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GUT-motivated noninvertible symmetry as a solution to the strong CP problem and the neutrino CP-violating phase

Tatsuo Kobayashi1,*, Hajime Otsuka2,3,†, Morimitsu Tanimoto4,‡, and Tsutomu T. Yanagida5,6,§

  • *Contact author: kobayashi@particle.sci.hokudai.ac.jp
  • †Contact author: otsuka.hajime@phys.kyushu-u.ac.jp
  • ‡Contact author: morimitsutanimoto@yahoo.co.jp
  • §Contact author: tsutomu.tyanagida@sjtu.edu.cn
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Phys. Rev. D 113, 095034 – Published 26 May, 2026

DOI: https://doi.org/10.1103/f7bw-qlgs

Abstract

The unsuppressed CP violation in QCD is a problem in the standard model. If we have some mechanism to guarantee real determinants of the quark mass matrices, the vanishing physical vacuum angle θ¯ indicates the CP invariance at the fundamental level. Thus, the small θ¯ is technically natural, since we have an enhanced CP symmetry in the limit of the vanishing θ¯=0. In fact, it was proved that the vacuum angle is never renormalized up to the four-loop level once it is fixed at 0 value at some high energy scale. The purpose of this paper is to construct a model that guarantees the real determinants of the quark mass matrices assuming a noninvertible symmetry. In the present model, we have only one CP violating phase and hence all observable phases such as phases in the Cabibbo-Kobayashi-Maskawa matrix, in the neutrino oscillation and in the leptogenesis are related. It should be remarkable that the correct sign of the baryon-number asymmetry in the present Universe is obtained and a narrow region for the CP violating phase δCP≃192°–197° is predicted.

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Phys. Rev. D 113, 095034– Published 26 May, 2026
  • Received 4 March 2026
  • Accepted 6 May 2026
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