One symmetry that holds a whole generation of matter.
SO(10) Unification
A larger symmetry, SO(10), fits a whole generation of matter, including a right-handed neutrino, into one 16-member multiplet.
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
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.
§2 · Why it might be true
SU(5) spreads each generation of matter across two multiplets. SO(10) is a larger symmetry that contains SU(5), and it holds the whole generation in one 16-member multiplet. Fritzsch and Minkowski studied SO(10) among several candidate groups in 1975.
The sixteenth member is a right-handed neutrino, which SO(10) requires and the Standard Model leaves out. Give it a very large mass, and the seesaw mechanism makes the ordinary neutrinos extremely light. Like a seesaw, the heavier one side gets, the lighter the other becomes.
SO(10) also contains the Pati-Salam group, so it can break in stages on its way to the Standard Model. Each route shifts the unification energy, and with it the expected proton lifetime.
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
- One spinor multiplet of SO(10) holds exactly the quarks and leptons of a generation plus a right-handed neutrino.
- Bludman, Kennedy and Langacker (1992) argued that the small neutrino masses implied by solar neutrino oscillations are most naturally explained by unified theories with a seesaw.
- Heterotic string theory compactifications can produce quarks and leptons as three 16-plets of SO(10), which ties the group to string model building.
§3 · What you'd need to test it
- 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)
§4 · Where it breaks
- 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.
Go deeper
Group structure: SO(10) contains SU(5) x U(1)_X and SU(4)_C x SU(2)_L x SU(2)_R, both of which contain U(1)_B-L. Under SU(5) the spinor 16 splits into 10 + 5-bar + 1, and the singlet is the right-handed neutrino.
Minimal Yukawa sector: Babu and Mohapatra (1993) coupled fermions to one complex 10 and one 126 of Higgs. The Standard Model doublet in the 126 picks up an induced vacuum value, which corrects the bad relations m_d = m_e and m_s = m_mu and links the Majorana neutrino mass matrix to the charged-fermion sector.
Proton decay in supersymmetric SO(10): Babu and Barr (1993) used the adjoint Higgs for doublet-triplet splitting, which turns dangerous dimension-five operators into dimension-six ones. Their analysis keeps the sin^2 theta_W prediction and argues that SU(5) cannot reach the same suppression without fine-tuning.
Breaking chains: Bandyopadhyay, Brahmachari and Raychaudhuri (2016) show how a TeV-scale right-handed W inside SO(10) selects one breaking order (left-right parity, then SU(4)_C, then SU(2)_R). In that chain unification moves to 10^18 GeV and proton decay drops out of reach.
▸§5 · Who built it, and when(5 sources, 4 established, 1 needs verification)
- EstablishedFritzsch & Minkowski (1975). 'Unified Interactions of Leptons and Hadrons.' Annals Phys. 93, 193
- Needs verificationGeorgi (1975). 'The State of the Art: Gauge Theories.' AIP Conf. Proc. 23, 575
- EstablishedBabu & Mohapatra (1993). 'Predictive neutrino spectrum in minimal SO(10) grand unification.' Phys. Rev. Lett. 70, 2845
- EstablishedBabu & Barr (1993). 'Natural suppression of Higgsino mediated proton decay in supersymmetric SO(10).' Phys. Rev. D 48, 5354
- EstablishedBandyopadhyay, Brahmachari & Raychaudhuri (2016). 'Implications of the CMS search for W_R on grand unification.' JHEP 02, 023
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