Chiral Effective Field Theory Predictions for Muon Capture on Deuteron and ${}^3\mathrm{He}$

The muon-capture reactions ${}^2\mathrm{H}({\mu }^{-},{\nu }_{\mu })nn$ and ${}^3\mathrm{He}({\mu }^{-},{\nu }_{\mu }){}^3\mathrm{H}$ are studied with nuclear potentials and charge-changing weak currents, derived in chiral effective field theory. The low-energy constants (LECs) $c_D$ and $c_E$, present in the three-nucleon potential and ($c_D$) 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 ${}^3\mathrm{He}$ are predicted to be $399\pm 3{\sec }^{-1}$ and $1494\pm 21{\sec }^{-1}$, 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 ${}^3\mathrm{He}$, a value for the induced pseudoscalar form factor is obtained in good agreement with the chiral perturbation theory prediction.

Figure 1

$c_D$-$c_E$ trajectories fitted to reproduce the experimental ${}^3\mathrm{H}$ and ${}^3\mathrm{He}$ BEs. See text for explanation.

Figure 2

The ratio ${\mathrm{GT}}^{\mathrm{TH}}/{\mathrm{GT}}^{\mathrm{EXP}}$ as a function of the LEC $c_D$.