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The muon capture rate on hydrogen and the values of $g_A$ and $g_{πNN}$

Motivated by the recent developments in the determination of the experimental values of the nucleon axial-vector coupling constant $g_A$ and the pion-nucleon coupling constant $g_{πNN}$, we carry out a heavy-baryon chiral perturbation calculation of the hyperfine-singlet $μp$ capture rate $Γ_0$ to next-to-next-to-leading order (N$^2$LO), with the use of the latest values of $g_A$ and $g_{πNN}$. The calculated N$^2$LO value is $Γ_0^{\rm theor}(μ^- p \to ν_μn) =718 \pm 7 \,s^{-1}$, where the estimated N$^3$LO contribution dominates the error. This value is in excellent agreement with the experimental value reported by the MuCap Collaboration.