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.

9 pages, 3 figures