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]

[math]\displaystyle{ L = \frac{1}{\sigma}\frac{dN}{dt}. }[/math]

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]

[math]\displaystyle{ L_\mathrm{int} = \int L \ dt. }[/math]

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

↑ ^1.0 ^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. http://cds.cern.ch/record/941318/files/p361.pdf.
↑ Tevatron sets new initial luminosity records, Fermilab Today news archive
↑ Tetsuo Abe et al.: Achievements of KEKB. In: Prog. Theor. Exp. Phys. 03A001, 2013, pp. 1–18, doi:10.1093/ptep/pts102.
↑ "SuperKEKB collider achieves the world's highest luminosity". 26 June 2020. https://www.kek.jp/en/newsroom/2020/06/26/1400/.
↑ LHC Report: The LHC is full!
↑ ^6.0 ^6.1 Heavy-Ion Operation of HL-LHC!
↑ "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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[Herr-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. http://cds.cern.ch/record/941318/files/p361.pdf.

[2] Tevatron sets new initial luminosity records, Fermilab Today news archive

[Abe2013-3] 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!

[:0-6] 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.