In particle physics, the Peccei–Quinn theory
is a well-known proposal for the resolution
of the strong CP problem. It was formulated
by Roberto Peccei and Helen Quinn. The theory
proposes that the QCD Lagrangian be extended
with a CP-violating term known as the θ term.
Because experiments have never measured a
value for θ, its value must be small if it
exists.
Peccei–Quinn theory predicts that the small
θ parameter is explained by a dynamic field,
rather than a constant value. Because particles
arise within quantum fields, Peccei–Quinn
theory predicts the existence of a new particle,
the axion. The potential which this field
carries causes it to have a value which naturally
cancels, making the θ parameter uneventfully
zero.
Peccei–Quinn symmetry presents θ as a functional
component—a global U(1) symmetry under which
a complex scalar field is charged. This symmetry
is spontaneously broken by the vacuum expectation
value obtained by this scalar field, and the
axion is the massless Goldstone boson of this
broken symmetry.
This Peccei–Quinn symmetry is inexact because
it is anomalously broken by QCD instantons.
If there is a compensatory term canceling
the QCD anomaly breaking term, the axion becomes
an exactly massless Goldstone boson and θ
is no longer fixed. The effective potential
of the axion is the summed potential above
the QCD scale; with the potential term induced
by nonperturbative QCD effects. If the axion
is fundamental, or emerges at a scale far
higher than the QCD scale, then the dimension
5 axion coupling term
a
T
r
[
F
∧
F
]
{\displaystyle a\mathrm {Tr} [F\wedge F]}
is suppressed by
1
/
Λ
{\displaystyle 1/\Lambda }
where
Λ
{\displaystyle \Lambda }
is the scale of the axion. Because of this,
in order for θ to be so small at the minimum
of the effective potential, the bare potential
has to be many orders of magnitude smaller
than the instanton induced potential, compounded
by the
Λ
{\displaystyle \Lambda }
factor. This requires quite a bit of reconciliation
with an approximate global symmetry, for which
there is no current explanation
