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 \pi\pi scattering amplitude have been determined using Roy dispersion relations. Combining this information with the Standard \chi PT expressions, we obtain the threshold parameters, low-energy phases and the O(p^4) constants
l
r
1
,
l
r
2
. The result
l
r
2
(
M
ρ
)=(1.6±0.4±0.9)×
10
−3
(
l
¯
2
=4.17±0.19±0.43
) reproduces the correct D-waves but it is incompatible with existing Standard \chi PT analyses of
K
l4
form factors beyond one loop.