See main article: article and Chirality (physics).
In particle physics, chiral symmetry breaking generally refers to the dynamical spontaneous breaking of a chiral symmetry associated with massless fermions. This is usually associated with a gauge theory such as quantum chromodynamics, the quantum field theory of the strong interaction, and it also occurs through the Brout-Englert-Higgs mechanism in the electroweak interactions of the standard model. 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.[1] Nambu was awarded the 2008 Nobel prize in physics "for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics".
See main article: Quantum chromodynamics and QCD vacuum.
Massless fermions in 4 dimensions are described by either left or right-handed spinors that each have 2 complex components. These have spin either aligned (right-handed chirality), or counter-aligned (left-handed chirality), with their momenta. 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. More generally they can form multiplets under some symmetry group
GL x GR{}
A Dirac mass term explicitly breaks the chiral symmetry. In quantum electrodynamics (QED) the electron mass unites left and right handed spinors forming a 4 component Dirac spinor. In the absence of mass and quantum loops, QED would have a
U(1)L x U(1)R
U(1)
U(1)
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". In the notation, (spin), a
0+
0-
Experimentally, however, it is observed that the masses of the
0-
1-
0+
1+
This is a primary consequence of the phenomenon of spontaneous symmetry breaking of chiral symmetry in the strong interactions. In QCD, the fundamental fermion sector consists of three "flavors" of light mass quarks,,, and , as well as three flavors of heavy quarks, charm quark, bottom quark, and top quark. If we assume the light quarks are ideally massless (and ignore electromagnetic and weak interactions), then the theory has an exact global
SU(3)L x SU(3)R
Beyond the idealization of massless quarks, the actual small quark masses (and electroweak forces) explicitly break the chiral symmetry as well. This can be described by a chiral Lagrangian where the masses of the pseudoscalar mesons are determined by the quark masses, and various quantum effects can be computed in chiral perturbation theory. This can be confirmed more rigorously by lattice QCD computations, which show that the pseudoscalar masses vary with the quark masses as dictated by chiral perturbation theory, (effectively as the square-root of the quark masses).
The three heavy quarks: the charm quark, bottom quark, and top quark, have masses much larger than the scale of the strong interactions, thus they do not display the features of spontaneous chiral symmetry breaking. However bound states consisting of a heavy quark and a light quark (or two heavies and one light) still display a universal behavior, where the
(0-,1-)
(0+,1+)
~\DeltaM ≈ 348MeV,~
| * | |
| D | |
| s(2317) |
If the three light quark masses of QCD are set to zero, we then have a Lagrangian with a symmetry group :
SU(3)L x SU(3)R x U(1)V x U(1)A~.
SU(3)
SU(3)c
A static vacuum condensate can form, composed of bilinear operators involving the quantum fields of the quarks in the QCD vacuum, known as a fermion condensate. This takes the form :
\langle
| a | |
| \bar{q} | |
| R |
| b | |
| q | |
| L |
\rangle=v\deltaab
SU(3)L
SU(3)R
SU(3)
The quark condensate is induced by non-perturbative strong interactions and spontaneously breaks the
~SU(3)L x SU(3)R~
~SU(3)V
~SU(2)
~SU(3)
U(1)A
Chiral symmetry breaking is apparent in the mass generation of nucleons, since no degenerate parity partners of the nucleon appear. 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).[3] For example, the proton, of mass contains two up quarks, each with explicit mass and one down quark with explicit mass . Naively, the light quark explicit masses only contribute a total of about 9.4 MeV to the proton's mass.[4]
For the light quarks the chiral symmetry breaking condensate can be viewed as inducing the so-called constituent quark masses. Hence, the light up quark, with explicit mass and down quark with explicit mass now acquire constituent quark masses of about . QCD then leads to the baryon bound states, which each contain combinations of three quarks (such as the proton (uud) and neutron (udd)). The baryons then acquire masses given, approximately, by the sums of their constituent quark masses.[5] [6]
See main article: Chiral model. One of the most spectacular aspects of spontaneous symmetry breaking, in general, is the phenomenon of the Nambu–Goldstone bosons. In QCD these appear as approximately massless particles. corresponding to the eight broken generators of the original
SU(3)L x SU(3)R~.
These states have small masses due to the explicit masses of the underlying quarks and as such are referred to as "pseudo-Nambu-Goldstone bosons" or "pNGB's". 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. The properties of these pNGB's can be calculated from chiral Lagrangians, using chiral perturbation theory, which expands around the exactly symmetric zero-quark mass theory. In particular, the computed mass must be small.
Technically, the spontaneously broken chiral symmetry generators comprise the coset space
~(SU(3)L x SU(3)R)/SU(3)V~.
SU(3)L x SU(3)R~.
Mesons containing a heavy quark, such as charm (D meson) or beauty, and a light anti-quark (either up, down or strange), can be viewed as systems in which the light quark is "tethered" by the gluonic force to the fixed heavy quark, like a ball tethered to a pole. 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.[7] They showed that chiral symmetry breaking causes the s-wave ground states
(0-,1-)
parity
(0+,1+)
\DeltaM
~\DeltaM ≈ 338MeV,~
D(0+,1+) → \pi+D(0-,1-)~,
~
| +,1 | |
| Ds(0 |
+)~
~
| +,1 | |
| Ds(0 |
+) → K+
| -,1 | |
| Du,d(0 |
-)~,
In 2003 the
| * | |
| D | |
| s(2317) |
| Ds |
\DeltaM ≈ 348MeV,
| *(2460) | |
| D | |
| s1+ |
Bs
ccs,bcs,bbs,