Some Recent Developments in Chiral Perturbation Theory∗

The first part of this talk concerns the application of chiral perturbation theory (CHPT) at unphysical quark masses. More precisely, lattice QCD (LQCD) allows one in principle to calculate hadronic matrix elements ab initio using capability computing on a discretized space-time. To connect to the real world, various extrapolations are necessary: LQCD operates at a finite volume V , at a finite lattice spacing a and at large (unphysical) quark massesmq. All these effects can be treated in suitably tailored effective field theories (EFTs) (for a recent review, see). Here, I consider the quark mass expansion of certain baryon observables. Various nucleon (baryon) observables have already been computed on the lattice, like e.g. masses of ground and excited states, magnetic moments, nucleon electromagnetic radii, the nucleon axial-vector coupling, and so on. CHPT in principle provides extrapolation functions for all these observables, parameterized in terms of a number of low-energy constants (LECs). These LECs relate many observables, they are not dependent on the process one considers. Given the present situation with only a few lattice results at reasonably small quark masses available, it is mandatory to incorporate as much phenomenological