The role of the strange quark in chiral symmetry breaking
This document is focused on QCD at low energies (below 1 GeV), where the breakdown of chiral symmetry takes place, explaining the existence of an octet of light pseudoscalar mesons (pi, K and eta). The dynamics of these states is related to the actual pattern of chiral symmetry breaking. The particular mass hierarchy of the light quark masses allows one to consider (and compare) two different chiral limits of interest, with m_u=m_d=0 and m_s kept at its physical value (N_f=2 massless flavours) or m_u=m_d=m_s=0 (N_f=3 massless flavours). The related chiral order parameters are discussed in terms of the Euclidean Dirac operator, highlighting the role of the fermion determinant and the sea strange-quark pairs, and indicating that order parameters should decrease when one goes from N_f=2 to N_f=3 chiral limits. The consequences of this suppression for the effective theory of QCD at low energies, i.e., Chiral Perturbation Theory, are considered, in particular the conditions under which chiral expansions are saturated by their leading order. The next-to-leading order low-energy constants L_4 and L_6, suppressed by the Zweig rule in the scalar sector but enhanced by the large value of the strange quark, are shown to play an essential role. Several sources of information are then analysed: a sum rule related to the dependence of the N_f=2 chiral condensate on the strange-quark mass indicates a signficant variation from m_s=0 to its physical value, lattice simulations yielding the dependence of pseudoscalar observables on the quark masses show a suppresion of leading-order contributions compared to next-to-leading ones in three-flavour chiral series, the comparison of low-energy pi-pi and pi-K scattering data using dispersive methods exhibits significant differences between N_f=2 and N_f=3 chiral symmetry breakings . All these elements point towards the need for a careful assessment of the convergence of N_f=3 Chiral Perturbation Theory, for which a framework is proposed.