chiral Weyl fermions, which means that the charged weak gauge bosons W and W only couple to left-handed quarks and leptons. Some theorists found this objectionable, and so conjectured a GUT extension of the weak force which has new, high energy W' and Z' bosons, which do couple with right handed quarks and leptons: to Here, SU(2) (pronounced “SU(2) left”) is none other than SU(2) from above, while B−L is the baryon number minus the lepton number. The electric charge formula in this model is given by where and are the left and right weak isospin values of the fields in the theory. There is also the chromodynamic SU(3). The idea was to restore parity by introducing a left-right symmetry. This is a group extension of (the left-right symmetry) by to the semidirect product This has two connected components where acts as an automorphism, which is the composition of an involutive outer automorphism of SU(3) with the interchange of the left and right copies of SU(2) with the reversal of U(1) . It was shown by Mohapatra & Senjanovic (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 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 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 walls. This left-right symmetry idea first appeared in the Pati–Salam model (1974) and Mohapatra–Pati models (1975). See also Electroweak theory Chirality (chemistry) Chirality (mathematics) Chiral symmetry breaking Handedness Spinors and Dirac fields Sigma model Chiral model Notes References External links To see a summary of the differences and similarities between chirality and helicity (those covered here and more) in chart form, one may go to Pedagogic Aids to Quantum Field Theory and click on the link near the bottom of the page entitled "Chirality and Helicity Summary". To see an in depth discussion of the two with examples,