Low-energy effective action for pions and a dilatonic meson

TL;DR

This paper develops a low-energy effective action for pions and a dilatonic scalar meson in QCD-like theories with near-conformal behavior, explaining the light scalar as a pseudo Nambu-Goldstone boson of approximate dilatation symmetry.

Contribution

It introduces a systematic effective field theory framework for pions and a dilatonic meson, justified by the Veneziano limit, capturing the dynamics near the conformal window.

Findings

The scalar meson can be as light as pions in near-conformal theories.

The effective action accounts for both chiral and dilatation symmetry breaking.

The approach provides a theoretical basis for lattice observations of light scalar mesons.

Abstract

Numerical simulations of QCD-like theories in which the number of flavors is adjusted so that the beta function is very small, but confinement and chiral symmetry breaking nevertheless take place, appear to reveal the presence of a flavor-singlet scalar meson which can be as light as the pions. Because the breaking of dilatation symmetry, quantified by the beta function, is small relative to QCD, a possible explanation is that the scalar meson is a pseudo Nambu-Goldstone boson associated with the approximate dilatation symmetry. We use this observation to systematically develop a low-energy effective action that accounts for both the pions and the "dilatonic" scalar meson. In order to justify the power counting that controls the couplings of the dilatonic meson we invoke the Veneziano limit, in which the number of fundamental-representation flavors $N_f$ grows in proportion with the number of colors $N_c$, while the ratio $N_f/N_c$ is kept close to, but below, the critical value where the conformal window is entered.