The pi pi S-wave scattering lengths

We match the known chiral perturbation theory representation of the pi pi s cattering amplitude to two loops with a phenomenological description that r elies on the Roy equations. On this basis, the corrections to Weinberg's lo w energy theorems for the S-wave scattering lengths are worked out to secon d order in the expansion in powers of the quark masses. The resulting predi ctions, a(0)(0) = 0.220 +/- 0.005, a(0)(2) = -0.0444 +/- 0.0010, contain re markably small uncertainties and thus allow a very sensitive experimental t est of the hypothesis that the quark condensate is the leading order parame ter of the spontaneously broken chiral symmetry. (C) 2000 Elsevier Science B,V. All rights reserved.