The QCD effective action at long distances

We describe the derivation, under a well-defined set of approximations, of a low-energy effective chiral langrangian of the strong interactions from QCD. The effective lagrangian includes only the Nambu-Goldstone modes (i.e. the octet of pseudoscalar particles) in the presence of external sources, with inclusion of the explicit chiral symmetry breaking due to the light quark masses M. The coupling constants of the O(p4) terms of the chiral lagrangian are calculated first to leading order in the 1/Nc expansion but with O(α) terms and higher orders neglected. Next, the corrections O(α) to the couplings which remain in the chiral limit M→0 are also taken into account. In view of our results, an improved chiral power counting for higher-order terms in the effective chiral lagrangian is proposed. (orig.)