This phenomenon is analogous to magnetization and superconductivity in condensed matter physics.
The basic idea was introduced to particle physics by Yoichiro Nambu, in particular, in the Nambu–Jona-Lasinio model, which is a solvable theory of composite bosons that exhibits dynamical spontaneous chiral symmetry when a 4-fermion coupling constant becomes sufficiently large.
Massless fermions in 4 dimensions are described by either left or right-handed spinors that each have 2 complex components.
In this case the chirality is a conserved quantum number of the given fermion, and the left and right handed spinors can be independently phase transformed.
In QCD, the gauge theory of strong interactions, the lowest mass quarks are nearly massless and an approximate chiral symmetry is present.
In this case the left- and right-handed quarks are interchangeable in bound states of mesons and baryons, so an exact chiral symmetry of the quarks would imply "parity doubling", and every state should appear in a pair of equal mass particles, called "parity partners".
The low masses of the pseudoscalar mesons, as compared to the heavier states, is also quite striking.
vector mesons are heavier still, appearing as short-lived resonances far (in mass) from their parity partners.
In QCD, the fundamental fermion sector consists of three "flavors" of light mass quarks, in increasing mass order: up u, down d, and strange s (as well as three flavors of heavy quarks, charm c, bottom b, and top t ).
If we assume the light quarks are ideally massless (and ignore electromagnetic and weak interactions), then the theory has an exact global
These are identified with the pseudoscalar mesons seen in the spectrum, and form an octet representation of the diagonal SU(3) flavor group.
If the three light quark masses of QCD are set to zero, we then have a Lagrangian with a symmetry group [a] :
that defines QCD as a Yang-Mills gauge theory and leads to the gluonic force that binds quarks into baryons and meson.
In this article we will not focus on the binding dynamics of QCD where quarks are confined within the baryon and meson particles that are observed in the laboratory (see Quantum chromodynamics).
[2] The pion decay constant, fπ ≈ 93 MeV , may be viewed as the measure of the strength of the chiral symmetry breaking.
[2] The quark condensate is induced by non-perturbative strong interactions and spontaneously breaks the
the original symmetry of nuclear physics called isospin, which acts upon the up and down quarks).
Chiral symmetry breaking and the quantum conformal anomaly account for approximately 99% of the mass of a proton or neutron, and these effects thus account for most of the mass of all visible matter (the proton and neutron, which form the nuclei of atoms, are baryons, called nucleons).
QCD then leads to the baryon bound states, which each contain combinations of three quarks (such as the proton (uud) and neutron (udd)).
[5][6] One of the most spectacular aspects of spontaneous symmetry breaking, in general, is the phenomenon of the Nambu–Goldstone bosons.
pNGB's are a general phenomenon and arise in any quantum field theory with both spontaneous and explicit symmetry breaking, simultaneously.
These two types of symmetry breaking typically occur separately, and at different energy scales, and are not predicated on each other.
[c] Technically, the spontaneously broken chiral symmetry generators comprise the coset space
This space is not a group, and consists of the eight axial generators, corresponding to the eight light pseudoscalar mesons, the nondiagonal part of
These systems give us a view of the chiral symmetry breaking in its simplest form, that of a single light-quark state.
In 1994 William A. Bardeen and Christopher T. Hill studied the properties of these systems implementing both the heavy quark symmetry and the chiral symmetries of light quarks in a Nambu–Jona-Lasinio model approximation.
The excited states of non-strange, heavy-light mesons are usually short-lived resonances due to the principal strong decay mode
was discovered by the BaBar collaboration, and was seen to be surprisingly narrow, with a mass gap above the
within a few percent of the model prediction (also the more recently confirmed heavy quark spin-symmetry partner,
Bardeen, Eichten and Hill predicted, using the chiral Lagrangian, numerous observable decay modes which have been confirmed by experiments.