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Hadron Brawler

Strong Nuclear Force / Quantum Chromodynamics Physics

\[V(r) = -\frac{4}{3}\frac{\alpha_s \hbar c}{r} + \sigma r\]
$29.99 USD
$29.99 USD
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Size guide S–5XL · inches

Try to pull a quark loose and the universe refuses. Quantum chromodynamics: gluons bind quarks so tightly they are never seen alone, only inside hadrons like protons. Hadron Brawler wears it in pixel art on a unisex tee. The physics panel below has the equation, every symbol and the sources.

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Details

Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

SizeWidthLengthSleeve
S182815.1
M202916.5
L223018
XL243119.5
2XL263221
3XL283322.4
4XL303423.7
5XL323525

Zum Größenvergleich: Größe M ist 20 in (50.80 cm) breit, etwa 3.143 × 1034 Planck-Längen (lP = 1.616255 × 10−35 m). Ein Maßband geht schneller.

Measurements in inches, ±1.5 in tolerance.

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Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

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The physics

The Cornell potential describes the force between a heavy quark and antiquark: Coulomb-like at short range, with an extra term that grows steadily with distance. That linear term, like a stretched string, is why quarks can never be pulled out of a hadron alone.

Hadron Brawler cannot lose a quark. He has tried.

Inside a proton the strong force behaves unlike any other. The formula on this page is the Cornell potential, fitted in 1975 by Estia Eichten and colleagues at Cornell to charmonium, a newly discovered pairing of a charm quark with its antiquark. It has two terms. At short range the first dominates: a pull shaped like electric attraction, but weak, because the strong coupling αs shrinks at short distances. That shrinking is asymptotic freedom, and it earned David Gross, David Politzer and Frank Wilczek the 2004 Nobel Prize. Up close, quarks rattle around almost freely.

Pull them apart and the second term takes over: σr, energy rising in a straight line with distance. The gluon field between the quarks does not spread out the way an electric field does. It narrows into a tube, and the tube costs about the same energy for every extra femtometre, roughly a giga-electronvolt per femtometre. That is a steady tension of around sixteen tonnes-force, acting across something smaller than a proton. A pull that never weakens means the quark never gets out.

What you get instead is a brawl. Once the tube holds enough energy, it becomes cheaper for the field to create a new quark and antiquark than to keep stretching. The tube snaps, and each broken end takes one of the new quarks. Hit a proton hard enough in a collider and this happens again and again, and what comes out is not free quarks but tight sprays of ordinary particles, called jets.

Colour charge, the property behind all of this, was proposed in 1964–65; quantum chromodynamics took its modern form in 1973. Nobody has ever isolated a single quark.

Hadron Brawler swings. The rope breaks into more rope.

Equations

\[V(r) = -\frac{4}{3}\frac{\alpha_s \hbar c}{r} + \sigma r\]
SymbolMeaningUnit
\(V(r)\) static quark–antiquark potential (Cornell form) \(\mathrm{J}\)
\(\alpha_s\) strong coupling \(\mathrm{1}\)
\(\hbar c\) reduced Planck constant × c \(\mathrm{J·m}\)
\(r\) quark separation \(\mathrm{m}\)
\(\sigma\) string tension (quoted in GeV/fm) \(\mathrm{J/m}\)

Sources

  1. Eichten et al. (1975) Spectrum of Charmed Quark-Antiquark Bound States, PRL 34, 369
  2. PDG 2024 review — Quantum Chromodynamics
  3. Encyclopaedia Britannica — Strong force
  4. NobelPrize.org — The Nobel Prize in Physics 2004 (asymptotic freedom)

Source Eichten, E. et al. (1975). Spectrum of Charmed Quark-Antiquark Bound States. Physical Review Letters 34, 369–372.doi.org/10.1103/PhysRevLett.34.369

Field notes

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