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 Γ₀=695 s^-1 while, for the triplet hyperfine state, we obtain the capture rate Γ₁=11.9 s^-1 and the neutron asymmetry α₁=0.93. If the existing formalism is used to relate these atomic capture rates to Γliq, the OMC rate in liquid hydrogen, then Γliq corresponding to our improved values of Γ₀ and Γ₁ is found to be significantly larger than the experimental value, primarily due to the updated larger value of gA. We argue that this apparent difficulty may be correlated to the specious anomaly recently reported for μ^-+→pn+ν_μ+γ, 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 Γliq.