  The first measurement of the radiative muon capture (RMC) rate on a proton
was recently carried out at TRIUMF. The TRIUMF group analyzed the RMC rate in
terms of the theoretical formula of Beder and Fearing, and found the surprising
result that the pseudoscalar coupling g_P is 1.5 times the value expected from
PCAC. To assess the reliability of the theoretical framework used by the TRIUMF
group to relate the RMC rate to the pseudoscalar form factor, we calculate the
RMC rate in chiral perturbation theory, which provides a systematic framework
to describe all the vertices involved in RMC, fulfilling gauge-invariance and
chiral-symmetry requirements in a transparent manner. As a first step we
present a chiral perturbation calculation at tree level which includes
sub-leading order terms.
