Pseudoscalar decay constants at large N_c

TL;DR

This paper calculates pseudoscalar decay constants at large N_c within an effective field theory that includes the eta' meson, revealing scale dependence due to the anomalous dimension of the singlet axial current.

Contribution

It extends the effective field theory framework to include eta' at large N_c and computes decay constants to one loop, highlighting scale dependence from anomalous dimensions.

Findings

Decay constants depend on the QCD running scale.

Effective couplings show scale dependence due to anomalous dimensions.

The approach combines expansions in momenta, quark masses, and 1/N_c.

Abstract

In the large N_c limit, the variables required to analyze the low energy structure of QCD in the framework of an effective field theory necessarily include the degrees of freedom of the eta'. We evaluate the decay constants of the pseudoscalar nonet to one loop within this extended framework and show that, as a consequence of the anomalous dimension of the singlet axial current, some of the effective coupling constants depend on the running scale of QCD. The calculation relies on a simultaneous expansion in powers of momenta, quark masses and 1/N_c. Talk given at the Workshop on Nonperturbative Methods in Quantum Field Theory, NITP/CSSM, University of Adelaide, Australia, Feb. 1998.