Radiative muon capture by a proton in chiral perturbation theory

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, ΓRMCexp, in terms of the theoretical formula of Beder and Fearing, and found the surprising result that gP≡fP(q2=−0.88mμ2) is 1.5 times the value expected from PCAC. To assess the reliability of the theoretical framework used by the TRIUMF group to relate ΓRMC to the pseudoscalar form factor fP, we calculate ΓRMC 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.