Luminosity (scattering theory)

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 (L_int), 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	6.0×10^30
Tevatron	p + p	5.0×10^31
HERA	proton + e^+	4.0×10^31
LHC	p + p	1×10^34
LEP	e^− + e^+	1.0×10^32
PEP	e^− + e^+	3.0×10^33
KEKB	e^− + e^+	1.0×10^34

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.