and details. Likewise, we remain very cursory with respect to the anomalous intrinsic parity sector in Sec. \[sec:other\].

Lattice QCD has started to make progress in the determination of LECs, especially for those involving masses and decay constants. We rely heavily on the flavour lattice averaging group (FLAG) reports [@Colangelo:2010et; @Aoki:2013ldr]. Specific results are quoted and compared with our continuum results in Secs. \[sec:nf2lattice\] and \[sec:nf3lattice\]. Some comments can also be found in Sec. \[sec:largenc\].

A summary of the main results can be found in the conclusions.

CHIRAL PERTURBATION THEORY {#sec:chpt}
==========================

[ChPT]{} dates back to current algebra but its modern form was introduced by the papers of Weinberg, Gasser and Leutwyler [@Weinberg:1978kz; @Gasser:1983yg; @Gasser:1984gg]. The underlying idea is to use the global chiral symmetry present in the QCD Lagrangian for two ([$n_f=2$]{}) or three ([$n_f=3$]{}) light quarks when the quark masses are put to zero. This symmetry is spontaneously broken in QCD. The Nambu-Goldstone bosons resulting from this breaking are identified with the pions ([$n_f=2$]{}) or the lightest pseudoscalar octet, $\pi$, $K$ and $\eta$ ([$n_f=3$]{}). The singlet axial symmetry is broken explicitly for QCD at the quantum level due to the $U(1)_A$ anomaly and we thus disregard it. A 