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]

L=1σdNdt.

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]

Lint=∫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
LEP | e− \+ e+ | 1.0×1032
PEP | e− \+ e+ | 3.0×1033
KEKB[3] | e− \+ e+ | 2.1×1034
SuperKEKB[4] | e− \+ e+ | 2.4×1034
LHC[5] | p \+ p | 2.1×1034
LHC[6] | p \+ Pb | 8.5×1029
LHC[6] | Pb \+ Pb | 6.1×1027
HL-LHC[7] | p \+ p | 5.0×1034

## References

1. ↑ 1.0 1.1 1.2 1.3 1.4 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. CERN. pp. 361–378. doi:10.5170/CERN-2006-002. ISBN 978-92-9083-267-6. https://cds.cern.ch/record/941318/files/p361.pdf.
2. ↑ Tevatron sets new initial luminosity records, Fermilab Today news archive
3. ↑ Tetsuo Abe et al.: Achievements of KEKB. In: Prog. Theor. Exp. Phys. 03A001, 2013, pp. 1–18, doi:10.1093/ptep/pts102.
4. ↑ "SuperKEKB collider achieves the world's highest luminosity". 26 June 2020. https://www.kek.jp/en/newsroom/2020/06/26/1400/.
5. ↑ LHC Report: The LHC is full!
6. ↑ 6.0 6.1 Heavy-Ion Operation of HL-LHC!
7. ↑ "Vol. 10 (2020): High-Luminosity Large Hadron Collider (HL-LHC): Technical design report" (in en-US). https://e-publishing.cern.ch/index.php/CYRM/issue/view/127.

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