$\pi K$ sum rules and the SU(3) chiral expansion

Abstract

A recently proposed set of sum rules, based on the pion-Kaon scattering amplitudes and their crossing-symmetric conjugates are analysed in detail. A key role is played by the $l=0$ $\pi\pi\to K\overline K$ amplitude which requires an extrapolation to be performed. It is shown how this is tightly constrained from analyticity, chiral counting and the available experimental data, and its stability is tested. A re-evaluation of the $O(p^4)$ chiral couplings $L_1$, $L_2$, $L_3$ is obtained, as well as a new evaluation of the large $N_c$ suppressed coupling $L_4$.Comment: 28 pages, 7 figures [v1: small corrections and improvements

Chiral Perturbation Theory

“…Furthermore, the Roy-Steiner equations for pion-kaon scattering with constraints from CHPT have been developed and analyzed in Refs. [101,102]. It was found that most of the low-energy data are only in poor agreement with the solutions of the Roy-Steiner equations.…”

Remarks on analyticity and unitarity in the presence of a strongly interacting light Higgs

“…[32,33] for the computation of similar integrals in the context of the longitudinal WLWL scattering, and refs. [34][35][36][37][38][39][40][41][42][43][44][45][46] for related studies in QCD. with equal amplitudes obtained substituting π 0 with h, i.e.…”

Non-Perturbative Study of the Light Pseudoscalar Masses in Chiral Dynamics

“…In refs. [71,72] chiral sum rules are used to fix the latter counterterms to larger values. These determinations, however, suffer of the generally poor (if any) convergence of the three flavour CHPT series [8,7,35], with sizable O(p 6 ) contributions.…”

“…(2.30) L (4,6) and L (5,8) , η by the Gell-Mann-Okubo relation, eq.(2.33). L (7,8) is solved from the equation, [71,72], and the absence of the vertical errorbar in the diamond refers to the fact that L (5,8) cannot be determined then from these references. Right panel: Contour-plot for L (7,8) as a function of L (4,6) and L (5,8) .…”

“…The full circle corresponds to the values in the last column of the same table and the diamond the value of L (4,6) in the fourth column, refs. [71,72]. Notice that no values for L r 5 and L r 8 are provided in these references and hence no value for L (5,8) can be either determined.…”