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Different scenarios of dynamical chiral symmetry breaking in the interacting instanton liquid model via flavor symmetry breaking

Yamato Suda and Daisuke Jido

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Phys. Rev. D 112, 034011 – Published 14 August, 2025

DOI: https://doi.org/10.1103/ddyf-s65h

Abstract

We investigate a type of dynamical chiral symmetry breaking (DχSB) for various current quark masses using the interacting instanton liquid model. The type of DχSB is classified based on the sign of the second derivative of the free energy density with respect to the quark condensate at the origin. We perform numerical simulations of the interacting instanton liquid model with the flavor SU(2) symmetric and (2+1)-flavor quarks. We find that the curvature is negative in the SU(2) case. This means the ordinary type of DχSB. In contrast, in the (2+1)-flavor case, a positive curvature is observed when the strange quark mass is as small as those of the up and down quarks. This suggests that the anomaly-driven type of DχSB can occur under the approximate flavor SU(3) symmetry. As the strange quark mass increases, the curvature gradually decreases and becomes negative when the strange quark mass is approximately three times larger than those of the light quarks. This difference can be understood in terms of the ’t Hooft vertex which induces a six-quark interaction in the Nf=3 case and does a four-quark interaction in the Nf=2 case. Our results might indicate that the ratio between the strange and light quark masses plays a crucial role in understanding the microscopic relationship between DχSB and the anomaly effect.

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Phys. Rev. D 112, 034011– Published 14 August, 2025
  • Received 28 April 2025
  • Accepted 1 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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