  We calculate ordinary and radiative muon capture on the proton in an
effective field theory of pions, nucleons and delta isobars, working to third
and second order in the small scale expansion respectively. Preceding
calculations in chiral effective field theories only employed pion and nucleon
degrees of freedom and were not able to reproduce the photon spectrum in the
pioneering experiment of radiative muon capture on the proton from TRIUMF. For
the past few years it has been speculated that the discrepancy between theory
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 hold true. We show
that contrary to expectations from naive dimensional analysis isobar effects on
the photon spectrum and the total rate in radiative muon capture are of the
order of a few percent, consistent with earlier findings in a more
phenomenological approach. We further demonstrate that both ordinary and
radiative muon capture constitute systems with a very well behaved chiral
expansion, both in standard chiral perturbation theory and in the small scale
expansion, and present some new ideas that might be at the 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 capture experiment on the
pseudoscalar form factor of the nucleon. We show that it is inconsistent with
the ordinary muon capture data.
