Calculating Cross Sections from Events + Luminosity

[Jodahr]

Hello,

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

I think this must be trivial...

thanks..

 

[Dickfore]

By dimensional analysis if you know the dimensions of each of the quantities involved.

 

[Jodahr]

ah..lol..I think it's just...events = sigma * luminosity...right?

 

[Dickfore]

Ok, how did you conclude that?

 

[Jodahr]

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...

 

[Dickfore]

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:
$$\frac{d N_{\mathrm{reactons}}}{d t} = K \, \mathcal{L}$$
where $\mathcal{L}$ is the luminosity of the incident beam, and:
$$K = N_{\mathrm{scatters}} \, \sigma$$
where $N_{\mathrm{scatters}}$ is the total number of scatterers in the target, and $\sigma$ is the total scattering cross-section for a single scattering event.

 

[Jodahr]

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"...

 

[mfb]

"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.