About the origins of the Supersymmetric Standard Model

Abstract

Could one use supersymmetry to relate the fermions, constituants of matter, with the bosons messengers of the interactions? This is, ideally, what a symmetry between fermions and bosons would be expected to do. However many obstacles seemed, long ago, to prevent supersymmetry from possibly being a fundamental symmetry of Nature. Which fermions and bosons could be related? Is spontaneous supersymmetry breaking possible at all? If yes, where is the corresponding spin-1/2 Goldstone fermion? Supersymmetric theories also involve Majorana fermions, unknown in Nature. And how could we define conserved quantum numbers like B and L, when these are carried by fundamental (Dirac) fermions only, not by bosons? An early attempt to relate the photon with a ``neutrino'' led us to R-invariance and to a new R quantum number carried by the supersymmetry generator, but this ``neutrino'' had to be reinterpreted as a new particle, the photino. We also had to introduce bosons carrying ``fermion numbers'' B and L, which became the squarks and sleptons. This led to the Supersymmetric Standard Model, involving SU(3) x SU(2) x U(1) gauge superfields interacting with chiral quark and lepton superfields, and two doublet Higgs superfields responsible for quark and lepton masses. R-parity, deeply related with B and L conservation laws, appeared as a remnant of the original R-invariance, reduced to a discrete symmetry so that the gravitino and gluinos can acquire masses. We also comment about supersymmetry breaking.

Invited talk at the International Symposium ``30 Years of Supersymmetry'', Minneapolis, October 13-15, 2000. 18 pages, 3 tables