# Luminosity (scattering theory)

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In scattering theory and accelerator physics, luminosity (L) is the ratio of the number of events detected (N) in a certain time (t) to the interaction cross-section (σ):[1]

$L = \frac{1}{\sigma}\frac{dN}{dt}.$

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.[1]

A related quantity is integrated luminosity (Lint), which is the integral of the luminosity with respect to time:[1]

$L_\mathrm{int} = \int L \ dt.$

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.[1]

## Examples of collider luminosity

Here are a few examples of the luminosity of certain experiments.[1]

Collider Interaction L (cm−2·s−1)
SPS p + p 6.0×1030
Tevatron p + p 5.0×1031
HERA proton + e+ 4.0×1031
LHC p + p 1×1034
LEP e + e+ 1.0×1032
PEP e + e+ 3.0×1033
KEKB e + e+ 1.0×1034

## References

1. Herr, W.; Muratori, B. (2006). "Concept of luminosity". In Brandt, D. CERN Accelerator School: Intermediate Course on Accelerator Physics, Zeuthen, Germany, 15-26 Sep 2003 (PDF). CERN. pp. 361–378. doi:10.5170/CERN-2006-002. ISBN 978-92-9083-267-6.