Glueba: Yang–Mills and the Mass Gap
Nuclear & Particle Physics arc, page 182 of 193. Back to The Pixelated Physics Universe
Who they are
Glueba is a knot of looped gluon flux: made of massless threads, and yet, it seems, heavy.
Glueba is a character of the Nuclear & Particle Physics arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Yang and Mills wrote down gauge theories with non-commuting symmetry groups in 1954. Their quanta are massless at the classical level and interact with each other. In quantum theory, pure SU(3) Yang–Mills (QCD without quarks) is believed to confine and to have a mass gap: the lightest excitation has strictly positive mass. Nobody has proved it. Lattice computer simulations support the gap: Morningstar and Peardon (1999) put the lightest pure-gauge glueball near 1.7 GeV. The Clay Mathematics Institute listed the problem among its Millennium Prize Problems in 2000, in a statement by Jaffe and Witten.
$$ \begin{gathered} \text{Prove: quantum Yang–Mills theory exists on } \mathbb{R}^{4} \text{ with mass gap } \Delta > 0 \\ \text{Lattice (no quarks): lightest glueball} \approx 1.7\ \mathrm{GeV} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $\mathbb{R}^{4}$ | four-dimensional spacetime | 1 |
| $\Delta$ | mass gap: energy of the lightest state above the vacuum | J |
| $\mathrm{GeV}$ | energy unit, 1 GeV = 1.602 × 10⁻¹⁰ J | J |
Honest caveat: This problem is UNSOLVED. The 1.7 GeV figure is a lattice estimate for a theory with no quarks, not a proof and not the gap itself. Glueballs in the real world, with quarks present, have not been conclusively identified.
Status: part of this topic is unsolved, unconfirmed or debated. The text above says which part; treat it as an open question, not settled fact.
Sources
- Yang & Mills (1954) Conservation of Isotopic Spin and Isotopic Gauge Invariance, Phys. Rev. 96, 191
- Jaffe & Witten, Quantum Yang–Mills Theory, Clay Mathematics Institute official problem description
- Morningstar & Peardon (1999) Glueball spectrum from an anisotropic lattice study, Phys. Rev. D 60, 034509
Crossovers
Glueba meets Backrowena (Spontaneous Symmetry Breaking). Backrowena's symmetry breaking gives gauge bosons mass in the electroweak theory, by way of the Higgs field. Glueba's mass gap would have to come from somewhere else: pure Yang–Mills has no Higgs, and proving its gap is an unsolved problem.
Glueba meets Hadron Brawler (Strong Nuclear Force / Quantum Chromodynamics). Hadron Brawler's confinement is observed. Glueba asks for proof that pure Yang–Mills theory has a mass gap, which is unsolved.
Glueba meets Theta Warden (Strong CP Problem). Theta Warden's angle is a term in the theory of the strong force. Glueba's mass gap is a property of the same gauge theory. Both are unsolved questions about QCD.
Wear the lore
Concept keywords: Yang–Mills and the Mass Gap, Glueba, Nuclear & Particle Physics, physics lore, Pixelated Physics