SU(5) with a superpartner for every known particle.
Supersymmetric SU(5)
Adding supersymmetry to SU(5) protects the Higgs mass and makes the three force strengths meet at one energy.
Placeholder for a 3D visualisation of Grand Unified Theories. The interactive scene will land in Phase 3. Grand unified theories place the strong, weak and electromagnetic forces inside one larger symmetry with a single coupling strength. Georgi and Glashow proposed a complete model based on the group SU(5) in 1974. Above a very high unification energy the three forces act as one. Below it the symmetry breaks, and the single force splits into the three we measure today. Quarks and leptons share multiplets, so new superheavy force carriers can turn one into the other. That makes the proton unstable, and proton decay is the family's main experimental test. The same theories predict superheavy magnetic monopoles formed in the early universe. Gravity stays outside this unification, so these theories unify the Standard Model forces and leave general relativity as it is.
§1 · The claim, in one sentence
Dimopoulos and Georgi built an SU(5) theory with softly broken supersymmetry in 1981; LEP data in 1991 suggested its couplings could meet at one energy, but the minimal version is now excluded by proton decay searches.
§2 · Why it might be true
Supersymmetry gives every known particle a heavier partner. Dimopoulos and Georgi used it in 1981 to protect the light Higgs doublets inside SU(5) from large quantum corrections to their mass.
The superpartners also change how the three force strengths evolve with energy. Picture three roads that almost meet, and the superpartners bend them into a clean three-way junction. In 1991 LEP data showed the couplings meeting near 10^16 GeV, provided superpartners appear around 1 TeV.
The model also changes how the proton decays. Heavy partners of the Higgs open a faster route, which favors decay into a kaon and an antineutrino. Plain SU(5) favors a positron and a pion instead.
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
- Amaldi, de Boer and Furstenau (1991) found that LEP couplings agree with a single unification scale of 10^16.0 plus or minus 0.3 GeV in the minimal supersymmetric model.
- Langacker and Luo (1991) independently found supersymmetric unification in striking agreement with precision electroweak data for superpartner masses up to about 1 TeV.
- Dimopoulos, Raby and Wilczek (1981) showed that the higher unification scale markedly reduces the predicted nucleon decay rate from heavy gauge bosons.
§3 · What you'd need to test it
- Superpartners of the known particles, which the 1991 coupling fit expected around 1 TeV, an expectation LHC searches have since pushed higher
- The three couplings meet at a single point near 10^16 GeV
- Proton decay mainly into a positive kaon and an antineutrino, driven by dimension-five operators
- Colored Higgs triplets far heavier than the Higgs doublets they are paired with
§4 · Where it breaks
- Murayama and Pierce (2002) showed that the minimal version is excluded by the Super-Kamiokande search for proton decay into a kaon and an antineutrino. Non-minimal supersymmetric SU(5) models remain under study.
- LHC searches at 13 TeV have found no gluinos or squarks, which puts pressure on simple scenarios with superpartners near the 1 TeV the 1991 fit assumed.
- Keeping the Higgs doublets light while their colored triplet partners stay superheavy needs an extremely precise adjustment of parameters, as Dimopoulos and Georgi noted.
Go deeper
Dimension-five operators: Sakai and Yanagida (1982) and Weinberg (1982) showed that supersymmetric unified models allow baryon-number-violating operators of dimension five, which involve the scalar partners of quarks. Weinberg found they make the proton decay too fast in the Dimopoulos-Georgi model unless extra symmetry forbids them.
Exclusion of the minimal model: Murayama and Pierce bound the colored Higgs triplet mass by requiring the couplings to unify. The resulting rate for p to K+ anti-nu exceeds the Super-Kamiokande limit, which reached 5.9 x 10^33 years in 2014. Making the first two generations of superpartners very heavy does not rescue it.
Doublet-triplet splitting: Masiero, Nanopoulos, Tamvakis and Yanagida (1982) built a supersymmetric SU(5) with naturally massless Higgs doublets, and Grinstein (1982) built one with light doublets and heavy colored partners. Flipped SU(5) x U(1) (Antoniadis, Ellis, Hagelin and Nanopoulos 1987) solves the problem with a missing-partner mechanism.
▸§5 · Who built it, and when(6 sources, 6 established)
- EstablishedDimopoulos & Georgi (1981). 'Softly Broken Supersymmetry and SU(5).' Nucl. Phys. B 193, 150
- EstablishedDimopoulos, Raby & Wilczek (1981). 'Supersymmetry and the Scale of Unification.' Phys. Rev. D 24, 1681
- EstablishedAmaldi, de Boer & Furstenau (1991). 'Comparison of grand unified theories with electroweak and strong coupling constants measured at LEP.' Phys. Lett. B 260, 447
- EstablishedLangacker & Luo (1991). 'Implications of precision electroweak experiments for M_t, rho_0, sin^2 theta_W and grand unification.' Phys. Rev. D 44, 817
- EstablishedMurayama & Pierce (2002). 'Not even decoupling can save minimal supersymmetric SU(5).' Phys. Rev. D 65, 055009
- EstablishedSuper-Kamiokande Collaboration, Abe et al. (2014). 'Search for proton decay via p to nu K+ using 260 kiloton-year data of Super-Kamiokande.' Phys. Rev. D 90, 072005
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