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

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.