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CP violation

Alexey A Petrov

Abstract

CP violation, which involves breaking the combined charge-conjugation (C) and parity (P) symmetries, is essential for understanding the observed matter-antimatter asymmetry in the universe. It is a key feature of the Standard Model, originating from complex phases in the Cabibbo-Kobayashi-Maskawa quark mixing matrix. Despite the successes of the SM, the amount of CP violation it predicts is not enough to explain baryogenesis, prompting searches for new sources of CP violation in other areas of particle physics. This article offers a pedagogical introduction to the theoretical foundations of C, P, and T symmetries and their combinations. It also emphasizes the importance of CP violation in modern particle physics and how it can be used to explore New Physics.

CP violation

Abstract

CP violation, which involves breaking the combined charge-conjugation (C) and parity (P) symmetries, is essential for understanding the observed matter-antimatter asymmetry in the universe. It is a key feature of the Standard Model, originating from complex phases in the Cabibbo-Kobayashi-Maskawa quark mixing matrix. Despite the successes of the SM, the amount of CP violation it predicts is not enough to explain baryogenesis, prompting searches for new sources of CP violation in other areas of particle physics. This article offers a pedagogical introduction to the theoretical foundations of C, P, and T symmetries and their combinations. It also emphasizes the importance of CP violation in modern particle physics and how it can be used to explore New Physics.

Paper Structure

This paper contains 14 sections, 3 theorems, 75 equations, 1 figure, 2 tables.

Table of Contents

  1. CP violation
  2. Introduction
  3. Classical limit: non-relativistic mechanics
  4. Classical limit: relativistic mechanics and electrodynamics
  5. C, P, and T in quantum mechanics: nonrelativistic case
  6. C, P, and T in relativistic quantum mechanics and quantum field theory
  7. Applications
  8. Kramer's degeneracy
  9. Furry's theorem
  10. CP-violation in the Standard Model
  11. Observing CP- and T-violation
  12. Experimental studies of CP-violation
  13. Experimental studies of T-violation
  14. Conclusions

Key Result

Theorem 1

In a time-reversal invariant fermionic system, all energy eigenstates are (at least) doubly degenerate.

Figures (1)

  • Figure 1: Parity transformation ${\mathbf r} \to -{\mathbf r}$ is equivalent to a reflection through a mirror followed by a rotation of $\pi$ radians around an axis defined by the mirror plane (artwork courtesy of Anna A. Petrov)

Theorems & Definitions (5)

  • Theorem 1: Kramer's degeneracy
  • Proof 1
  • Theorem 2: Furry's theorem
  • Proof 2
  • Corollary 1