CP violation is an effect in particle physics that has, of late, been of considerable interest. A CP-violating process is one which is not symmetric under the combined operations of charge conjugation (C) and parity reversal (P), collectively referred to as CP. The operation of charge conjugation replaces every particle with its respective antiparticle, and the operation of parity reversal reflects the system such that left and right are interchanged. CP violation is one of the cornerstones of the theory of baryogenesis, which describes how the universe came to be made of matter and not equal amounts of matter and antimatter. CP-violating interactions discriminate between matter and antimatter, a distinction that is rare in particle physics.

### The Discovery of CP Violation

Initially, it was believed that parity reversal was an exact symmetry of nature, i.e., that a mirror-image universe would evolve in exactly the same manner as this universe, only reflected across some plane. All theories of gravity and electromagnetism are exactly symmetric under parity reversal. However, it was discovered in the late 1950s, by C.S. Wu, that the weak nuclear force is not only asymmetrical under parity reversal but that the parity violation is *maximal*, meaning that some weak interactions have a particular preferred orientation and that corresponding interactions in the opposite orientation are not observed. These interactions, involving neutrinos, were then found to once again be symmetric if the parity reversal were followed by a charge conjugation. So, CP was postulated as being an exact symmetry of nature.

Alas, it was not to be. A few years later, it was discovered by Cronin and Fitch that CP was also violated, this time in the decay process of the neutral kaon. This came as a shock to the entire particle physics community, as their experiment was expected to be a routine confirmation of CP symmetry. Initially, there was an attempt to explain the results without resorting to CP violation but further experiments confirmed that a CP-violating interaction was occuring. Cronin and Fitch later won the Nobel Prize in Physics for their work.

### The Role of the Kaon

The neutral kaon is not its own antiparticle, unlike the neutral pion, and so it is not unchanged under charge conjugation. Thus, when the CP operation is performed on a K^{0}, the result will be a form of its antiparticle ~~K~~^{0}. This is clearly a different particle so the K^{0} are not *eigenstates* of the CP *operator*. Now kaons usually decay into pions, and from conservation of charge they will either be neutral pions or pairs of oppositely-charged pions. Both of these cases *are* eigenstates of CP and thus have a definite value (the '*eigenvalue*') associated with them. Since CP is its own inverse, these eigenvalues must be either 1 or -1. If CP is an exact symmetry then the sign of its eigenvalue is conserved in particle interactions

So the conclusion is that when the kaon decays into pions it must have a definite CP eigenvalue and therefore must be in an eigenstate of CP. To create this, we combine equal parts of the K^{0} and ~~K~~^{0} to form two new, CP-eigenstate particles, which can be called K_{1} and K_{2}. K_{1} has a CP eigenvalue of +1 and decays to two pions, and K_{2} has a CP eigenvalue of -1 and decays to three pions. Each or the 'observed' kaons (K^{0} and ~~K~~^{0}) is a combination of K_{1} and K_{2} and oscillates between them as it propagates.

CP, however, is *not* an exact symmetry, and so occasionally a K_{2} will decay into two pions. Thus, the eigenstates of the weak interaction are not the CP eigenstates K_{1} and K_{2} but slightly unequal combinations of the original K^{0}'s called "K short" (K_{S}) and "K long" (K_{L}). The names refer to the fact that, since three pions have a greater mass than two pions, a decay into two pions will happen, on average, more rapidly than a decay into three pions.

The difference in lifetime between K_{S} and K_{L} was the key to the original observation of CP violation. Since the difference in their lifetimes is greater than two orders of magnitude, one can obtain a pure K_{L} beam simply by sending a K^{0} beam down a pipe and waiting for a certain distance before observing it. Moreover, the fraction of K_{S} remaining in the beam at a certain point should be calculable. CP violation was discoverd in the simple observation that far more two-pion events were appearing far down the beamline than could be explained by any remaining component of K_{S}, suggesting the existence of the process K_{L} -> 2π. Other experiments have confirmed this effect. For example, K_{L} decays more often to π^{-}μ^{+} than π^{+}μ^{-}, which is a clear violation of charge conjugation symmetry.

### Future

For many years, the kaon was the only case where CP violation was observed. In the last decade, however, CP violation was observed in neutral B mesons, by both the Belle collaboration in Japan and the BaBar collaboration at SLAC. The CP violation observed in B decays has been found to be mostly consistent with the predictions of the Standard Model. Currently, there are hopes to measure CP violation in neutrino oscillation, which may be more prominent an effect than in meson physics.

The CP operation combines with time reversal to form the CPT operation. The laws of quantum mechanics require that the laws of physics are symmetric under CPT, and this is borne out by experiment.

Sources include my senior undergraduate particle physics notes, David Griffiths's book Introduction to Elementary Particles, Wikipedia entries "Kaon", "CP symmetry", "P symmetry", and "CPT symmetry", the Particle Data Group site at http://pdg.lbl.gov/ , and http://lhcb-public.web.cern.ch/lhcb-public/html/cpviolationtoc.htm , as well as Cronin and Fitch's Nobel lectures at http://www.nobel.se/. Thanks to tdent and unperson for feedback and encouragement.

**(CC)**
This writeup is copyright 2004,2006,2008 D.G. Roberge and is released under the Creative Commons Attribution-NoDerivs-NonCommercial licence.