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Equation 7 · Part 3 · What a Particle Detector Actually Measures

Symbol hatN_bkg

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

What this part means

hatNbN_bkg occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Its job in the formula

hatNbN_bkg occurs above the fraction bar. The numerator is divided by the entire denominator below it.

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 subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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