Capture rate and neutron helicity asymmetry for ordinary muon capture on hydrogen

Applying heavy-baryon chiral perturbation theory to ordinary muon capture (OMC) on a proton, we calculate the capture rate and neutron helicity asymmetry up to next-to-next-to-leading order. For the singlet hyperfine state, we obtain the capture rate Gamma (o)=695 s(-1) while, for the triplet hyperfine state, we obtain the capture rate Gamma (1)=11.9 s(-1) and the neutron asymmetry alpha (1)=0.93. If the existing formalism is used to relate these atomic capture rates to Gamma (liq) the OMC rate in liquid hydrogen, then Gamma (hq) corresponding to our improved values of Gamma (o) and Gamma (1) is found to be significantly larger than the experimental value, primarily due to the updated larger value of g(A). We argue that this apparent difficulty may be correlated to the specious anomaly recently reported for mu (-) +p-->n+ nu (mu)+ gamma, and we suggest a possibility to remove these two "problems" simply and simultaneously by reexamining the molecular physics input that underlies the conventional analysis of Gamma (liq).