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={\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 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