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Supersymmetric SU(5) vs SO(10) Unification

Grand Unified Theories · within family

	Supersymmetric SU(5) Frontier	SO(10) Unification Frontier
Proposed	1981	1975
Key figures	Savas Dimopoulos, Howard Georgi	Harald Fritzsch, Peter Minkowski, Howard Georgi
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.	Fritzsch and Minkowski proposed in 1975 that SO(10) can unify the forces and place every particle of a generation, a right-handed neutrino included, in a single multiplet.
Predictions	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	Every generation contains a right-handed neutrino, and ordinary neutrino masses come from the seesaw mechanism A gauged B-L symmetry, the difference between baryon and lepton number, breaks at a scale tied to the heavy neutrino masses Most versions predict proton decay, with a lifetime and dominant channel set by the breaking route; routes that push unification toward 10^18 GeV put it beyond current searches Some supersymmetric SO(10) constructions can suppress the Higgsino-driven proton decay that troubles supersymmetric SU(5)
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.	Minimal models need large Higgs multiplets, such as a 126, to give neutrinos their seesaw masses, and the group does not fix the Higgs content. In most versions the heavy right-handed neutrinos sit far above collider energies, so the seesaw is tested only indirectly. Non-supersymmetric versions rely on intermediate breaking stages to keep the proton stable for long enough, which adds new scales chosen by hand.
Key unresolved problem	The doublet-triplet problem: the Higgs doublets must stay light while their colored partners sit near the unification scale, and the minimal model manages this only by fine-tuning.	The breaking route: SO(10) can descend to the Standard Model by several paths, and each path changes the unification energy, the proton lifetime and the neutrino masses.
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Supersymmetric SU(5)

1981 · Frontier

SO(10) Unification

1975 · Frontier

Proposed

1981

1975

Key figures

Savas Dimopoulos, Howard Georgi

Harald Fritzsch, Peter Minkowski, Howard Georgi

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.

Fritzsch and Minkowski proposed in 1975 that SO(10) can unify the forces and place every particle of a generation, a right-handed neutrino included, in a single multiplet.

Predictions

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

Every generation contains a right-handed neutrino, and ordinary neutrino masses come from the seesaw mechanism
A gauged B-L symmetry, the difference between baryon and lepton number, breaks at a scale tied to the heavy neutrino masses
Most versions predict proton decay, with a lifetime and dominant channel set by the breaking route; routes that push unification toward 10^18 GeV put it beyond current searches
Some supersymmetric SO(10) constructions can suppress the Higgsino-driven proton decay that troubles supersymmetric SU(5)

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.

Minimal models need large Higgs multiplets, such as a 126, to give neutrinos their seesaw masses, and the group does not fix the Higgs content.
In most versions the heavy right-handed neutrinos sit far above collider energies, so the seesaw is tested only indirectly.
Non-supersymmetric versions rely on intermediate breaking stages to keep the proton stable for long enough, which adds new scales chosen by hand.

Key unresolved problem

The doublet-triplet problem: the Higgs doublets must stay light while their colored partners sit near the unification scale, and the minimal model manages this only by fine-tuning.

The breaking route: SO(10) can descend to the Standard Model by several paths, and each path changes the unification energy, the proton lifetime and the neutrino masses.

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