Radiative Muon Capture on Hydrogen and the Induced Pseudoscalar Coupling

The first measurement of the elementary process ${\mu }^{-}p\to {\nu }_{\mu }n\gamma$ is reported. A photon pair spectrometer was used to measure the partial branching ratio $(2.10\pm 0.22)\times {10}^{-8\mathrm{}}$ for photons of $k>\mathrm{}60\mathrm{}\mathrm{MeV}$. The value of the weak pseudoscalar coupling constant determined from the partial branching ratio is $g_p\left(q^2{=-0.88m}_{\mu }^2\right)=(9.8\pm 0.7\pm 0.3)g_a\left(0\right)$, where the first error is the quadrature sum of statistical and systematic uncertainties and the second error is due to the uncertainty in ${\lambda }_{\mathrm{op}}$, the decay rate of the ortho to para $p\mu p$ molecule. This value of $g_p$ is $\sim 1.5$ times the prediction of partial conservation of axial current and pion-pole dominance.