Determination of Strong Coupling Constant from Inclusive Semileptonic Decays of Charmed Mesons

TL;DR

This paper determines the strong coupling constant at the charm quark mass scale using inclusive semileptonic decays of charmed mesons within the heavy quark expansion framework, providing a precise experimental value.

Contribution

It presents a novel determination of th(m_c^2) using experimental decay data and the heavy quark expansion, aligning well with theoretical predictions from the renormalization group.

Findings

th(m_c^2) = 0.445 b1 0.009 b1 0.114

Values from different D mesons are consistent

The measured th(m_c^2) agrees with the running from th(m_Z^2)

Abstract

Employing the heavy quark expansion model with the kinetic scheme, we evaluate $\alpha_S(m_c^2)$, the strong coupling constant at the charm quark mass $m_c$ with data on inclusive semileptonic decays of charmed mesons. Using the experimental values of semileptonic decay widths of the $D^0$ and the $D^+$, the value of $\alpha_{s}(m_c^{2})$ is determined to be $0.445\pm0.009\pm0.114$, where the first uncertainty is experimental and the second systematic. This reported $\alpha_{s}(m_c^{2})$ is in good agreement with the value of $\alpha_{s}(m_c^{2})$ calculated by running $\alpha_S(m_Z^2)$ at the $Z^0$ boson mass $m_Z$ with the renormalization group evolution equation. In addition, values of $\alpha_{s}(m_c^{2})$ obtained individually from each of the $D^0$, $D^+$, and $D_s^+$ mesons are found to be consistent being of the same origin.