Rm. Davidson, ONE-LOOP CORRECTIONS TO THRESHOLD GAMMA-P-]P-PI-0 PRODUCTION IN THE LINEAR SIGMA-MODEL, Physical review. C. Nuclear physics, 47(6), 1993, pp. 2492-2501
One-loop corrections to threshold neutral pion photoproduction from pr
otons are calculated in the linear sigma model. The total Born plus on
e-loop result is similar to that found using chiral perturbation theor
y (CHPT), and expansion of the threshold amplitude in M(pi)/M reproduc
es the CHPT result to order (M(pi)/M)2. It is also shown that expansio
n of the amplitude in the external kinematical variables reproduces th
e ''old'' low-energy theorem. An in-depth study is made, in this model
, of the validity and accuracy of expanding the amplitude in the exter
nal kinematical variables.