| CP symmetry | |
|---|---|
| Name | CP symmetry |
| Field | Quantum field theory |
| Introduced | 1950s |
| Notable people | James Cronin; Val Fitch; Makoto Kobayashi; Toshihide Maskawa; Murray Gell-Mann |
CP symmetry
CP symmetry is the combined transformation of charge conjugation (C), which swaps particles with their antiparticles, and parity (P), which inverts spatial coordinates. In relativistic quantum field theory CP maps field operators to their conjugates with spatial reflection, and its (non)conservation has deep implications for the laws of particle physics. CP violation is central to explanations of the observed baryon asymmetry of the Universe.
In quantum theory, C and P are linear or antiunitary operators acting on the Hilbert space of states. Charge conjugation C transforms a field ψ(x) to an operator proportional to ψ̄(x) or its charge-conjugated version; parity P acts as ψ(t,→x) → γ^0 ψ(t,−→x) for Dirac fields in a chosen representation. The combined CP operation is typically represented by an operator CP satisfying (CP)ψ(t,→x)(CP)^−1 = η_CP ψ̄(t,−→x), where η_CP is a phase. In Lagrangian formalism one inspects whether the action S or the Hamiltonian H commutes with CP. For gauge theories such as Quantum electrodynamics or Quantum chromodynamics the transformation rules are determined by gauge representations and spin. CP invariance constrains allowed terms in effective field theory Lagrangians: CP-odd operators (e.g., θ-term in QCD) break the symmetry explicitly.
CP is a discrete spacetime/internal symmetry with status comparable to time reversal (T). The CPT theorem guarantees that any local, Lorentz-invariant, unitary quantum field theory with a Hermitian Hamiltonian is invariant under the combined CPT transformation; thus CP violation implies T violation assuming CPT conservation. In the Standard Model, CP violation arises from complex phases in Yukawa couplings leading to complex entries in the Cabibbo–Kobayashi–Maskawa matrix and, for leptons, the Pontecorvo–Maki–Nakagawa–Sakata matrix. CP properties classify particles and interactions, affect selection rules, and restrict possible effective field theory operators used in searches for new physics at facilities like CERN and Fermilab.
The first observation of CP violation occurred in 1964 in neutral kaon decays by James Cronin and Val Fitch at Brookhaven National Laboratory. Subsequent precision measurements have been performed by experiments such as BaBar at SLAC National Accelerator Laboratory, Belle at KEK, and LHCb at CERN's Large Hadron Collider. CP-violating observables include decay rate asymmetries, indirect CP violation via mixing (as in the K0–K̄0 and B0–B̄0 systems), and direct CP violation in decay amplitudes. Electric dipole moment (EDM) searches for the neutron electric dipole moment and atomic EDMs (e.g., in mercury or polar molecules) provide sensitive tests for new CP-odd sources. Neutrino oscillation experiments such as T2K and NOvA probe leptonic CP phases in the PMNS matrix.
Within the Standard Model, CP violation is accommodated by a single irreducible complex phase in the CKM matrix for quarks, formalized by Kobayashi and Maskawa who extended the Cabibbo angle framework. For leptons, the PMNS matrix may contain one Dirac and two Majorana phases, relevant for neutrinoless double beta decay if neutrinos are Majorana particles. Beyond-Standard-Model proposals introduce additional CP-violating phases: supersymmetric models (MSSM), left–right symmetric models, two-Higgs-doublet models, and models with heavy sterile neutrinos relevant for leptogenesis. The strong CP problem, manifest in the smallness of the θ-angle in QCD, motivates solutions such as the Peccei–Quinn theory and the postulated axion particle, introduced to dynamically relax θ to zero.
Sakharov conditions require baryon number violation, C and CP violation, and departure from thermal equilibrium to generate a baryon asymmetry. The magnitude of CP violation in the Standard Model via the CKM mechanism is widely regarded as insufficient to account for the observed baryon-to-photon ratio measured in cosmic microwave background studies (e.g., by Planck). Alternative mechanisms such as electroweak baryogenesis and leptogenesis invoke additional CP-violating sources at higher energies; leptogenesis connects CP-violating decays of heavy right-handed neutrinos to a lepton asymmetry subsequently converted to a baryon asymmetry by sphaleron processes in the early Universe.
CP concepts extend beyond elementary particles to composite systems and condensed-matter analogues. In atomic and molecular physics, CP-odd interactions induce permanent electric dipole moments tested in precision spectroscopy. Neutral meson mixing is a paradigmatic two-state quantum system illustrating CP-violating interference between mass eigenstates and decay amplitudes. In engineered quantum systems, time-reversal and parity operations are studied in quantum simulation platforms such as ultracold atoms and superconducting qubits to emulate CP-like transformations. Studies at the intersection of quantum information and particle physics explore how CP-violating phases manifest as measurable phases or asymmetries in entangled states and interferometric protocols.
Category:Symmetry in physics Category:Particle physics Category:Quantum field theory