Lower bounds to the I = 0, I = 2 ππ s-wave scattering lenghts

Abstract

Roy's exact partial wave equations allow us to find bounds for any linear combination of the isospin I = 0 and s-wave scattering lengths, with positive coefficients. The bound is a function of the quantity a D = a 2 (0) + a 2 (2), where a 2 ( I) are the D-wave sacttering lengths. Thus, we can draw on the ( a 0 (0), a 0 (2)) plane an allowed domain whose boundary is fairly close to the phenomenological region. For a value of a D = 1.7×10 −3, we find the following particular bounds: a 0 (0)⩾−0.49, a 0 (2)⩾−0.29.