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QCD with an infrared fixed point: The pion sector

Roman Zwicky*

  • Higgs Centre for Theoretical Physics, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom and Theoretical Physics Department, CERN, Esplanade des Particules 1, Geneva CH-1211, Switzerland

  • *roman.zwicky@ed.ac.uk
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Phys. Rev. D 109, 034009 – Published 8 February, 2024

DOI: https://doi.org/10.1103/PhysRevD.109.034009

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 quark mass anomalous dimension at the infrared fixed point is γ*=1. First, by matching the long-distance scalar adjoint correlation function. Second, by perturbing the fixed point by a small quark mass, the mq-dependence of the pion mass is reproduced by renormalization group arguments. Third, consistency of the trace anomaly and the Feynman-Hellmann theorem, for small mq, imply the same result once more. This suggests the following picture for the conformal window; close to its upper boundary γ* is zero and grows as the number of fermions is reduced until its lower boundary γ*=1 is reached, where chiral symmetry breaking sets in. Below, the strongly coupled gauge theory with γ*=1 is infrared dual to the free theory of pions. A possible dilaton sector of the scenario will be addressed in a companion paper.

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Phys. Rev. D 109, 034009– Published 8 February, 2024
  • Received 30 October 2023
  • Accepted 16 January 2024
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