Muon capture by a proton in heavy baryon chiral perturbation theory

Abstract

The matrix element for muon capture by a proton is calculated to ${O(p}^3)$ within heavy baryon chiral perturbation theory using the new ${O(p}^3)$ Lagrangian of Ecker and Mojžiš. External nucleon fields are renormalized using the appropriate definition of the wave function renormalization factor $Z_N.$ Our expression for $Z_N$ differs somewhat from that found in the existing literature, but is the one which is consistent with the Lagrangian we use and the one which ensures, within our approach, the nonrenormalization of the vector coupling as required by the conserved vector current. Expressions for the standard muon capture form factors are derived and compared to experimental data and we determine three of the coefficients of the Ecker-Mojžiš Lagrangian, namely, $b_7,\hspace{0.5em}{b}_{19},$ and $b_{23}.$