Quark Masses and Chiral Symmetry

The low energy properties of the standard model are governed by the Lagrangian of SU(3)_colourx U(1)_e.m.. If the masses of the three light quarks as well as the electromagnetic interaction are neglected, this Lagrangian is invariant under a group of chiral transformations. Since the ground state is not symmetric under this group, the spectrum contains massless Goldstone bosons which dominate the low energy structure of the theory. As the quark masses are turned on, the Goldstone bosons pick up mass, but the poles generated by them still dominate the behvior of the Green’s functions at small momenta. I show how to systematically determine the low energy structure of the theory by considering a simultaneous expansion in powers of the momenta and in powers of m_u, m_d, m_s. As applications of the method, I discuss some low energy predictions for form factors, for ππ-scattering and for η-decay and review the information on the quark mass ratios m_u: m_d: m_s which follows from the mass spectrum of the pseudoscalar mesons.