Integrating out strange quarks in ChPT

TL;DR

This paper analyzes how integrating out strange quarks affects two-flavour chiral perturbation theory, providing relations for low-energy constants at two-loop order.

Contribution

It derives the strange quark mass dependence of two-flavour chiral LECs by reducing three-flavour ChPT in a specific limit, including two-loop order relations.

Findings

Relations for F, B, and l_i at two-loop order.

Strange quark mass dependence of two-flavour LECs.

Reduction of three-flavour to two-flavour ChPT in a specific limit.

Abstract

We study three flavour chiral perturbation theory in a limit where the strange quark mass is much larger than the external momenta and the up and down quark masses, and where the external fields are those of two-flavour chiral perturbation theory. In this case, the theory reduces to the one of SU(2)_L x SU(2)_R. Through this reduction, one can work out the strange quark mass dependence of the LECs in the two-flavour case. We present the pertinent relations at two-loop order for F,B and l_i.