Integrating out strange quarks in ChPT: Terms at order p6

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 mu and md. In this framework, the low-energy constants of SU(2)R×SU(2)L depend on the value of the heavy quark masses. In a recent article, we have worked out, for the coupling constants li which occur at order p4 in the chiral expansion, the dependence on the strange quark mass at two-loop accuracy. Here, we provide analogous relations for some of the couplings ci which are relevant at order p6. 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 mu=md=0, ms≠0. This provides the matching for 27 linear combinations of the 28 couplings.