  The reaction pi- d -> n n gamma 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 pi- p -> gamma n 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 pi- d -> n n gamma 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 pi- d -> n n
gamma 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.
