# 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):[1]

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

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]

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

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 accelerators.[1]

Collider Interaction L (cm−2·s−1)
SPS p + p 6.0×1030
Tevatron[2] p + p 4.0×1032
HERA p + e+ 4.0×1031
LHC[3] p + p 2.1×1034
LEP e + e+ 1.0×1032
PEP e + e+ 3.0×1033
KEKB[4] e + e+ 2.1×1034
SuperKEKB[5] e + e+ 2.4×1034
LHC[6] p + Pb 8.5×1029
LHC[6] Pb + Pb 6.1×1027

## References

1. Herr, W.; Muratori, B. (2006). "Concept of luminosity" (PDF). In Brandt, D. (ed.). CERN Accelerator School: Intermediate Course on Accelerator Physics, Zeuthen, Germany, 15-26 Sep 2003. CERN. pp. 361–378. doi:10.5170/CERN-2006-002. ISBN 978-92-9083-267-6.
2. ^ Tevatron sets new initial luminosity records, Fermilab Today news archive
3. ^ LHC Report: The LHC is full!
4. ^ Tetsuo Abe et al.: Achievements of KEKB. In: Prog. Theor. Exp. Phys. 03A001, 2013, pp. 1–18, doi:10.1093/ptep/pts102.
5. ^ "SuperKEKB collider achieves the world's highest luminosity". 26 June 2020.
6. ^ a b Heavy-Ion Operation of HL-LHC!