DOI 10.1007/s100520000499
Large Nc in chiral perturbation theory
Institute for Theoretical Physics, University of Bern,
Sidlerstrasse 5, 3012 Bern, Switzerland
Received: 14 July 2000 / Published online: 27 October 2000 - © Springer-Verlag 2000
Abstract
The construction of the effective
Lagrangian relevant for the mesonic sector of QCD in the large
Nc 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 Nc 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/Nc.
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)
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/Nc, but requires specific unnatural parity contributions
in the effective Lagrangian that restore renormalization group
invariance.
Copyright Società Italiana di Fisica, Springer-Verlag 2000
