Comment on the Prediction of Two-loop Standard Chiral Perturbation Theory for Low-Energy ππScattering

Abstract

Four of the six parameters defining the two-loop ππscattering amplitude have been determined using Roy dispersion relations. Combining this information with the Standard χPT expressions, we obtain the threshold parameters, low-energy phases and the O(p^4) constants $l_1^r,l_2^r$. The result $l_2^r(M_{\ddot{I}})=(1.6\pm 0.4\pm 0.9)\times 10^{-3}({\bar{l}}_2=4.17\pm 0.19\pm 0.43$) reproduces the correct D-waves but it is incompatible with existing Standard χPT analyses of $K_{l4}$ form factors beyond one loop.

14 pages, Latex209, 2 figures