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Published equation contexts

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

Why this formula appears here

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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NobsN_{\mathrm{obs}}

Symbol N_obs

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

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N^bkg\hat{N}_{\mathrm{bkg}}

Symbol hatN_bkg

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

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A\mathcal{A}

Symbol A

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

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ε\varepsilon

Symbol varepsilon

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

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L\mathcal{L}

Symbol L

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

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Nobs−N^bkgN_{\mathrm{obs}} - \hat{N}_{\mathrm{bkg}}

Numerator: N_obs - hatN_bkg

The complete quantity above the fraction bar.

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A ε L\mathcal{A}\,\varepsilon\,\mathcal{L}

Denominator: AvarepsilonL

The complete quantity below the fraction bar; it must be nonzero for this division.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

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

Equation 7 · 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.

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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