Left-right symmetry
Encyclopedia
Left–right symmetry is a general principle in physics
which holds that valid physical laws must not produce a different result for a motion that is left-handed than motion that is right-handed. The most common application is expressed as equal treatment of clockwise and counter-clockwise rotations from a fixed frame of reference.
The general principle is often referred to by the name chiral
symmetry. The rule is absolutely valid in the classical mechanics
of Newton
and Einstein
, but results from quantum mechanical
experiments show a difference in the behavior of left-chiral versus right-chiral subatomic particles.
, the electroweak model breaks parity
maximally. All its fermion
s are chiral
Weyl fermions, which means that the weak gauge bosons
only couple to left-handed quarks and leptons. Some theorists found this objectionable, and so proposed a GUT
extension of the weak force which has new, high energy W' and Z' bosons
which couple with right handed quarks and leptons.
to
Here, SU(2)L left) is none other than SU(2)W and B−L is the baryon number minus the lepton number
. An advantage of this model over the Standard Model is that the electric charge formula in this model is given by
;
where
are the weak isospin values of the fields in the theory.
There is also the chromodynamic SU(3)C. The idea was to restore parity by introducing a left-right symmetry. This is a group extension
of Z2 (the left-right symmetry) by
to the semidirect product
This has two connected component
s where Z2 acts as an automorphism
, which is the composition of an involutive outer automorphism of SU(3)C with the interchange of the left and right copies of SU(2) with the reversal of U(1)B−L. It was shown by R. N. Mohapatra and G. Senjanovic in 1975 that left-right symmetry
can be spontaneously broken
to give a chiral low energy theory, which is the Standard Model of Glashow, Weinberg and Salam and it also connects the small observed neutrino masses to the breaking of left-right symmetry via the seesaw mechanism
.
In this setting the chiral quark
s
1/3
and
are unified into an irrep
The lepton
s are also unified into an irrep
The Higgs bosons needed to implement the breaking of left-right symmetry down to the Standard Model
are
This then predicts three sterile neutrino
s, which is perfectly consistent with neutrino oscillation
data. Within the seesaw mechanism, the sterile neutrinos become superheavy without affecting physics at low energies.
Because the left-right symmetry is spontaneously broken, left-right models predict domain wall
s.
This left-right symmetry idea first appeared in the Mohapatra-Pati models and Pati-Salam model
, and later in trinification.
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
which holds that valid physical laws must not produce a different result for a motion that is left-handed than motion that is right-handed. The most common application is expressed as equal treatment of clockwise and counter-clockwise rotations from a fixed frame of reference.
The general principle is often referred to by the name chiral
Chirality (physics)
A chiral phenomenon is one that is not identical to its mirror image . The spin of a particle may be used to define a handedness for that particle. A symmetry transformation between the two is called parity...
symmetry. The rule is absolutely valid in the classical mechanics
Classical mechanics
In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...
of Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
and Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
, but results from quantum mechanical
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
experiments show a difference in the behavior of left-chiral versus right-chiral subatomic particles.
Particle Physics
In theoretical physicsTheoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
, the electroweak model breaks parity
Parity (physics)
In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:...
maximally. All its fermion
Fermion
In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
s are chiral
Chirality (physics)
A chiral phenomenon is one that is not identical to its mirror image . The spin of a particle may be used to define a handedness for that particle. A symmetry transformation between the two is called parity...
Weyl fermions, which means that the weak gauge bosons
W and Z bosons
The W and Z bosons are the elementary particles that mediate the weak interaction; their symbols are , and . The W bosons have a positive and negative electric charge of 1 elementary charge respectively and are each other's antiparticle. The Z boson is electrically neutral and its own...
only couple to left-handed quarks and leptons. Some theorists found this objectionable, and so proposed a GUT
Grand unification theory
The term Grand Unified Theory, often abbreviated as GUT, refers to any of several similar candidate models in particle physics in which at high-energy, the three gauge interactions of the Standard Model which define the electromagnetic, weak, and strong interactions, are merged into one single...
extension of the weak force which has new, high energy W' and Z' bosons
W' and Z' bosons
In particle physics, W' and Z' bosons refer to hypothetical new gauge bosons that arise from extensions of the electroweak symmetry of the Standard Model. They are named in analogy with the Standard Model W and Z bosons....
which couple with right handed quarks and leptons.
to
Here, SU(2)L left) is none other than SU(2)W and B−L is the baryon number minus the lepton number
Lepton number
In particle physics, the lepton number is the number of leptons minus the number of antileptons.In equation form,so all leptons have assigned a value of +1, antileptons −1, and non-leptonic particles 0...
. An advantage of this model over the Standard Model is that the electric charge formula in this model is given by
;where
are the weak isospin values of the fields in the theory.There is also the chromodynamic SU(3)C. The idea was to restore parity by introducing a left-right symmetry. This is a group extension
Group extension
In mathematics, a group extension is a general means of describing a group in terms of a particular normal subgroup and quotient group. If Q and N are two groups, then G is an extension of Q by N if there is a short exact sequence...
of Z2 (the left-right symmetry) by
to the semidirect product
Semidirect product
In mathematics, specifically in the area of abstract algebra known as group theory, a semidirect product is a particular way in which a group can be put together from two subgroups, one of which is a normal subgroup. A semidirect product is a generalization of a direct product...
This has two connected component
Connected space
In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint nonempty open subsets. Connectedness is one of the principal topological properties that is used to distinguish topological spaces...
s where Z2 acts as an automorphism
Automorphism
In mathematics, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure. The set of all automorphisms of an object forms a group, called the automorphism...
, which is the composition of an involutive outer automorphism of SU(3)C with the interchange of the left and right copies of SU(2) with the reversal of U(1)B−L. It was shown by R. N. Mohapatra and G. Senjanovic in 1975 that left-right symmetry
Left-right symmetry
Left–right symmetry is a general principle in physics which holds that valid physical laws must not produce a different result for a motion that is left-handed than motion that is right-handed...
can be 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....
to give a chiral low energy theory, which is the Standard Model of Glashow, Weinberg and Salam and it also connects the small observed neutrino masses to the breaking of left-right symmetry via the seesaw mechanism
Seesaw mechanism
In theoretical physics, the seesaw mechanism is a mechanism within grand unification theory, and in particular in theories of neutrino masses and neutrino oscillation, where it can be used to explain the smallness of observed neutrino masses relative to those of quarks and leptons.There are several...
.
In this setting the chiral quark
Quark
A quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
s
1/3
and
are unified into an irrep
The lepton
Lepton
A lepton is an elementary particle and a fundamental constituent of matter. The best known of all leptons is the electron which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons , and neutral...
s are also unified into an irrep
The Higgs bosons needed to implement the breaking of left-right symmetry down to the Standard Model
are
This then predicts three sterile neutrino
Sterile neutrino
Sterile neutrinosIn scientific literature, these particles are also variously referred to as right-handed neutrinos, inert neutrinos, heavy neutrinos, or neutral heavy leptons . are a hypothetical type of neutrino that do not interact via any of the fundamental interactions of the Standard Model...
s, which is perfectly consistent with neutrino oscillation
Neutrino oscillation
Neutrino oscillation is a quantum mechanical phenomenon predicted by Bruno Pontecorvowhereby a neutrino created with a specific lepton flavor can later be measured to have a different flavor. The probability of measuring a particular flavor for a neutrino varies periodically as it propagates...
data. Within the seesaw mechanism, the sterile neutrinos become superheavy without affecting physics at low energies.
Because the left-right symmetry is spontaneously broken, left-right models predict domain wall
Domain wall
A domain wall is a term used in physics which can have one of two distinct but similar meanings in magnetism, optics, or string theory. These phenomena can all be generically described as topological solitons which occur whenever a discrete symmetry is spontaneously broken.-Magnetism:In magnetism,...
s.
This left-right symmetry idea first appeared in the Mohapatra-Pati models and Pati-Salam model
Pati-Salam model
In physics, the Pati–Salam model is a Grand Unification Theory was proposed in 1974 by nobel laureate Abdus Salam and Jogesh Pati. The unification is based on there being four quark color charges, dubbed red, green, blue and violet , instead of the conventional three, with the new "violet" quark...
, and later in trinification.