Testing $\chi$PT with the masses of the Nambu-Goldstone bosons

The spontaneous breakdown of an approximate symmetry implies that the spectrum of the theory contains approximately massless particles. The hidden symmetry very strongly constrains their masses. A numerical evaluation of these constraints on the lattice would allow a more precise determination of the quark mass ratios m_u:m_d:m_s and thereby reduce some of the uncertainties encountered in precision flavour physics.