In particle physics, the Peccei–Quinn theory is a well-known, long-standing proposal for the resolution of the strong CP problem formulated by Roberto Peccei and Helen Quinn in 1977. The theory introduces a new anomalous symmetry to the Standard Model along with a new scalar field which spontaneously breaks the symmetry at low energies, giving rise to an axion that suppresses the problematic CP violation. This model has long since been ruled out by experiments and has instead been replaced by similar invisible axion models which utilize the same mechanism to solve the strong CP problem. Overview Quantum chromodynamics (QCD) has a complicated vacuum structure which gives rise to a CP violating θ-term in the Lagrangian. Such a term can have a number of non-perturbative effects, one of which is to give the neutron an electric dipole moment. The absence of this dipole moment in experiments requires the fine-tuning of the θ-term to be very small, something known as the strong CP problem. Motivated as a solution to this problem, Peccei–Quinn (PQ) theory introduces a new complex scalar field in addition to the standard Higgs doublet. This scalar field couples to d-type quarks through Yukawa terms, while the Higgs now only couples to the up-type quarks. Additionally, a new global chiral anomalous U(1) symmetry is introduced, the Peccei–Quinn symmetry, under which is charged, requiring some of the fermions also have a PQ charge. The scalar field also has a potential where is known as the decay constant, necessarily set to the electroweak scale GeV to ensure that the scalar field behaves similarly to the Higgs field. The potential results in having the vacuum expectation value of . Spontaneous symmetry breaking of the Peccei–Quinn symmetry below the electroweak scale gives rise to a pseudo-Goldstone boson known as the axion , with the resulting Lagrangian taking the form where the first term is the Standard Model (SM) and axion Lagrangian which includes axion-fermion interactions arising from the Yukawa terms. The second term is the CP violating θ-term, with the strong coupling constant, the gluon field strength tensor, and the dual field strength tensor. The third term is known as the color anomaly, a consequence of the Peccei–Quinn symmetry being anomalous, with determined by the choice of PQ charges for the quarks. If the symmetry is also anomalous in the electromagnetic sector, there will additionally be an anomaly term coupling the axion to photons.