Two-point function of strangeness-carrying vector-currents in two-loop Chiral Perturbation Theory

TL;DR

This paper calculates the two-point function of strangeness-carrying vector currents in two-loop Chiral Perturbation Theory, providing a finite, scale-independent expression useful for phenomenological applications.

Contribution

It presents the first finite, scale-independent $O(p^6)$ calculation of the correlator in $SU(3)$ Chiral Perturbation Theory, and determines the counterterm combination $Q_V$ using IMFESR.

Findings

The correlator is finite and scale-independent at $O(p^6)$.

The counterterm $Q_V$ is determined phenomenologically.

The results improve understanding of strangeness vector currents.

Abstract

We present our calculation of the correlator $<T\{V_sV_s^\dag\} >$ between two external vector-currents with the quantum-numbers of a charged kaon. The renormalized expression to $O(p^6)$ in $SU(3) \times SU(3)$ standard chiral perturbation theory is finite and scale-independent. The result is used to determine, via an IMFESR, the phenomenologically relevant finite $O(p^6)$-counterterm combination $Q_V$ in a way which is not sensitive to isospin breaking.