Muon Capture on Deuteron and 3He

We present the results of a recent simultaneous study of the muon capture reactions ²H(?? ^?, ?? _?? )nn and ³He(?? ^?, ?? _?? )³H. The initial and final A = 2 and 3 nuclear wave functions are obtained from the Argonne v ₁₈ or chiral N3LO two-nucleon potential, in combination with, respectively, the Urbana IX or chiral N2LO three-nucleon potential in the case of A?=?3. The weak current consists of polar- and axial-vector components. The former are related to the isovector piece of the electromagnetic current via the conserved-vector-current hypothesis. These and the axial currents are derived either in a meson-exchange or in a chiral effective field theory (??EFT) framework. In the first case, there is one parameter which is fixed by reproducing the Gamow-Teller matrix element in tritium ??-decay (GT^EXP). In the second case, the low-energy constants, two in the polar and one in the axial-vector current, are fixed, respectively, by reproducing the A?=?3 magnetic moments and GT^EXP. The total rates are found to be 392.0 ± 2.3 s^?1 for A?=?2, and 1484 ± 13 s^?1 for A?=?3, where the spread accounts for the model dependence relative to the adopted interactions and currents (and cutoff sensitivity in the ??EFT currents).