Chiral Extrapolation of the Strangeness Changing K pi Form Factor

TL;DR

This paper uses two-loop Chiral Perturbation Theory to extrapolate lattice data on the K pi scalar form factor, determining key values and slopes, and compares results with experimental data to assess convergence.

Contribution

It provides a detailed two-loop chiral extrapolation of the K pi scalar form factor and decay constant ratios, improving understanding of their behavior and experimental agreement.

Findings

Scalar form factor at zero momentum transfer determined

Good agreement with experimental values for form factors

Large slope observed in the form factor

Abstract

We perform a chiral extrapolation of lattice data on the scalar K pi form factor and the ratio of the kaon and pion decay constants within Chiral Perturbation Theory to two loops. We determine the value of the scalar form factor at zero momentum transfer, at the Callan-Treiman point and at its soft kaon analog as well as its slope. Results are in good agreement with their determination from experiment using the standard couplings of quarks to the W boson. The slope is however rather large. A study of the convergence of the chiral expansion is also performed.