Radiative Muon Capture on Hydrogen and the Induced Pseudoscalar Coupling

Abstract

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