Runing of Axial Coupling Constant

Abstract

We illustrate that both of massless pseudoscalar meson fields and constitutent quark fields are dynamical field degrees of freedom in energy region between chiral symmetry spontaneously broken scale and quark confinement scale. This physical configuration yields a renormalization running axial coupling constant $g_{_A}(\mu)$. The one-loop renormalization prediction $g_{_A}(\mu=m_{_N})=0.75$ and $g_{_A}(\mu=m_\pi)=0.96$ agree with $\beta$ decay of neutron and $\pi^0\to\gamma\gamma$ respectively. We also calculate $\rho^\pm\to\gamma\pi$ and $\omega\to\gamma\pi$ decays up to the next to leading order of $N_c^{-1}$ expansion and including all order effects of vector meson momentum expansion. The results strongly support prediction of renormalization running, $g_{_A}(\mu=m_\rho)=0.77$.