New Consistency Conditions on Pion-Pion Amplitudes and Their Determination to Fourth Order in External Momenta

N. N. Khuri
1967 Physical Review  
We derive a set of new consistency conditions for the pion-pion scattering amplitude. These conditions hold for any s, t, u in the cube, 0 5 s, t, u 2 P2, with the four external mass variables off -mass -shell and restricted such that 4:. = 0, qt = s, 432 = t, and c$ = u. Using these consistency conditions, we determine the coefficients of the power series expansion of the pion-pion amplitude up to and including second order terms in the variables s, t, u, and c$ . We use this expansion to
more » ... s expansion to calculate the pion-pion S-wave scattering lengths and thus check the consistency of Weinberg's recent calculation of these numbers to one higher order. The final result is to within 10% the same as that obtained by Weinberg.
doi:10.1103/physrev.153.1477 fatcat:xkoyg257endlnh4tkyzjkrrq6a