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 N N 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 shortdistance physics in this process controlled from pp → de + νe the theoretical uncertainty in the nn scattering length extracted from π − d → nnγ is reduced by a factor larger than three, to < ∼ 0.05 fm. In Quantum Chromodynamics (QCD) the up and down quark masses are much smaller than the typical scale of hadron masses, M QCD ∼ 1 GeV/c 2 , and so the QCD Lagrangian has an approximate SU (2) L × SU (2) R symmetry. This symmetry is spontaneously broken by the QCD vacuum, leaving only SU (2) isospin as a manifest symmetry of low-energy hadronic processes. The spontaneously-broken symmetry results in the existence of three (pseudo-)Nambu-Goldstone bosons, the pions, and means that the quantum-field-theoretic operator corresponding to the Noether currents of the broken generators changes pion number by one. External electroweak fields couple to these currents, and so the chiral SU (2) L × SU (2) R symmetry of QCD imposes relationships between the pion-baryon couplings and the axial couplings of baryons measured in electroweak processes. One of these is the Goldberger-Treiman relation:which expresses the πN N coupling constant g πN N in terms of the nucleon's axial coupling g A and the pion decay constant f π . (M is the nucleon mass.) The symmetries of QCD have other consequences for low-energy reactions involving pions. Introducing a photon field into the theory according to the dictates of U (1) em gauge invariance shows that the leading piece of the amplitude for the photoproduction of π + or π − at threshold is given by the Kroll-Ruderman (KR) term:In the single-nucleon sector the combination of U (1) em and QCD's spontaneously-broken SU (2) L × SU (2) R enforces relations like Eqs. (1) and (2). In this paper we explore the analog of these relations in the two-nucleon sector. We first exhibit a relationship between the shortdistance physics in N N → N N π reactions and electroweak processes such as pp fusion, tritium beta decay, and muon absorption on deuterium µ − d → nnν µ . We then show that the same two-nucleon physics occurs in some reactions involving photons, in particular in the process π − d → nnγ. The two-nucleon coupling in this reaction is then directly proportional to the twonucleon coupling of the axial current. Knowledge of one coupling therefore yields the other, so that precise information about π − d → nnγ (or its crossed partner γd → nnπ + ) constrains pp fusion. Conversely, calculations of tritium beta decay and pp fusion c...

The reaction π − d → nnγ is calculated in chiral perturbation theory so as to facilitate an extraction of the neutron-neutron scattering length (a nn ). We include all diagrams up to O(Q 3 ).This includes loop effects in the elementary π − p → γn amplitude and two-body diagrams, both of which were ignored in previous calculations. We find that the chiral expansion for the ratio of the quasi-free (QF) to final-state-interaction (FSI) peaks in the final-state neutron spectrum converges well. Our third-order calculation of the full spectrum is already accurate to better than 5%. Extracting a nn from the shape of the entire π − d → nnγ spectrum using our calculation in its present stage would thus be possible at the ±0.8 fm level. A fit to the FSI peak only would allow an extraction of a nn with a theoretical uncertainty of ±0.2 fm. The effects that contribute to these error bars are investigated. The uncertainty in the nn rescattering wave function dominates. This suggests that the quoted theoretical error of ±0.3 fm for the most recent π − d → nnγ measurement may be optimistic. The possibility of constraining the nn rescattering wave function used in our calculation more tightly-and thus reducing the error-is briefly discussed.

The charge-symmetry-breaking amplitudes for the recently observed dd → απ 0 reaction are investigated. Chiral perturbation theory is used to classify and identify the leading-order terms.Specific forms of the related one-and two-body tree level diagrams are derived. As a first step toward a full calculation, a few tree-level two-body diagrams are evaluated at each considered order, using a simplified set of d and α wave functions and a plane-wave approximation for the initial dd state. The leading-order pion-exchange term is shown to be suppressed in this model because of poor overlap of the initial and final states. The higher-order one-body and shortrange (heavy-meson-exchange) amplitudes provide better matching between the initial and final states and therefore contribute significantly and coherently to the cross section. The consequences this might have for a full calculation, with realistic wave functions and a more complete set of amplitudes, are discussed.

The experimental and theoretical issues and challenges for extracting the neutron-neutron scattering length are discussed. Particular emphasis is placed on recent results and their impact on the field. Comments are made regarding current experimental and theoretical possibilities.

A model for the dd → αππ reaction, based on two parallel NN → dπ reactions, is extended to incorporate a complete set of input amplitudes. While low-energy cross sections are underestimated, the rich structure observed in the α-particle momentum distributions for 0.8 < T d < 1.9 GeV (the ABC effect) is extraordinarily well reproduced. In addition, a recent measurement of deuteron analyzing powers agrees quite well with our predictions, both in frequency and magnitude of the oscillations.