Sigmarel: Five Sigma Discovery
Measurement, Noise & the Lab arc, page 127 of 193. Back to The Pixelated Physics Universe
Who they are
Sigmarel has one line, and says it often: “1 in 3.5 million or it didn't happen.”
Sigmarel is a character of the Measurement, Noise & the Lab arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
The particle-physics discovery convention is 5σ, a one-sided p-value of about 2.9 × 10⁻⁷, roughly 1 in 3.5 million.
$$ \begin{gathered} Z = \Phi^{-1}(1 - p) \\ Z = 5 \;\Rightarrow\; p \approx 2.87 \times 10^{-7} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $Z$ | significance (number of σ) | — |
| $p$ | one-sided p-value | — |
| $\Phi$ | standard Gaussian cumulative distribution | — |
Sources
- Particle Data Group, R. L. Workman et al., Prog. Theor. Exp. Phys. 2022, 083C01, 'Statistics' review
Crossovers
Sigmarel meets Enrayne (N-Ray Delusion). Enrayne saw N-rays that no one else could reproduce. Sigmarel guards the gate that keeps such claims out: a 5σ discovery threshold, with blind checks and independent experiments behind it.
Sigmarel meets Trialsworn (Look-Elsewhere Effect). Sigmarel's 5σ local bump may not survive Trialsworn: if you searched many places, the global significance is lower. That is why discovery claims report both.
Sigmarel meets Diphantom (750 GeV Diphoton Excess). Diphantom's 750 GeV bump excited physicists in 2015, but it never reached Sigmarel's 5σ and faded with more data in 2016. The gate held.
Wear the lore
Concept keywords: Five Sigma Discovery, Sigmarel, Measurement, Noise & the Lab, physics lore, Pixelated Physics