Collider luminosity ($dN/dt=L\sigma$)

The beam-overlap factor $L$ relating a reaction's cross section $\sigma$ to its ideal production rate $dN/dt$. Integrated collider luminosity $\mathcal{L}=\int Ldt$ has units of inverse area and gives the expected production count $\mathcal{L}\sigma$ when $\sigma$ is constant.

An absolute collider luminosity calibration that scans the transverse separation of two colliding beams while measuring an interaction rate. Known bunch populations and the overlap integral determine the visible monitor cross section. Correlations between horizontal and vertical profiles require a joint overlap treatment.

The time integral of the incident-beam overlap flux, with inverse-area units. For a fixed production cross section, the mean produced event count is $N={\mathcal{L}}_{\mathrm{int}}\sigma$. A selected count includes efficiency and acceptance, often integrated over final-state kinematics. This is distinct from astrophysical radiative luminosity, which has power units.