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1 ABOUT THE ORIGINS OF THE SUPERSYMMETRIC STANDARD MODEL a ∗

By P. Fayet

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 Goldstone fermion? Supersymmetric theories also 2 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)×SU(2)×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 origina

Year: 2001
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