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Equation 7 · Part 4 · What a Particle Detector Actually Measures

Symbol A

σ^  =  Nobs−N^bkgA ε L,\hat{\sigma} \;=\; \frac{N_{\mathrm{obs}} - \hat{N}_{\mathrm{bkg}}}{\mathcal{A}\,\varepsilon\,\mathcal{L}} ,
A\mathcal{A}

What this part means

A occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Its job in the formula

A occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

This is where the corrections come from. A published cross-section has roughly the structure σ^  =  Nobs−N^bkgA ε L\hat{\sigma} \;=\; \frac{N_{\mathrm{obs}} - \hat{N}_{\mathrm{bkg}}}{\mathcal{A}\,\varepsilon\,\mathcal{L}} . where the numerator is an observed count minus an estimated background and the denominator contains acceptance, efficiency and integrated luminosity. Of the four quantities on the right, only the raw observed count is straightforwardly measured. The background estimate, the acceptance and the efficiency are all obtained from, or heavily constrained by, simulation.

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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