====== CP Symmetry ======

<tabbox Intuitive> 

  * [[https://www.symmetrymagazine.org/article/charge-parity-violation|Charge-parity violation]] by Symmetry Magazine
  * [[http://web.mit.edu/physics/news/physicsatmit/physicsatmit_06_sciollafeature.pdf|The Mystery of CP Violation]] by Gabriele Sciolla 

  
<tabbox 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:**


{{ :advanced_notions:cpvobservables.png?nolink |}}

----


  * An amazing discussion can be found [[https://paul.physicsnotes.org/doku.php?id=distillery:cpv|here]].
  * A nice introduction is [[https://arxiv.org/abs/hep-ph/0406326|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 [[https://arxiv.org/pdf/1608.05240.pdf|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.


<tabbox Abstract> 

  * An extensive discussion of how to consistently define a CP symmetry in gauge theories can be found in [[https://arxiv.org/abs/hep-ph/9506272|Automorphisms in Gauge Theories and the Definition of CP and P]] by W. Grimus and M. N. Rebelo
  * [[https://arxiv.org/abs/math-ph/0012006|The Pin Groups in Physics]] by Berg et. al. 

  
<tabbox 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.

</tabbox>