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

Abstract

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 Δ(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 the 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.