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

Tatsuo Kobayashi, Hajime Otsuka, Morimitsu Tanimoto, Tsutomu T. Yanagida

TL;DR

This work addresses the strong CP problem by enforcing real determinants of quark mass matrices through a non-invertible symmetry in a GUT-inspired SM, yielding $\bar{\theta}=0$ at high scale with CP invariance enhanced in that limit. CP violation in the quark sector arises from an induced phase $\phi$ in the $(2,2)$ entries of the Yukawa matrices after integrating out a heavy Higgs, while the determinants remain real, providing an axion-less solution. The model additionally incorporates a seesaw mechanism with a real diagonal $M_{N_R}$ and a complex scalar $\eta$ whose vev breaks CP spontaneously, leading to concrete predictions: $\delta_{CP} \approx 192^\circ$–$197^\circ$ and $m_{\beta\beta} \approx 9$–$11$ meV (NH), with $\sum m_i \approx 69$–$74$ meV, consistent with NuFIT. It also naturally links the CP phase responsible for leptogenesis to the low-energy CKM/PMNS phases, yielding the correct sign for the baryon asymmetry when the lightest RHN is $N_{R1}$, and making testable neutrino-sector predictions for upcoming experiments.

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 $\bar θ$ indicates the CP invariance at the fundamental level. Thus, the small ${\bar θ}$ is technically natural, since we have an enhanced CP symmetry in the limit of the vanishing $\bar θ=0$. 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 which guarantees the real determinants of the quark mass matrices assuming a non-invertible symmetry.

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

TL;DR

This work addresses the strong CP problem by enforcing real determinants of quark mass matrices through a non-invertible symmetry in a GUT-inspired SM, yielding at high scale with CP invariance enhanced in that limit. CP violation in the quark sector arises from an induced phase in the entries of the Yukawa matrices after integrating out a heavy Higgs, while the determinants remain real, providing an axion-less solution. The model additionally incorporates a seesaw mechanism with a real diagonal and a complex scalar whose vev breaks CP spontaneously, leading to concrete predictions: – and – meV (NH), with – meV, consistent with NuFIT. It also naturally links the CP phase responsible for leptogenesis to the low-energy CKM/PMNS phases, yielding the correct sign for the baryon asymmetry when the lightest RHN is , and making testable neutrino-sector predictions for upcoming experiments.

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 indicates the CP invariance at the fundamental level. Thus, the small is technically natural, since we have an enhanced CP symmetry in the limit of the vanishing . 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 which guarantees the real determinants of the quark mass matrices assuming a non-invertible symmetry.

Paper Structure

This paper contains 10 sections, 29 equations, 1 figure, 4 tables.

Table of Contents

  1. Introduction
  2. Non-invertible selection rules
  3. Model
  4. Phenomenology
  5. The CKM matrix
  6. The charged lepton mass matrix
  7. The CP violation in the neutrino oscillations
  8. Predictions of the CP phase and the neutrino-less double beta decay
  9. The universe's baryon asymmetry
  10. Conclusions

Figures (1)

  • Figure 1: The predicted $\delta_{\rm CP}$ versus $m_{\beta\beta}$ for NH. The region between the horizontal red (blue dashed) lines denotes $1\,(2)\sigma$ allowed one of $\delta_{\rm CP}$ in NuFIT 6.0 Esteban:2020cvm.