Chiral Effective Field Theory Predictions for Muon Capture on Deuteron and $^3$He

The muon-capture reactions 2H(μ-,νμ)nn and 3He(μ-,νμ)3H are studied with nuclear potentials and charge-changing weak currents, derived in chiral effective field theory. The low-energy constants (LECs) cD and cE, present in the three-nucleon potential and (cD) axial-vector current, are constrained to reproduce the A=3 binding energies and the triton Gamow-Teller matrix element. The muon-capture rates on deuteron and 3He are predicted to be 399±3  sec-1 and 1494±21  sec-1, respectively. The spread accounts for the cutoff sensitivity, as well as uncertainties in the LECs and electroweak radiative corrections. By comparing the calculated and precisely measured rates on 3He, a value for the induced pseudoscalar form factor is obtained in good agreement with the chiral perturbation theory prediction.