Abstract
We analyze the radiative capture of the negative muon in hydrogen using amplitudes derived within the chiral Lagrangian approach. Besides the leading and next to leading order terms, given by the well-known Rood-Tolhoek Hamiltonian, we extract from these amplitudes the corrections of the next order in $1/M$ $(M$ is the nucleon mass). In addition, we estimate within the same formalism also the $\ensuremath{\Delta}(1232)$ isobar excitation effects and processes described by an anomalous Lagrangian. The model we consider allows us to put the \ensuremath{\Delta} isobar off-shell. Our calculations show sensitivity of capture rates and photon spectra to Z, one of the off-shell parameters, related to the $\ensuremath{\pi}N\ensuremath{\Delta}$ vertex. We have found that the model can provide the photon spectra, which are in the interval $60 \mathrm{MeV}<~k<~{k}_{\mathrm{max}}$ $(k$ is the photon momentum) close to the experimental one.
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