$$s = \frac{qB\ell^{2}}{8p}, \qquad \frac{\sigma_p}{p} \;\propto\; \frac{p}{B\ell^{2}}$$

Equation 2 · Particle Physics

What a Particle Detector Actually Measures

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Momentum is not measured. Geometry is measured, and momentum is computed from it under an assumed field map. A charged particle in a solenoidal field follows a helix, and the deviation of its path from a straight line over a chord — the sagitta — carries the momentum information: $s = \frac{qB\ell^{2}}{8p}, \qquad \frac{\sigma_p}{p} \;\propto\; \frac{p}{B\ell^{2}}$. Here s is the sagitta, B the field, $\ell$ the path length in the field and p the momentum [ 2 ] . Two consequences follow directly and are worth stating plainly, because they explain most of the architecture of a collider detector.

Meanings in this article

• $s$: the sagitta.
• $B$: the field.
• $p$: the momentum [ 2 ].

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