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Feynman Diagram Hoodie

TWO IN, ONE PHOTON, TWO OUT | Pixelated Physics

\[\frac{d\sigma}{d\Omega} = \frac{\alpha^2}{4s}\left(1+\cos^2\theta\right)\]
$54.99 USD
$54.99 USD
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An electron and a positron meet and annihilate. What comes out is a muon and an antimuon. The tree-level Feynman diagram for e⁺e⁻ → γ* → μ⁺μ⁻, wrapped in its exact 1 + cos²θ angular distribution. Two in, two out. Pixel-art unisex hoodie in black; equation, symbols and sources in the physics panel below.

Color
Size

Size guide S–5XL · inches

Shipping calculated at checkout by destinationMade to order, ships in 2–5 business days

Details

Size & fitS–5XL

Unisex Heavy Blend hoodie (Gildan 18500), classic fit.

SizeWidthLengthSleeve
S202733.5
M222834.5
L242935.5
XL263036.5
2XL283137.5
3XL303238.5
4XL323339.5
5XL343440.5

Measurements in inches. Width and length ±1 in, sleeve (from center back) ±0.75 in.

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Delivery times & where we ship

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.

Full refund & replacement policy

The physics

An electron and a positron meet and annihilate. What comes out is a muon and an antimuon.

In between there is a single photon that is never seen. It is virtual: in the centre-of-mass frame it carries the whole collision energy with no momentum, which a real photon cannot do. Richard Feynman’s diagrams, introduced in 1949, turn each such story into one term of the calculation.

At lowest order the answer is short. The muons come out with probability proportional to 1 + cos²θ, twice as likely along the beam line as at right angles to it. That curve is the outline drawn around the diagram.

Time runs up the page. The lines meet at two vertices, each worth a factor of the electric charge.

Two in, one photon, two out.

Equations

\[\frac{d\sigma}{d\Omega} = \frac{\alpha^2}{4s}\left(1+\cos^2\theta\right)\]
\[\sigma = \frac{4\pi\alpha^2}{3s}\quad (\hbar = c = 1,\; \sqrt{s}\gg m_\mu)\]
SymbolMeaningUnit
\(\sigma\) total cross section \(\mathrm{m^2}\)
\(d\sigma/d\Omega\) differential cross section per solid angle \(\mathrm{m^2/sr}\)
\(\alpha\) fine-structure constant, about 1/137 \(\mathrm{1}\)
\(s\) square of the centre-of-mass energy \(\mathrm{GeV^2}\)
\(\theta\) angle between the outgoing muon and the incoming electron \(\mathrm{rad}\)
\(m_\mu\) muon mass \(\mathrm{GeV}\)

Sources

  1. Feynman (1949) Space-Time Approach to Quantum Electrodynamics, Phys. Rev. 76, 769
  2. Peskin & Schroeder, An Introduction to Quantum Field Theory (1995), Sec. 5.1
  3. Griffiths, Introduction to Elementary Particles, 2nd ed., Ch. 7

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