QCD with an Infrared Fixed Point -- Pion Sector

TL;DR

This paper investigates how gauge theories near an infrared fixed point can reproduce pion physics, suggesting a specific anomalous dimension value and a duality with free pion theories at the conformal window's lower boundary.

Contribution

It demonstrates that chiral symmetry breaking and pion properties can be explained by an infrared fixed point with a quark mass anomalous dimension of 1, providing a new perspective on the conformal window.

Findings

Matching scalar correlation functions supports the fixed point hypothesis.

Pion mass dependence on quark mass aligns with renormalisation group predictions.

Trace anomaly and Feynman-Hellmann theorem consistency reinforce the results.

Abstract

The possibility that gauge theories with chiral symmetry breaking below the conformal window exhibit an infrared fixed point is explored. With this assumption three aspects of pion physics are reproduced if the the quark mass anomalous dimension at the infrared fixed point is $\gamma_* = 1$: First, by matching the long-distance scalar adjoint correlation function. Second, by perturbing the fixed point by a small quark mass, the $m_q$-dependence of the pion mass is reproduced by renormalisation group arguments. Third, consistency of the trace anomaly and the Feynman-Hellmann theorem, for small $m_q$, imply the same result once more. This suggests the following picture for the conformal window: close to its upper boundary $\gamma_*$ is zero and grows as the number of fermions is reduced until its lower boundary $\gamma_*=1$ is reached, where chiral symmetry breaking sets in. Below, the strongly coupled gauge theory with $\gamma_*=1$ is infrared dual to the free theory of pions. A possible dilaton sector of the scenario will be addressed in a companion paper.