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  • Open Access

Nonperturbative origin of the electroweak scale: RGE in strongly-coupled dark gauge theories via the Dyson-Schwinger approach

Marco Frasca1,*, Anish Ghoshal2,†, and Nobuchika Okada3,‡

  • 1Rome, Italy
  • 2Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093 Warsaw, Poland
  • 3Department of Physics and Astronomy, University of Alabama, Tuscaloosa, Alabama 35487, USA

  • *Contact author: marcofrasca@mclink.it
  • †Contact author: anish.ghoshal@fuw.edu.pl
  • ‡Contact author: okadan@ua.edu
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Phys. Rev. D 111, 115016 – Published 16 June, 2025

DOI: https://doi.org/10.1103/czm7-1ccc

Abstract

We propose a novel pathway to generate the electroweak scale (EW) via nonperturbative dynamics of a dark gauge sector based on the SU(N) gauge group. Imposing the scale invariance of the theory, we investigate the electroweak symmetry breaking (EWSB) which is triggered dynamically via the condensation of gauge fields. Instead of the usual dimension-4 triggered breaking, a dimension 6 term (with Wilson coefficient compatible with Standard Model Effective Field Theory (SMEFT) bounds) coupling the Higgs boson and the Yang-Mills field quadratic term in the Lagrangian provides feedback from the gauge to the Higgs sector. We provide a novel method to estimate a nonperturbative EW scale generation using the exact solution of a truncated set of the background equations of motion in Yang-Mills theory in terms of Jacobi elliptic functions and the exact beta-function valid in the strongly coupled regimes via the Dyson-Schwinger approach. Particularly, we find an analytical result for the renormalization group equation (RGE) of the gauge coupling in the SU(N) sector in the strongly coupled regime. The dynamics studied in this paper pave the way to a more realistic model building with possible resolution to the hierarchy problem and, in general, dynamical generation of scales.

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Phys. Rev. D 111, 115016– Published 16 June, 2025
  • Received 12 August 2024
  • Accepted 21 May 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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