The Context in which CP-Symmetry can be placed is in terms of what is known as "CP-Violation". "Charge-Parity" or "CP" is all about symmetry. In The Standard Model, The Big Bang should have produced equal amounts of matter, and anti-matter; as such, there should have been total cancellation of both. (matter: protons, neutrons, electrons / anti-matter: antiprotons, antineutrons, positrons)
Simply put, during the Big Bang, the Laws of nature acted differently for anti-matter, and matter.
IF the Laws of nature did act the same on both matter and anti-matter we would have total CP-Symmetry.
A force as yet unknown during the singularity of the Big Bang produced an asymmetric amount of anti-matter, and matter.
CP-Violation took place. The result was an inequality that resulted in the Universe.
The weak force by itself can only account for a tiny amount of CP-violation. Possibly to explain the amount of protons, neutrons and electrons that would be needed to condense into a single matter galaxy.
The Standard Model is incomplete in explaining the hidden force(s) that led to the massive CP-Violation that produced the Universe.
The observable Universe is estimated to consist of about 10 billion galaxies that consist of matter. And again, an estimated 4% of the Universe is "regular" matter. The other 96% is postulated to be dark matter, and dark energy. Both of which we (as yet) are not able to directly measure.
CP-symmetry is a symmetry obtained by a combination of the C-symmetry and the P-symmetry. C-symmetry is the symmetry of physical laws under a charge-conjugation transformation, P-symmetry is the symmetry of physical laws under parity transformation. When it was found that both these symmetries were violated individually, it looked plausible that a combination of the two would be preserved by all physical laws. Simply stated, the preservation of CP-symmetry by all physical phenomena would mean that all physical laws preserve form when a charge-inversion transformation (positive to negative and vice-versa inversion of quantum charges, including electric) and a parity-inversion transformation ('left' to 'right' and vice versa; inversion; or, simply the reversal of the coordinate axis in a Cartesian coordinate system used to describe the system under consideration) are done simultaneously. But to the dismay of physicists, it was discovered in 1964 by the group of Cristenson, Cronin, Fitch and Turlay in a kaon decay experiment that this symmetry too was violated, and only a weaker version of the symmetry could be preserved by physical phenomena, which was CPT-symmetry. Because of the CPT-symmetry, a violation of the CP-symmetry is equivalent to a violation of the T-symmetry.
Recently, a new generation of experiments, including the BaBar Experiment at the Stanford Linear Accelerator Center (SLAC) and the Belle Experiment at the High Energy Accelerator Research Organisation (KEK), Japan, have observed CP violation using B mesons. Before these experiments, it was a logical possibility that all CP violation was confined to kaon physics. These experiments dispelled any doubt that the interactions of the Standard Model violated CP.
The CP violation of the Standard model is incorporated by including a complex phase in the CKM matrix. A necessary condition for the appearance of the complex phase, and thus for CP-violation, is the presence of at least three generations of quarks.
There is no experimentally known violation of the CP-symmetry in Quantum Chromodynamics. The strong CP problem is the question of why no such violation is detected even though the theory in principle allows for it.
CP violation is also necessary to explain why our universe contains vastly different amounts of matter and anti-matter. It seems unlikely that the CP violation observed in the Standard Model is sufficient to explain this difference. On-going experiments hope to uncover additional sources of CP violation.
- Branco, G. C. and Lavoura, L. and Silva, J. P., CP violation. Clarendon Press, Oxford (1999). ISBN 0-198-50399-7.
- Bigi, I. and Sanda, A., CP violation. Cambridge University Press (1999). ISBN 0-521-44349-0.
- Griffiths, David J. (1987). Introduction to Elementary Particles, Wiley, John & Sons, Inc. ISBN 0471603864.
-  I. Bigi, CP violation, an essential mystery in Nature's grand design. Invited lecture given at the XXV ITEP Winter school of Physics, February 18-27, 1997, Moscow, Russia, at 'Frontiers in Contemporary Physics', May 11-16, 1997, Vanderbilt University, Nashville, USA, and at the International School of Physics 'Enrico Fermi', CXXXVII Course 'Heavy Flavour Physics: A Probe of Nature's Grand Design', Varenna, Italy, July 8-18, 1997. hep-ph/9803479.
- What is direct CP-violation?