Ordinary and radiative muon capture on the proton and the pseudoscalar form factor of the nucleon

We calculate ordinary and radiative muon capture on the proton in an effect ive field theory of pions, nucleons and delta isobars, working to third and second order in the small scale expansion, respectively. Preceding calcula tions in chiral effective field theories only employed pion and nucleon deg rees of freedom and were not able to reproduce the photon spectrum in the p ioneering experiment of radiative muon capture on the proton from TRIUMF Fo r the past few years it has been speculated that the discrepancy between th eory and experiment might be due to Delta (1232) related effects, which are only included via higher-order contact interactions in the standard chiral approach. In this report we demonstrate that this speculation does not hol d true. We show that contrary to expectations from naive dimensional analys is, isobar effects on the photon spectrum and the total rate in radiative m uon capture are of the order of a few percent, consistent with earlier find ings in a more phenomenological approach. We further demonstrate that both ordinary and radiative muon capture constitute systems with a very well-beh aved chiral expansion, both in the standard chiral perturbation theory and in the small scale expansion, and present some new ideas that might be at t he bottom of the still unresolved discrepancy between theory and experiment in radiative muon capture. Finally, we comment upon the procedure employed by the TRIUMF group to extract new information from their radiative muon c apture experiment on the pseudoscalar form factor of the nucleon. We show t hat it is inconsistent with the ordinary muon capture data. (C) 2001 Elsevi er Science B.V. All rights reserved.