fraction

The passage around this formula

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.

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