Peccei-Quinn theory
Encyclopedia
In particle physics
, the Peccei–Quinn theory is the best known proposal for the resolution of the strong CP problem. The theory proposes that the QCD
Lagrangian
be extended with a CP-violating term known as the θ parameter. Because experiments have never measured a value for θ, its value must be small or zero.
Peccei–Quinn theory predicts that the θ parameter is explained by dynamic field, rather than a constant value. Because quantum fields produce particles, 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 effectively zero.
Peccei-Quinn symmetry is a possible additional ingredient - a global 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.
This Peccei-Quinn symmetry can't possibly be exact because it is anomalously broken by QCD instantons. If there were a compensating term canceling the QCD anomaly breaking term, the axion becomes an exactly massless Goldstone boson and θ is no longer fixed. The effective potential for the axion is the sum of the 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, the dimension 5 axion coupling term
is suppressed by 1/Λ where Λ is the scale where the axion appears. 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 factor. This requires quite a bit of adjusting for an approximate global symmetry, which needs explaining.
Particle physics
Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...
, the Peccei–Quinn theory is the best known proposal for the resolution of the strong CP problem. The theory proposes that the QCD
Quantum chromodynamics
In theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of color-charged fermions...
Lagrangian
Lagrangian
The Lagrangian, L, of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics by Irish mathematician William Rowan Hamilton known as...
be extended with a CP-violating term known as the θ parameter. Because experiments have never measured a value for θ, its value must be small or zero.
Peccei–Quinn theory predicts that the θ parameter is explained by dynamic field, rather than a constant value. Because quantum fields produce particles, Peccei–Quinn theory predicts the existence of a new particle, the axion
Axion
The axion is a hypothetical elementary particle postulated by the Peccei-Quinn theory in 1977 to resolve the strong CP problem in quantum chromodynamics...
. The potential which this field carries causes it to have a value
Vacuum expectation value
In quantum field theory the vacuum expectation value of an operator is its average, expected value in the vacuum. The vacuum expectation value of an operator O is usually denoted by \langle O\rangle...
which naturally cancels, making the θ parameter effectively zero.
Peccei-Quinn symmetry is a possible additional ingredient - a global U(1) symmetry
Symmetry
Symmetry generally conveys two primary meanings. The first is an imprecise sense of harmonious or aesthetically pleasing proportionality and balance; such that it reflects beauty or perfection...
under which a complex scalar field is charged. This symmetry is spontaneously broken
Spontaneous symmetry breaking
Spontaneous symmetry breaking is the process by which a system described in a theoretically symmetrical way ends up in an apparently asymmetric state....
by the value obtained by this scalar field, and the axion
Axion
The axion is a hypothetical elementary particle postulated by the Peccei-Quinn theory in 1977 to resolve the strong CP problem in quantum chromodynamics...
is the massless goldstone boson
Goldstone boson
In particle and condensed matter physics, Goldstone bosons or Nambu–Goldstone bosons are bosons that appear necessarily in models exhibiting spontaneous breakdown of continuous symmetries...
of this symmetry breaking. If the symmetry is a gauge symmetry then the axion is "eaten up" by the gauge boson
Gauge boson
In particle physics, gauge bosons are bosonic particles that act as carriers of the fundamental forces of nature. More specifically, elementary particles whose interactions are described by gauge theory exert forces on each other by the exchange of gauge bosons, usually as virtual particles.-...
, meaning that the gauge boson
Gauge boson
In particle physics, gauge bosons are bosonic particles that act as carriers of the fundamental forces of nature. More specifically, elementary particles whose interactions are described by gauge theory exert forces on each other by the exchange of gauge bosons, usually as virtual particles.-...
becomes massive and the axion does not exist anymore as a physical degree of freedom (see Higgs mechanism
Higgs mechanism
In particle physics, the Higgs mechanism is the process in which gauge bosons in a gauge theory can acquire non-vanishing masses through absorption of Nambu-Goldstone bosons arising in spontaneous symmetry breaking....
). This is phenomenologically
Particle physics phenomenology
Particle physics phenomenology is the part of theoretical particle physics that deals with the application of theory to high-energy particle physics experiments. Within the Standard Model, phenomenology is the calculating of detailed predictions for experiments, usually at high precision...
desirable because it leaves no massless particles, which are indeed not seen experimentally.
This Peccei-Quinn symmetry can't possibly be exact because it is anomalously broken by QCD instantons. If there were a compensating term canceling the QCD anomaly breaking term, the axion becomes an exactly massless Goldstone boson and θ is no longer fixed. The effective potential for the axion is the sum of the 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, the dimension 5 axion coupling term
is suppressed by 1/Λ where Λ is the scale where the axion appears. 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 factor. This requires quite a bit of adjusting for an approximate global symmetry, which needs explaining.