How low-energy weak reactions can constrain three-nucleon forces and the neutron-neutron scattering length

We show that chiral symmetry and gauge invariance enforce relations between the short-distance physics that occurs in a number of electroweak and pionic reactions on light nuclei. Within chiral perturbation theory, this is manifested via the appearance of the same axial isovector two-body contact term in pi(-)d --> nngamma, p-wave pion production in NN collisions, tritium beta decay, pp fusion, nud scattering, and the hep reaction. Using a Gamow-Teller matrix element obtained from calculations of pp fusion as input, we compute the neutron spectrum obtained in pi(-)d --> nngamma. With the short-distance physics in this process controlled from pp --> de(=)nu(e), the theoretical uncertainty in the nn scattering length extracted from pi(-)d --> nngamma is reduced by a factor larger than 3, to approximately < or = 0.05 fm.