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

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 $0.445\pm 0.009\pm 0.114$, 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.