Relations between SU(2)- and SU(3)-LECs in chiral perturbation theory

TL;DR

This paper explores how low-energy constants in two-flavour chiral perturbation theory depend on the strange quark mass, providing two-loop accuracy relations and implications for effective field theories.

Contribution

It derives detailed relations between SU(2) and SU(3) low-energy constants, including at two-loop order, enhancing understanding of quark mass dependence in chiral perturbation theory.

Findings

Derived two-loop relations for low-energy constants.

Established dependence of SU(2) constants on strange quark mass.

Discussed implications for effective field theory calculations.

Abstract

Chiral perturbation theory in the two--flavour sector allows one to analyse Green functions in QCD in the limit where the strange quark mass is considered to be large in comparison to the external momenta and to the light quark masses m_u and m_d. In this framework, the low--energy constants of SU{2}_R \times SU{2}_L depend on the value of the heavy quark masses. For the coupling constants which occur at order p^2 and p^4 in the chiral expansion, we worked out the dependence on the strange quark mass at two--loop accuracy, and provided analogous relations for some of the couplings c_i which are relevant at order p^6. This talk comments on the methods used, and illustrates implications of the results obtained.