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arXiv · 2107.00658

Soft pion scattering in infrared-conformal gauge-fermion theories

Daniel C. Hackett·Ethan T. Neil
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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.

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Daniel C. Hackett, Ethan T. Neil. 2021-07-01. Soft pion scattering in infrared-conformal gauge-fermion theories. https://doi.org/10.1103/physrevd.106.016007

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