Chirality (physics)

Invariance under parity transformation by a Dirac fermion is called chiral symmetry.

So a standard clock, with its spin vector defined by the rotation of its hands, has left-handed helicity if tossed with its face directed forwards.

[a] For massless particles – photons, gluons, and (hypothetical) gravitons – chirality is the same as helicity; a given massless particle appears to spin in the same direction along its axis of motion regardless of point of view of the observer.

A massless particle moves with the speed of light, so no real observer (who must always travel at less than the speed of light) can be in any reference frame where the particle appears to reverse its relative direction of spin, meaning that all real observers see the same helicity.

[c] Particle physicists have only observed or inferred left-chiral fermions and right-chiral antifermions engaging in the charged weak interaction.

Interactions involving right-handed or opposite-handed fermions have not been shown to occur, implying that the universe has a preference for left-handed chirality.

Many pieces of the Standard Model of physics are non-chiral, which is traceable to anomaly cancellation in chiral theories.

Vector gauge theories with massless Dirac fermion fields ψ exhibit chiral symmetry, i.e., rotating the left-handed and the right-handed components independently makes no difference to the theory.

Spontaneous chiral symmetry breaking may also occur in some theories, as it most notably does in quantum chromodynamics.

The most common application is expressed as equal treatment of clockwise and counter-clockwise rotations from a fixed frame of reference.

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.

Consider quantum chromodynamics (QCD) with two massless quarks u and d (massive fermions do not exhibit chiral symmetry).

formed through nonperturbative action of QCD gluons, into the diagonal vector subgroup SU(2)V known as isospin.

As a consequence, the effective theory of QCD bound states like the baryons, must now include mass terms for them, ostensibly disallowed by unbroken chiral symmetry.

Most usually, N = 3 is taken, the u, d, and s quarks taken to be light (the eightfold way), so then approximately massless for the symmetry to be meaningful to a lowest order, while the other three quarks are sufficiently heavy to barely have a residual chiral symmetry be visible for practical purposes.

There is also the chromodynamic SU(3)C. The idea was to restore parity by introducing a left-right symmetry.

It was shown by Mohapatra & Senjanovic (1975)[5] 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 also connects the small observed neutrino masses to the breaking of left-right symmetry via the seesaw mechanism.

In this setting, the chiral quarks and are unified into an irreducible representation ("irrep") The leptons are also unified into an irreducible representation The Higgs bosons needed to implement the breaking of left-right symmetry down to the Standard Model are This then provides three sterile neutrinos which are perfectly consistent with current[update] neutrino oscillation data.

Within the seesaw mechanism, the sterile neutrinos become superheavy without affecting physics at low energies.