Parity-violating asymmetry in the ${}^3\mathrm{He}$($\mathrm{n⃗},p$)${}^3\mathrm{H}$ reaction

The longitudinal asymmetry induced by parity-violating (PV) components in the nucleon-nucleon potential is studied in the charge-exchange reaction ${}^3\mathrm{He}$($\mathrm{n⃗},p$)${}^3\mathrm{H}$ at vanishing incident neutron energies. An expression for the PV observable is derived in terms of $T$-matrix elements for transitions from the ${}^{2S+1}{L}_J={}^1{S}_0$ and ${}^3{S}_1$ states in the incoming $n$-${}^3\mathrm{He}$ channel to states with $J=0$ and 1 in the outgoing $p$-${}^3\mathrm{H}$ channel. The $T$-matrix elements involving PV transitions are obtained in first-order perturbation theory in the hadronic weak-interaction potential, while those connecting states of the same parity are derived from solutions of the strong-interaction Hamiltonian with the hyperspherical-harmonics method. The coupled-channel nature of the scattering problem is fully accounted for. Results are obtained corresponding to realistic or chiral two- and three-nucleon strong-interaction potentials in combination with either the DDH or pionless EFT model for the weak-interaction potential. The asymmetries, predicted with PV pion and vector-meson coupling constants corresponding (essentially) to the DDH “best values” set, range from –9.44 to –2.48 in units of ${10}^{-8}$, depending on the input strong-interaction Hamiltonian. This large model dependence is a consequence of cancellations between long-range (pion) and short-range (vector-meson) contributions and is of course sensitive to the assumed values for the PV coupling constants.