The quark axial vector coupling and heavy meson decays

Form factors and decay widths for $D^{\ast }\to D\gamma$ and $D^{\ast }\to D\pi$ decays are estimated in a relativistic constituent quark model. Relativistic corrections due to light quarks are found to be substantial and to suppress the vector and axial vector form factors. The CLEO experimental value of $R^0_{\gamma}\equiv \Gamma (D^{\ast 0}\rightarrow D^{0} \gamma)/ \Gamma (D^{\ast 0}\rightarrow D^{0} \pi^{0})=0.572\pm 0.057\pm 0.081$isusedtodeterminethequarkaxialvectorcoupling$g_A$, which is found to be $0.6-0.8$ for $m_u=(350-200)MeV$ correspondingly, as compared with the chiral model result $g_A=0.8-0.9$. The heavy meson-pion strong coupling $g$ is found to be $0.4-0.6$, much smaller than $g=1$ which is expected in the large $N_C$ and nonrelativistic limit, but consistent with some heavy hadron chiral theory and QCD sum rule results. The failure of nonrelativistic treatment for the light quark in the heavy meson decays is also emphasized.