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Dynamical CP Violation from Non-Invertible Selection Rules

Hiroshi Okada, Hajime Otsuka

Abstract

We propose a novel mechanism in which leptonic CP-violating phases are generated dynamically through the radiative breaking of non-invertible selection rules. In this framework, tree-level mass matrices, initially constrained by a CP-like symmetry within a non-invertible structure, acquire flavor-dependent phases once loop corrections are incorporated. Furthermore, these corrections can also generate mass terms, thereby addressing the mass hierarchy problem. As an illustrative example, we employ the Inverse Seesaw (ISS) model to demonstrate how the Majorana mass of the light sterile neutrino $N_L$ arises via this mechanism while simultaneously realizing CP violation. Although our analysis is carried out within the ISS framework, the mechanism has broader implications, potentially offering new perspectives on CP-related problems such as the strong CP problem, leptogenesis, and baryogenesis. This work thus establishes a foundation for exploring the dynamical breaking of non-invertible selection rules as a novel origin of CP violation in particle physics.

Dynamical CP Violation from Non-Invertible Selection Rules

Abstract

We propose a novel mechanism in which leptonic CP-violating phases are generated dynamically through the radiative breaking of non-invertible selection rules. In this framework, tree-level mass matrices, initially constrained by a CP-like symmetry within a non-invertible structure, acquire flavor-dependent phases once loop corrections are incorporated. Furthermore, these corrections can also generate mass terms, thereby addressing the mass hierarchy problem. As an illustrative example, we employ the Inverse Seesaw (ISS) model to demonstrate how the Majorana mass of the light sterile neutrino arises via this mechanism while simultaneously realizing CP violation. Although our analysis is carried out within the ISS framework, the mechanism has broader implications, potentially offering new perspectives on CP-related problems such as the strong CP problem, leptogenesis, and baryogenesis. This work thus establishes a foundation for exploring the dynamical breaking of non-invertible selection rules as a novel origin of CP violation in particle physics.

Paper Structure

This paper contains 4 sections, 28 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. $Z_3$ Tambara-Yamagami fusion rule and generalized CP
  3. Model setup
  4. Summary and discussion

Figures (1)

  • Figure 1: Majorana mass matrices $m_L$ and $m_R$ at one-loop level. Here, $Z_3$ TY charges are given in parenthesis. One clearly finds that this one-loop dynamically violates $Z_3$ TY selection rule since $a\otimes a\neq {\mathbbm{1}}$ although each of vertex is invariant under $Z_3$ TY.