Chiral Effective Lagrangian in the large-Nc limit: the nonet case

Abstract

A U_L(3) \otimes U_R(3) low-energy effective lagrangian for the nonet of pseudogoldstone bosons that appear in the large-Nc limit of QCD is presented including terms up to four derivatives and explicit symmetry breaking terms up to quadratic in the quark masses. The one-loop renormalization of the couplings is worked out using the heat-kernel technique and dimensional renormalization. The calculation is carried through for U_L(n_l) \otimes U_R(n_l), thus allowing for a generic number n_l of light quark flavours. The crucial advantages that the expansion in powers of 1/N_c bring about are discussed. Special emphasis is put in pointing out what features are at variance with the SU_L \otimes SU_R results when the singlet η' is included in the theory.

41 pages, Latex

References in corpus (5)

• On the Foundations of Chiral Perturbation Theory
• Extension of the Chiral Perturbation Theory Meson Lagrangian to Order $P^6$
• Bounds on the light quark masses
• On the large-$N_c$ behavior of the $L_7$ coupling in $\chi$PT
• Constraints on Chiral Perturbation Theory Parameters from QCD Inequalities

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