Majorons and Orbifolds

An orbifold is the orbit space of a manifold with a group action; this sculpture depicts the orbifold T3 / S3 – the quotient of the 3-torus by the symmetric group on 3 letters.

In particle physics, majorons (named after Ettore Majorana) are a hypothetical type of Goldstone boson that are theorized to mediate the neutrino mass violation of lepton number or B-L in certain high energy collisions such as

e⁻ + e⁻ → W⁻ + W⁻ + J

Where two electrons collide to form two W bosons and the majoron J. The U(1)_B–L symmetry is assumed to be global so that the majoron isn't "eaten up" by the gauge boson and spontaneously broken. Majorons were originally formulated in four dimensions by Y. Chikashige, R. N. Mohapatra and R. D. Peccei to understand neutrino masses by the seesaw mechanism and are being searched for in the neutrinoless double beta decay process. There are theoretical extensions of this idea into supersymmetric theories and theories involving extra compactified dimensions. By propagating through the extra spatial dimensions the detectable number of majoron creation events vary accordingly. Mathematically, majorons may be modeled by allowing them to propagate through a material while all other Standard Model forces are fixed to an orbifold point.