Chiral coupling constantsl¯1andl¯2

Abstract

A Roy equation analysis of the available ππ phase shift data is performed with the I = 0 S-wave scattering length a 0 0 in the range predicted by the one-loop standard chiral perturbation theory. A suitable dispersive framework is developed to extract the chiral coupling constantsl 1 ,l 2 and yieldsl 1 = −1.70±0.15 andl 2 ≈ 5.0. We remark on the implications of this determination to (combinations of) threshold parameter predictions of the three lowest partial waves.

Comparison of $\pi K$ scattering in SU(3) chiral perturbation theory and dispersion relations

“…The results for the l i , i = 1, 2, 4 of ref. [9] may then be translated into the SU(3) coupling constants which are listed in Table 2. Although the results of Table 1 and Table 2 are in general agreement, those in Table 1 amount to a consistent new determination.…”

“…As an illustration we use the dispersive polynomial established in ref. [9] to evaluate the SU (3) low energy constants with the three sets of phase shifts described there. These results are presented in Table 1 (masses, decay constants and renormalization scale as in sec.…”

“…In SU (2) chiral perturbation theory up to two-loop accuracy, the amplitude is described by three functions of a single (Mandelstam) variable, whose absorptive parts are given in terms of those of the three lowest partial waves [8]. One replaces them by an dispersive representation which yields an amplitude with an effective low energy polynomial and a dispersive tail [6,9]. A dispersion relation representation with two subtractions is an ideal starting point for rewriting them in a form whereby a comparison with the chiral representation can be made, when the S-and P -wave absorptive parts alone are retained.…”

form-factors and – scattering

“…12, this is a borderline assumption even for the present sensitivity. Neither was there dependence on s π found for the reduced form-factor 22) thus the latter is assumed to be constant. Furthermore f s (s π ) was parametrized as…”

“…This together with the discrepancy between the SU (2) CHPT constantsl 1 andl 2 obtained from the K ℓ4 fit [5] and Roy equation analysis at O(p 4 ) [22] and O(p 6 ) [23] motivated us to calculate the two-loop contribution to K ℓ4 . 4 Form-Factors at Next-to-Next-to-Leading Order…”