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A twist on broken \(\mathrm{U}(3) \times \mathrm{U}(3)\) supersymmetry. (English) Zbl 07899156

Summary: What symmetry breaking would be required for gauginos from a supersymmetric theory to behave like left-handed quarks of the Standard Model? Starting with a supersymmetric \(\mathrm{SU}(3) \times\mathrm{SU}(3) \times \mathrm{U}(1) \times \mathrm{U}(1)\) gauge theory, the 18 adjoint-representation gauginos are replaced with 2 families of 9 gauginos in the \((3,3^*)\) representation of the group. After this explicit breaking of supersymmetry, two-loop quadratic divergences still cancel at a unification scale. Coupling constant unification is supported by deriving the theory from an \(\mathrm{SU}(3) \times\mathrm{SU}(3) \times\mathrm{SU}(3) \times \mathrm{SU}(3)\) Grand Unified Theory (GUT). \(\operatorname{Sin}^2\) of the Weinberg angle for the GUT is 1/4 rather than 3/8, leading to a lower unification scale than usually contemplated, \(\sim 10^9\) GeV. After spontaneous gauge symmetry breaking to \(\mathrm{SU}(3) \times \mathrm{SU}(2) \times \mathrm{U}(1)\), the theory reproduces the main features of the Standard Model for two families of quarks and leptons, with gauginos playing the role of left-handed quarks and sleptons playing the role of the Higgs boson. An extension to the theory is sketched that incorporates the third family of quarks and leptons.

MSC:

81-XX Quantum theory
Full Text: DOI

References:

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