CPinvariant

CPinvariant, often written as CP-invariant, describes a property of a physical theory in which the combined charge conjugation (C) and parity (P) symmetries are exact. The CP operation transforms a state into its antiparticle while applying a mirror reflection in spatial coordinates. A CP-invariant theory yields identical probabilities for a process and for its CP-conjugate process, and thus identical rates for the corresponding transitions.

Formally, if the Hamiltonian of a theory is CP-symmetric, the transition amplitude for a process A → B equals the amplitude for the CP-conjugate process Abar → Bbar. In practice, CP invariance is tested in weak interactions, where CP violation has been observed. In the Standard Model, CP symmetry is not exact due to a complex phase in the Cabibbo–Kobayashi–Maskawa (CKM) quark-mixing matrix and potentially in the leptonic sector via the PMNS matrix. CP violation was first observed in neutral kaon decays in 1964 and later in B-meson decays, establishing that the SM is not CP-invariant.

CP invariance is distinct from CPT invariance. The CPT theorem guarantees that any local, Lorentz-invariant quantum field theory preserves CPT, so CP violation implies T violation if CPT holds.

In broader contexts, CP invariance is a guiding principle in model-building. The degree of CP violation has profound implications for baryogenesis, since sufficient CP violation is one of the Sakharov conditions needed to explain the matter-antimatter asymmetry of the universe. Many beyond-Standard-Model theories explore scenarios with restored CP symmetry at high energy or with new CP-violating phases.