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CP-symmetry is a symmetry obtained by a combination of the C-symmetry and the P-symmetry. 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 would preserve form when a charge-inversion transformation (positive to negative and vice-versa inversion of electric charges) 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 in the 1950s, it was found that this symmetry too was violated and only a weaker version of the symmetry could be preserved by physical phenomena, which was a CPT-symmetry. Because of the CPT-symmetry, a violation of the CP-symmetry is equivalent to a violation of the T-symmetry.
The electroweak theory is known to violate the CP-symmetry by a complex phase in the CKM matrix. 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.
-  I. Bigi, CP violation, an essential mystery in Nature's grand design. Invited lecture given at the XXV ITEP Winterschoold 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.
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