CP Symmetry

Intuitive

• Charge-parity violation by Symmetry Magazine
• The Mystery of CP Violation by Gabriele Sciolla

Concrete

Kaon Flavor Eigenstates:

\begin{equation*} |K^0\rangle = |\bar{s}d \rangle \qquad |\overline{K}^0\rangle = |s \bar{d} \rangle \end{equation*} $$CP\!: \; |K^0\rangle \longleftrightarrow |\overline{K}^0 \rangle$$

Kaon CP Eigenstates:

\begin{equation*} |K_{CP \pm}\rangle = \frac{1}{\sqrt{2}} \left( |K^0\rangle \pm |\overline{K}^0 \rangle \right) \end{equation*}

Kaon Propagating Mass Eigenstates:

$$|K_L \rangle \sim |K_{CP-}\rangle + \epsilon_K |K_{CP+}\rangle$$

Observables:

• An amazing discussion can be found here.
• A nice introduction is The Theory of CP-Violation -- in as Much of a Nutshell as Will Fit on 8 Pages by Patricia Ball
• For a nice PhD thesis on the topic, see CP and other Symmetries of Symmetries by Andreas Trautner
• Great textbooks on CP violation is "CP Violation" by Branco, Lavoura, and Silva and "Discrete Symmetries and CP Violation: From Experiment to Theory" by Marco Sozzi
• Other famous books on CP violation are "CP Violation" by Jarlskog, and "CP Violation" by Bigi and Sanda

CP Violation in the Neutrino Sector

• The CP phase in the neutrino sector has not been measured yet. The newest current results can be found in https://arxiv.org/abs/1805.05917.

Abstract

• An extensive discussion of how to consistently define a CP symmetry in gauge theories can be found in Automorphisms in Gauge Theories and the Definition of CP and P by W. Grimus and M. N. Rebelo
• The Pin Groups in Physics by Berg et. al.

Why is it interesting?

A CP transformation transforms a particle into the corresponding antiparticle. A intact CP symmetry therefore means that particles and antiparticles are indistinguishable. However, we know from experiments that CP is a broken symmetry since, for example, there are more particles than antiparticles in the visible universe.