Peccei-Quinn theory

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In particle physics, the Peccei-Quinn theory is the most famous proposed solution to the strong CP problem, involving new massless particles called axions. One may add to the QCD Lagrangian a term which is CP-violating, and its parameter is known as θ parameter. However such a term has never been measured experimentally, implying that θ is either zero or very close to that. The strong CP problem is the quest for explanation of the vanishing of θ.

Peccei-Quinn theory proposes that the θ parameter be made into a dynamic field rather than being an arbitrary constant. Since in quantum field theory, each field produces a particle, this field must correspond to a hypothetical particle known as the axion. The potential which this field naturally obtains causes it to have a value which makes the effective θ parameter vanish.

Peccei-Quinn symmetry is a possible additional ingredient - a U(1) symmetry under which a complex scalar field is charged. This symmetry is spontaneously broken by the value obtained by this scalar field, and the axion is the massless goldstone boson of this symmetry breaking. If the symmetry is a gauge symmetry then the axion is "eaten up" by the gauge boson, meaning that the gauge boson becomes massive and the axion does not exist anymore as a physical degree of freedom (see Higgs mechanism). This is phenomenologically desirable because it leaves no massless particles, which are indeed not seen experimentally.