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We show that chiral symmetry and gauge invariance enforce relations betweenthe short-distance physics that occurs in a number of electroweak and pionicreactions on light nuclei. Within chiral perturbation theory this is manifestedvia the appearance of the same axial isovector two-body contact term in pi- d-> n n gamma, p-wave pion production in NN collisions, tritium beta decay, ppfusion, nu d scattering, and the hep reaction. Using a Gamow-Teller matrixelement obtained from calculations of pp fusion as input we compute the neutronspectrum obtained in pi- d -> n n gamma. With the short-distance physics inthis process controlled from p p -> d e+ nu_e the theoretical uncertainty inthe nn scattering length extracted from pi- d -> n n gamma is reduced by afactor larger than three, to <~0.05 fm.Comment: REVTeX4, 4 pages (5 pages since the arXiv doesn't collapse refs), 3  eps figures; revised version to appear in PRL, conclusions unchange

How Low-Energy Weak Reactions Can Constrain Three-Nucleon Forces and the Neutron-Neutron Scattering Length