← All parts of this equation

Equation 7 · Part 11 · What a Particle Detector Actually Measures

Numerator: N_obs - hatN_bkg

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

What this part means

The complete quantity above the fraction bar.

Its job in the formula

NoN_obs - 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.

Read this part in the article →

Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

Open the illustrated fractions: division written vertically guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.