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):

L =

        1
        σ
      
    
    
      
        
          d
          N
        
        
          d
          t
        
      
    
    .
  

{\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.

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.

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