The muon capture rate on hydrogen and the values of $g_A$ and $g_{\ddot{I}€NN}$

Abstract

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 $g_{\ddot{I}€NN}$, we carry out a heavy-baryon chiral perturbation calculation of the hyperfine-singlet $\hat{I}¼p$ capture rate $\hat{I}{“}_0$ to next-to-next-to-leading order (N${}^2$LO), with the use of the latest values of $g_A$ and $g_{\ddot{I}€NN}$. The calculated N${}^2$LO value is $\hat{I}{“}_0^{\mathrm{theor}}(\hat{I}{¼}^{-}p\to \hat{I}{½}_{\hat{I}}¼n)=718\pm 7s^{-1}$, 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.

7 pages, brief report. A few changes have been made to the original paper. To appear in Phys. Rev. C