Linking infrared and ultraviolet parameters of pion-like states in strongly coupled gauge theories

TL;DR

This paper establishes numerical relations linking infrared and ultraviolet parameters of pion-like states in strongly coupled gauge theories, validated against lattice results, with implications for composite Higgs and dark matter models.

Contribution

It extends a relativistic constituent-quark model approach beyond QCD to general strongly-coupled theories, deriving relations between key parameters of pion-like states.

Findings

Good agreement with lattice results for SU(2) gauge theory with two fermion flavors.

Numerical relations between gauge coupling, decay constant, and charge radius established.

Potential applications to composite Higgs and dark matter models.

Abstract

It has been shown previously that in a relativistic constituent-quark model, predictions for the electromagnetic form factor of the pi meson match not only experimental data but also, in the limit of large momentum transfers, the asymptotics derived from Quantum Chromodynamics (QCD). This is remarkable since no parameters are introduced to provide for this infrared-ultraviolet link. Here, we follow this approach, going beyond QCD. We obtain numerical relations between the gauge coupling constant, the decay constant and the charge radius of the pion-like meson in general strongly-coupled theories. These relations are compared to published lattice results for SU(2) gauge theory with two fermion flavours, and a good agreement is demonstrated. Further applications of the approach, to be explored elsewhere, include composite Higgs and dark-matter models.