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Luminosity (scattering theory)

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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):

L = 1 σ d N d t . {\displaystyle 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·s or the non-SI units of b·s. 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.

A related quantity is integrated luminosity (Lint), which is the integral of the luminosity with respect to time:

L i n t = ∫ L   d t . {\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.

Examples of collider luminosity

Here are a few examples of the luminosity of certain accelerators.

Collider Interaction L (cm·s)
SPS p + p 6.0×10
Tevatron p + p 4.0×10
HERA p + e 4.0×10
LEP e + e 1.0×10
PEP e + e 3.0×10
KEKB e + e 2.1×10
SuperKEKB e + e 2.4×10
LHC p + p 2.1×10
LHC p + Pb 8.5×10
LHC Pb + Pb 6.1×10
HL-LHC p + p 5.0×10

References

  1. ^ Herr, W.; Muratori, B. (2006). "Concept of luminosity" (PDF). In Brandt, D. (ed.). 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.
  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.
  5. LHC Report: The LHC is full!
  6. ^ Heavy-Ion Operation of HL-LHC!
  7. "Vol. 10 (2020): High-Luminosity Large Hadron Collider (HL-LHC): Technical design report". e-publishing.cern.ch. Retrieved 2022-11-30.
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