Soft pion scattering in infrared-conformal gauge-fermion theories

TL;DR

This paper investigates how soft pion scattering behaves in gauge-fermion theories near an infrared conformal fixed point, revealing that the scattering length diverges as fermion mass approaches zero, contrasting with QCD predictions.

Contribution

It introduces a theoretical framework showing the divergence of pion scattering length in infrared-conformal theories and suggests lattice calculations as a probe for infrared scale invariance.

Findings

Pion scattering length diverges as fermion mass approaches zero.

Contrasts with QCD where scattering length vanishes.

Proposes lattice calculations to detect infrared conformality.

Abstract

We consider the problem of soft scattering for the analogue of pion states in gauge-fermion theories which approach a conformal fixed point in the infrared limit. Introducing a fermion mass into such a theory will explicitly break both scale invariance and chiral symmetry, leading to confinement and a spectrum of bound states. We argue that in such a theory, the pion scattering length diverges in the limit of zero fermion mass, in sharp contrast to QCD-like theories where the chiral Lagrangian predicts a vanishing scattering length. We demonstrate this effect both with a simple dimensional argument, and in a generalized linear sigma model which we argue can be used to describe the interactions of light scalar and pseudoscalar bound states in the soft limit of a mass-deformed infrared-conformal theory. As a result, lattice calculations of pion scattering lengths could be a sensitive probe for infrared scale invariance in gauge-fermion theories.