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

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 $$f_{a_1 }$$ . We further show that strongly coupled theories with near-conformal dynamics are expected to feature an approximate custodial chiral symmetry, with interesting phenomenological consequences.