Eur. Phys. J. Plus (2014) 129: 148
https://doi.org/10.1140/epjp/i2014-14148-5

Regular Article

The unobservable axial-pion mixing in QCD and near-conformal dynamics

Helsinki Institute of Physics, University of Helsinki, P.O. Box 64, FI-000140, Helsinki, Finland

^* e-mail: roshan.foadi@gmail.com

Received: 17 March 2014
Revised: 3 June 2014
Accepted: 5 June 2014
Published online: 10 July 2014

Abstract

We study a chiral quark model of π, σ, ρ, and a ₁ mesons in the large-N _c limit. We show that the quadratic a ₁ − π mixing can be set to zero at zero momentum, thus protecting the g _σππ and g _ρππ couplings from being contaminated by the corresponding vertices with one or both pions replaced by the axial-vector meson. We further require the chiral-quark Lagrangian to feature an approximate classical scale invariance, the latter being only broken by dimension-two mass terms, and that the longitudinal vector meson scattering amplitudes grow at most like s, where √s is the center-of-mass energy. This allows us to accurately predict the correct value of g _σππ , g _ρππ , and the a ₁ decay constant . We further show that strongly coupled theories with near-conformal dynamics are expected to feature an approximate custodial chiral symmetry, with interesting phenomenological consequences.