Leptons treated as quarks that carry a fourth color.
Pati-Salam Model
Lepton number is a fourth color, so each lepton sits beside three quarks in one shared 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
Pati and Salam proposed in 1974 that lepton number is a fourth color charge, which puts quarks and leptons in shared families linked by new force carriers.
§2 · Why it might be true
Quarks come in three colors, the charges of the strong force. Pati and Salam proposed in 1974 that leptons carry a fourth color. Quarks and leptons of one generation then form a single family of 16 particles.
Picture a paint box that had three colors and gains a fourth. Mixing across all four needs new force carriers, called leptoquark bosons, that carry both quark and lepton number. Exchanging one turns a quark into a lepton.
The model treats left-handed and right-handed particles alike at high energy, which brings in a right-handed partner of the W boson. It combines several symmetry groups instead of one, so it is a partial unification. It often reappears as a middle stage when SO(10) breaks down to the Standard Model.
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
- The model fits the 16 quarks and leptons of a generation, a right-handed neutrino included, into one left-handed and one right-handed multiplet. SO(10) later joined the two into a single 16.
- Its left-right structure offers a reason why neutrinos are so light. Mohapatra and Senjanovic (1980) tied that lightness to the large mass of the right-handed W.
- Realistic SO(10) models break through a Pati-Salam stage, so the model survives as a step inside larger unified theories.
§3 · What you'd need to test it
- Vector leptoquark bosons drive rare decays that the Standard Model forbids, such as a long-lived neutral kaon decaying into a muon and an electron
- A heavy right-handed W boson carries weak interactions of right-handed particles
- In the minimal seesaw realization, neutrino masses are tied to the right-handed W mass: the heavier that boson, the lighter the neutrinos
§4 · Where it breaks
- In the conventional model, rare kaon decays force the symmetry to break above the PeV scale, far out of collider reach. The exact bound depends on how quarks pair with leptons, and general fermion mixing still leaves leptoquarks above 86 TeV.
- Pati-Salam combines three groups, each with its own coupling, so the forces stay partly separate unless the model sits inside a larger group.
- Bringing leptoquarks down to the TeV scale needs extra vectorlike fermions that the original model did not have.
Go deeper
Gauge group: the 1974 paper gauges a subgroup of SU(4)_L x SU(4)_R x SU(4') and puts fermions in 16-fold chiral multiplets. The form used today is SU(4)_C x SU(2)_L x SU(2)_R. SU(4)_C contains SU(3) color and U(1)_B-L, so B-L becomes a gauge charge, and each 16 contains a right-handed neutrino.
Rare-decay limits: Valencia and Willenbrock (1994) showed that rare K, pi and B decays are the most sensitive probes, depending on which quark generation pairs with which lepton. Calibbi, Crivellin and Li (2018) avoid the PeV bound by adding vectorlike fermions, which allows TeV-scale leptoquarks studied in connection with B-meson anomalies.
Left-right symmetry and the seesaw: Mohapatra and Pati (1975) developed the left-right symmetric gauge structure. In SU(2)_L x SU(2)_R x U(1) models, Mohapatra and Senjanovic (1980) derived m_nu ~ m_e^2 / (g m_W_R) for each generation.
Cross-reference: the Non-Commutative Geometry family in this chapter derives the same gauge group from a spectral triple (Spectral Pati-Salam Unification, Chamseddine, Connes and van Suijlekom 2013). This variant covers the 1974 field theory and its tests. The NCG variant covers why spectral geometry might select it.
▸§5 · Who built it, and when(5 sources, 5 established)
- EstablishedPati & Salam (1974). 'Lepton Number as the Fourth Color.' Phys. Rev. D 10, 275
- EstablishedMohapatra & Pati (1975). 'Left-Right Gauge Symmetry and an Isoconjugate Model of CP Violation.' Phys. Rev. D 11, 566
- EstablishedMohapatra & Senjanovic (1980). 'Neutrino Mass and Spontaneous Parity Nonconservation.' Phys. Rev. Lett. 44, 912
- EstablishedValencia & Willenbrock (1994). 'Quark-lepton unification and rare meson decays.' Phys. Rev. D 50, 6843
- EstablishedCalibbi, Crivellin & Li (2018). 'Model of vector leptoquarks in view of the B-physics anomalies.' Phys. Rev. D 98, 115002
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