Matching Chiral Perturbation Theory and the Dispersive Representation of the Scalar Kpi Form Factor

TL;DR

This paper matches two-loop chiral perturbation theory with a dispersive approach for the scalar Kpi form factor, enabling precise determination of low-energy constants and testing Standard Model predictions.

Contribution

It provides a novel method to connect chiral perturbation theory with dispersive representations, extracting key low-energy constants and non-standard couplings.

Findings

Determined two O(p^6) LECs from the matching.

Estimated the scalar form factor slope and Callan-Treiman deviation.

Constrained non-standard couplings beyond the Standard Model.

Abstract

We perform a matching of the two loop-chiral perturbation theory representation of the scalar Kpi form factor to a dispersive one. Knowing the value of F_K/F_pi and f_+(0) in the Standard Model (SM) allows to determine two O(p^6) LECs, the slope of the scalar form factor and the deviation of the Callan-Treiman theorem. Going beyond the SM and assuming the knowledge of the slope of the scalar form factor from experiment, the matching allows us to determine the ratio of F_K/F_pi, f_+(0), a certain combination of non-standard couplings, the deviation of the Callan-Treiman theorem and the two O(p^6) LECs.