Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2000-07-11
Eur.Phys.J.C17:623-649,2000
Physics
High Energy Physics
High Energy Physics - Phenomenology
56 pages
Scientific paper
10.1007/s100520000499
The construction of the effective Lagrangian relevant for the mesonic sector of QCD in the large N_c limit meets with a few rather subtle problems. We thoroughly examine these and show that, if the variables of the effective theory are chosen suitably, the known large N_c counting rules of QCD can unambiguously be translated into corresponding counting rules for the effective coupling constants. As an application, we demonstrate that the Kaplan-Manohar transformation is in conflict with these rules and is suppressed to all orders in 1/N_c. The anomalous dimension of the axial singlet current generates an additional complication: The corresponding external field undergoes nonmultiplicative renormalization. As a consequence, the Wess-Zumino-Witten term, which accounts for the U(3)_R x U(3)_L anomalies in the framework of the effective theory, contains pieces that depend on the running scale of QCD. The effect only shows up at nonleading order in 1/N_c, but requires specific unnatural parity contributions in the effective Lagrangian that restore renormalization group invariance.
Kaiser Robert
Leutwyler Heinrich
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