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Extending the symmetries of the generalized CP-symmetric 2HDM scalar potential to the Yukawa sector

Sergio Carrolo1,*, Howard E. Haber2,†, Luis Lourenco3,‡, and João P. Silva4,§

  • 1Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, D-80805 München, Germany
  • 2Santa Cruz Institute for Particle Physics, University of California, 1156 High Street, Santa Cruz, California 95064, USA
  • 3Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Emil-Hilb-Weg 22, 97074 Würzburg, Germany
  • 4Departamento de Física and CFTP, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, 1, P-1049-001 Lisboa, Portugal

  • *Contact author: scarrolo@mpp.mpg.de
  • †Contact author: haber@scipp.ucsc.edu
  • ‡Contact author: luis.marques-lourenco@uni-wuerzburg.de
  • §Contact author: jpsilva@cftp.tecnico.ulisboa.pt
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Phys. Rev. D 112, 035024 – Published 15 August, 2025

DOI: https://doi.org/10.1103/pkmr-l9px

Abstract

There are only six independent types of symmetry-constrained (renormalizable) scalar potentials in the two Higgs doublet model (2HDM). For example, the scalar sector symmetry known as Z2⊗Π2, generated by the simultaneous application of two independent symmetries acting on the scalar fields, and the generalized CP symmetry known as GCP2 yield equivalent 2HDM scalar potentials. A similar situation arises for the scalar sector symmetries known as U(1)⊗Π2 and GCP3, respectively. In this paper, we show that this “degeneracy” remains when the definitions of the corresponding symmetries are extended to the Yukawa sector with three quark generations. The proof involves the exploration of all possible extensions of the corresponding symmetries to the Yukawa sector, consistent with the phenomenological constraints of nonzero quark masses and a nontrivial quark mixing matrix. Moreover, we find that this result is a peculiarity of a Yukawa sector with three quark generations. In particular, with two quark generations, we find that models based on the extension of Z2⊗Π2 to the Yukawa sector are inequivalent with those based on GCP2.

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Phys. Rev. D 112, 035024– Published 15 August, 2025
  • Received 3 April 2025
  • Accepted 17 July 2025
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