# Luminosity (scattering theory)

In scattering theory and accelerator physics, luminosity (L) is the ratio of the number of events detected (dN) in a certain period of time (dt) to the cross-section (σ):

$L={\frac {1}{\sigma }}{\frac {dN}{dt}}.$ It has the dimensions of events per time per area, and is usually expressed in the cgs units of cm−2·s−1 or the non-SI units of b−1·s−1. In practice, L is dependent on the particle beam parameters, such as beam width and particle flow rate, as well as the target properties, such as target size and density.

A related quantity is integrated luminosity (Lint), which is the integral of the luminosity with respect to time:

$L_{\mathrm {int} }=\int L\ dt.$ The luminosity and integrated luminosity are useful values to characterize the performance of a particle accelerator. In particular, all collider experiments aim to maximize their integrated luminosities, as the higher the integrated luminosity, the more data is available to analyze.

## Examples of collider luminosity

Here are a few examples of the luminosity of certain accelerators.

Collider Interaction L (cm−2·s−1)
SPS p + p 6.0×1030
Tevatron p + p 4.0×1032
HERA p + e+ 4.0×1031
LHC p + p 2.1×1034
LEP e + e+ 1.0×1032
PEP e + e+ 3.0×1033
KEKB e + e+ 2.1×1034
SuperKEKB e + e+ 2.4×1034
LHC p + Pb 8.5×1029
LHC Pb + Pb 6.1×1027