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Completely asymptotically free chiral theories with scalars

Giacomo Cacciapaglia1,2,*, Francesco Sannino2,3,4,5,†, and Sophie Wagner2,‡

  • *Contact author: cacciapa@lpthe.jussieu.fr
  • †Contact author: sannino@cp3.sdu.dk
  • ‡Contact author: sowag21@student.sdu.dk
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Phys. Rev. D 114, 075020 – Published 13 October, 2026

DOI: https://doi.org/10.1103/mbrx-d3fg

Abstract

We provide the conditions for complete asymptotic freedom for chiral gauge theories including scalars, as motivated by grand unified models. These are generalized Georgi-Glashow and Bars-Yankielowicz theories that feature a scalar field transforming either in the fundamental or in the adjoint of the gauge group. In both scenarios, we consider the addition of multiple chiral fermion families. We systematically analyse the interplay between gauge, Yukawa, and quartic couplings required for all interactions to remain asymptotically free at short distances. We find that, for both scalar representations, complete asymptotic free models can be obtained for a specific number of colors and multiplicity of vectorlike and chiral families.

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Phys. Rev. D 114, 075020– Published 13 October, 2026
  • Received 30 June 2026
  • Accepted 3 September 2026
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