lambda_b(p, s_b) \to \Lambda_c(2625)^+$ form factors within the Heavy Quark Effective Theory (HQET) framework including $\mathcal{O}(1/m_c^2)$. Besides taking into account the Standard Model-like vector and axial contributions, we further determine tensor and pseudo-tensor form factors. Our work constitutes a step forward with respect to previous analyses allowing for a comprehensive study of the matrix element parametrisation stemming from the HQET formalism. Finally, we demonstrate that the resulting form factors agree well with lattice Quantum Chromodynamics (LQCD) determinations stressing the need and relevance of the newly derived $1/m_c^2$ corrections.