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 π^-d→nnγ, p-wave pion production in NN collisions, tritium β decay, pp fusion, νd 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 π^-d→nnγ. With the short-distance physics in this process controlled from pp→de⁺ν_e, the theoretical uncertainty in the nn scattering length extracted from π^-d→nnγ is reduced by a factor larger than 3, to ≲0.05  fm.