Prospects for observing chiral symmetry breaking in lepton colliders

Abstract

Weak interactions in neutron $\beta$-decay exhibit parity violation through the preferential emission of right-handed antineutrinos. We identify this symmetry breaking with a reduction of phase space due to the small neutrino mass. During a brief interval of momentum exchange, a small mass neutrino puts the emission process close to the bifurcation horizon of Rindler space, doubly covered by Minkowski space ${\cal M}$ as dictated by the Equivalence Principle of general relativity. In the limit of arbitrarily small mass, this two-sheet covering effectively collapses into a single sheet, reducing the dimension of Dirac spinors from four to two, leaving neutrinos single-handed. This predicts a similar reduction to single-handed particle states in electrons created at TeV energies, which may be tested with the planned linear leptonic colliders. If confirmed, right-handed small mass neutrinos are expected to exist at sufficiently low energies.