Georgi-Glashow SU(5)

§1 · The claim, in one sentence

Georgi and Glashow proposed in 1974 that three of nature's forces come from one SU(5) force; the minimal SU(5) model predicts a proton decay rate that experiments have ruled out, while larger SU(5) models are still studied.

Why this was rejected

• ▸Ellis, Gaillard, Nanopoulos and Rudaz (1980) estimated the minimal SU(5) proton lifetime at 8 x 10^30 years, uncertain by about two orders of magnitude. Super-Kamiokande (2020) excludes lifetimes below 2.4 x 10^34 years for decay into a positron and a neutral pion.
• ▸Amaldi, de Boer and Furstenau (1991) used LEP coupling measurements to show that a single unification point in the minimal non-supersymmetric model is excluded by more than seven standard deviations.

§2 · Why it might be true

The family stance

Grand unified theories propose that the three forces of the Standard Model come from a single symmetry at very high energy, and leave gravity for a later step. Whether nature follows this pattern is unconfirmed. The proposed merger happens far beyond any accelerator, typically near 10^16 GeV in supersymmetric versions, and quarks and leptons merge into shared multiplets at the same time. The traces at low energy would be fixed relations between the measured coupling strengths and, in most models, a proton that eventually decays.

§2.5 · Evidence

• Each generation of quarks and leptons fits into two SU(5) multiplets, a five and a ten.
• Later models, including supersymmetric SU(5), keep its symmetry group and its assignment of particles, so the framework outlived the minimal model.

§3 · What you'd need to test it

• The proton decays, most visibly into a positron and a neutral pion, with a lifetime the minimal model puts near 10^31 years
• The three Standard Model coupling strengths become equal at a single, very high unification energy
• The weak mixing angle, which sets how the weak and electromagnetic forces blend, is fixed by the symmetry and can be checked against measurement
• Stable superheavy magnetic monopoles can form when the unified symmetry breaks in the early universe, in numbers set by the cosmological history

§4 · Where it breaks

• Super-Kamiokande found no proton decaying into a positron and a neutral pion and set a lifetime limit above 2.4 x 10^34 years, far beyond the minimal prediction.
• Precise LEP data show that the three couplings of the non-supersymmetric model miss a single meeting point by more than seven standard deviations.
• The model offers no reason why the light Higgs doublet stays light while its colored partner, which also drives proton decay, must be superheavy.
• A hot early universe would fill with monopoles. Removing them needs an extra ingredient such as inflation, which Guth linked to monopole suppression in 1981.