CP violation is the failure of a theory to be invariant under the combination of charge conjugation and parity. Under CPT invariance it is equivalent to time-reversal violation.
A direct CP asymmetry compares decay widths for a process and its CP symmetry conjugate. Let two decay amplitudes contribute with real nonnegative magnitudes , absorptive phases and weak phases . Then and . Expanding the absolute squares givesThus two nonzero contributions and both kinds of relative phase are required in this example. Equal total decay widths under CPT symmetry constrain the sum over channels and do not forbid individual channel asymmetries.
A weak phase is a phase in a coupling or decay amplitude that reverses sign in the CP symmetry conjugate process. A physically relevant difference must survive allowed field rephasings; a complex coupling alone does not prove CP violation.
The fermion electric dipole moment operator couples a fermion pseudotensor bilinear to the electromagnetic field tensor. Its nonrelativistic interaction is proportional to , so it is odd under parity and time reversal and signals CP violation.
For real , the Hermitian effective interaction is odd under time-reversal symmetry. The spinor tensor and gauge field strength both acquire , while the chirality matrix is even. Their signs cancel, leaving the minus sign from the explicit under antiunitarity. By the CPT theorem this is also CP violation. It is not a renormalizable tree-level Standard Model term, but a radiatively generated low-energy dipole is allowed because of the CP-violating phase in the CKM matrix.
A CP-violating phase is a complex phase in couplings or mixing matrices that cannot be removed by field redefinitions and changes sign under CP conjugation.
Multiplying individual fields by constant phases changes the apparent phases of interaction coefficients. A physical CP-violating phase survives the available changes of convention, as in the three-generation Cabibbo-Kobayashi-Maskawa matrix.
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CP violation refers to the phenomenon where the combined operations of charge conjugation (C) and parity (P) do not yield the same physics for certain processes. Charge conjugation transforms a particle into its antiparticle, while parity transformation involves flipping the spatial coordinates (like mirroring). In essence, if a physical process behaves differently when particles are swapped for antiparticles (C transformation) and mirrored (P transformation), then CP violation is occurring.
