Integrating out strange quarks in ChPT: terms at order p^6

TL;DR

This paper derives relations for certain low-energy constants in two-flavour chiral perturbation theory at order p^6, considering the influence of the strange quark mass, extending previous work at order p^4.

Contribution

It provides the first detailed two-loop order relations for p^6 couplings in the heavy strange quark limit within two-flavour ChPT.

Findings

Derived relations for 27 linear combinations of p^6 couplings.

Extended previous p^4 order results to p^6 order.

Focused on couplings relevant to vector and axial-vector currents.

Abstract

Chiral perturbation theory in the two-flavour sector allows one to analyse Green functions in QCD in a limit where the strange quark mass is considered to be large in comparison to the external momenta and to the light quark masses. In this framework, the pertinent low-energy constants depend on the value of the heavy quark masses. In a recent article, we have worked out, for the coupling constants which occur at order p^4, the dependence on the strange quark mass at two-loop accuracy. Here, we provide analogous relations for some of the couplings which are relevant at order p^6. To keep the calculations somewhat reasonable in size, we consider only those 28 couplings which enter the Green functions built from vector- and axial-vector quark currents in the chiral limit. This provides the matching for 27 linear combinations of the 28 couplings.