Luminosity (particle)

The luminosity, in the context of particle scattering and particle accelerators, is the ratio between (detected) scattering events per unit time N˙\dot{N} and the Cross section σ\sigma of the event:

L=N˙σ[collisionscm2 s]\mathcal{L}=\frac{\dot{N}}{\sigma}\quad\left[ \frac{\text{collisions}}{\text{cm}^{2}\ \text{s}} \right]

If we call ΦB\Phi_{B} the flux of incident particles from a particle beam and NTN_{T} the number of particles in the target, we can also say

L=ΦBNT\mathcal{L}=\Phi_{B}N_{T}

The integral of the luminosity over a period of time is called the integrated luminosity:

Lint=∫t1t2L dt\mathcal{L}_\text{int}=\int_{t_{1}}^{t_{2}} \mathcal{L}\ dt

These quantities determine how many collisions a particle accelerator is capable of creating and as such the amount of data being generated for analysis. The product of integrated luminosity and cross section is the number of collisions measured:

Ncoll=LintσN_\text{coll}=\mathcal{L}_\text{int}\sigma

As such, they are useful metrics to measure the performance of an accelerator: more luminosity means more data. Proton-proton collisions at the LHC at CERN can reach 1034 collisions cm−2 s−110^{34}\text{ collisions}\text{ cm}^{-2}\text{ s}^{-1}.