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 on time on 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]

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

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
LEP	e− + e+	1.0×1032
PEP	e− + e+	3.0×1033
KEKB[3]	e− + e+	2.1×1034
SuperKEKB[4]	e− + e+	5.1×1034
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