Calculating Cross Sections from Events + Luminosity

In summary, the conversion between the number of events and luminosity in a cross section can be done through dimensional analysis. The proportionality constant, or the cross section, is determined by the number of scatterers and the dynamics of the scattering event. The term "integrated luminosity" is often used interchangeably with "luminosity" in informal discussions, but for formal publications, it should always be referred to as "integrated luminosity".
  • #1
Jodahr
10
0
Hello,

How can I convert the number of events + the luminosity in a cross section?

I think this must be trivial...

thanks..
 
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  • #2
By dimensional analysis if you know the dimensions of each of the quantities involved.
 
  • #3
ah..lol..I think it's just...events = sigma * luminosity...right?
 
  • #4
Ok, how did you conclude that?
 
  • #5
hm?...I wanted to get a cross section limit for monojet signals...and I always found only the luminosity and the events...and event has no dimension..luminosity is inverse barn and XS is barn..so..if I really only need those paramaters..then it's trivial...I thought maybe I also need sth else...
 
  • #6
Usually luminosity is a flux density, with dimension L-2 T-1, instead of dimension L-2. Thus, what we get as a result proportional to luminosity is not # of events, but, instead, an event rate (# events per unit time) with a dimension T-2.

The proportionality constant must have a dimension L2. However, the proportionality constant should be proportional to the number of scatterers, which is dimensionless. The proportionality constant corresponding to ONE scatterer is a characteristic of the dynamics of the scattering event, and is customarily referred to as a cross-section.

What I tried to say could be summarized as:
[tex]
\frac{d N_{\mathrm{reactons}}}{d t} = K \, \mathcal{L}
[/tex]
where [itex]\mathcal{L}[/itex] is the luminosity of the incident beam, and:
[tex]
K = N_{\mathrm{scatters}} \, \sigma
[/tex]
where [itex] N_{\mathrm{scatters}}[/itex] is the total number of scatterers in the target, and [itex]\sigma[/itex] is the total scattering cross-section for a single scattering event.
 
  • #7
Thanks a lot...
but I think in the paper I have read they have used the integrated luminosity...because they have used exactly the dimension "inverse barn"...
 
  • #8
"Integrated luminosity" is sometimes just called "luminosity" - wrong, but shorter, and fine for talks/meetings and so on, where it is clear what is meant. In papers and other publications, it should be called "integrated luminosity" everywhere.
 

1. How do you calculate the cross section of an event?

The cross section of an event is calculated by dividing the number of observed events by the product of the luminosity and the efficiency of the detector. This is known as the formula for the cross section: σ = N / (L × ε), where N is the number of observed events, L is the luminosity, and ε is the detector efficiency.

2. What is luminosity in the context of calculating cross sections from events?

Luminosity is a measure of how many collisions occur per unit time in a particle accelerator. It takes into account the number of particles in the beams, as well as their size and speed. Luminosity is an important factor in calculating cross sections because it determines the rate at which events are produced.

3. How does detector efficiency affect the calculation of cross sections?

Detector efficiency refers to the likelihood that an event will be detected by the particle detector. If an event goes undetected, it will not be included in the calculation of the cross section. Therefore, a higher detector efficiency will result in a more accurate cross section measurement.

4. Can the cross section be calculated for any type of event?

Yes, the cross section can be calculated for any type of event that is being observed in a particle accelerator. This includes events such as collisions between protons or electrons, as well as decays of particles into other particles.

5. How is the uncertainty in the cross section calculation determined?

The uncertainty in the cross section calculation is determined by taking into account the statistical and systematic uncertainties in the measurement. Statistical uncertainties arise from the limited number of events observed, while systematic uncertainties are caused by factors such as detector limitations or calibration errors. These uncertainties are typically expressed as a percentage of the measured cross section.

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