Radiative Muon Capture and Induced Pseudoscalar Coupling Constant in Nuclear Matter

The recent TRIUMF experiment for $\mu^- p \to n \nu_{\mu} \gamma$ gave a surprising result that the induced pseudoscalar coupling constant $g_P$ was larger than the value obtained from $\mu^- p \to n \nu_{\mu}$ experiment as much as 44 %. Reexamining contribution of the axial vector current in electromagnetic interaction, we found an additional term to the matrix element which was used to extract the $g_P$ value from the measured photon energy spectrum. This additional term, which plays a key role to restore the reliability of $g_P (- 0.88 m_{\mu}^2) = 6.77 g_A (0)$, is shown to affect the $g_P$ quenching problems in nucleus.