Bayesian Extraction of HQET Parameters from Inclusive Semi-Leptonic Decay of the $\Lambda_{c}^{+}$ Baryon

TL;DR

This paper introduces a Bayesian method to extract non-perturbative HQET parameters from inclusive semi-leptonic decays of the $\Lambda_c^+$ baryon, overcoming complex kinematic transformations and providing the first data-driven determination of these parameters.

Contribution

A novel Bayesian inference technique for reconstructing electron energy moments in $\Lambda_c^+$ decays and a first data-driven extraction of HQET parameters for the baryon.

Findings

Successful reconstruction of electron energy moments in the $\Lambda_c^+$ rest frame.

First data-driven determination of $\mu_{\pi}^2(\Lambda_c^+)$ and $ ho_D^3(\Lambda_c^+)$.

Development of a global fit method in the 1S mass scheme.

Abstract

We extract the non-perturbative Heavy Quark Effective Theory (HQET) parameters from the inclusive semi-leptonic decay $\Lambda_c^+ \to X e^+ \nu_e$. Unlike charmed mesons produced near threshold, $\Lambda_c^+$ baryons produced in $e^+e^-$ annihilation exhibit a complex momentum distribution, making the transformation of the electron energy spectrum from the laboratory frame to the $\Lambda_c^+$ rest frame non-trivial. To address this, we develop a novel Bayesian inference method to reconstruct the electron energy moments in the $\Lambda_c^+$ rest frame. By performing a global fit of theoretical predictions in the 1S mass scheme to these extracted moments, we determine the HQET parameters $\mu_{\pi}^2(\Lambda_c^+)$ and $\rho_D^3(\Lambda_c^+)$ for the first time using a purely data-driven approach.