Ordinary muon capture on a proton in manifestly Lorentz invariant baryon chiral perturbation theory

The amplitude for ordinary muon capture on the proton is evaluated, through the first four orders in the expansion parameter, in a manifestly Lorentz invariant form of baryon chiral perturbation theory. Expressions for the low energy constants in terms of physical quantities are obtained in each of the several renormalization schemes which have been proposed for forcing the relativistic approach to obey the same counting rules as obtained in heavy baryon chiral perturbation theory. The advantages and disadvantages of these schemes are discussed, using the muon capture results as an example, with the aim of gaining insight as to which scheme is preferable for practical calculations.