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 ${\pi }^{-}d\to nn\gamma$, $p$-wave pion production in $NN$ collisions, tritium $\beta$ decay, $pp$ fusion, $\nu d$ 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 ${\pi }^{-}d\to nn\gamma$. With the short-distance physics in this process controlled from $pp\to d{e}^{+}{\nu }_e$, the theoretical uncertainty in the $nn$ scattering length extracted from ${\pi }^{-}d\to nn\gamma$ is reduced by a factor larger than 3, to $\lesssim 0.05\mathrm{fm}$.

• Received 17 March 2006

DOI:https://doi.org/10.1103/PhysRevLett.96.232301