Bayesian Extraction of HQET Parameters from Inclusive Semi-Leptonic Decay of the ${\mathrm{\Lambda }}_c^{+}$ Baryon

We extract the non-perturbative Heavy Quark Effective Theory (HQET) parameters from the inclusive semi-leptonic decay ${\mathrm{\Lambda }}_c^{+}\to X{e}^{+}{\nu }_e$. Unlike charmed mesons produced near threshold, ${\mathrm{\Lambda }}_c^{+}$ 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 ${\mathrm{\Lambda }}_c^{+}$ rest frame non-trivial. To address this, we develop a novel Bayesian inference method to reconstruct the electron energy moments in the ${\mathrm{\Lambda }}_c^{+}$ rest frame. By performing a global fit of theoretical predictions in the 1S mass scheme to these extracted moments, we determine the HQET parameters ${\mu }_{\pi }^2({\mathrm{\Lambda }}_c^{+})$ and ${\rho }_D^3({\mathrm{\Lambda }}_c^{+})$ for the first time using a purely data-driven approach.