differential cross section and normalization

Asked by Alan Hernández

Dear Madanalysis experts,

I'm trying to plot a differential cross section. I've read the previous questions https://answers.launchpad.net/madanalysis5/+question/680493 and https://answers.launchpad.net/madanalysis5/+question/244358 I think the solution seems to be very obvious, so please forgive me for this basic question but it is not clear for me.

I have generated N=10000 events and I obtain the cross section 599 pb, so the luminosity is 0.016 fb-1,
then I write

set dat.xsection = 599
set main.lumi = 0.016

and for example, I want the differential cross section dsigma/d PT(t1), I use

plot PT([t1] ) number_of_bins 0 500

I understand the number_of_bins should be chosen correctly to get a normalization mapping the differential cross section. I also understand that finding the correct number of bins is as easy as multiply or divide but I can not recognize what I should multiply (or divide). I think it is related to the lumi 0.016 fb-1. Where should I begin to understand it? Maybe I'm not understanding the relation between the normalization and the mapping to the units pb/GeV. Sorry again for this question.

Thanks in advance

Alan

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Jack Y. Araz
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Best Jack Y. Araz (jackaraz) said :
#1

Hi Alan

So here is how it works, you want your pt range to be between 0-500 GeV so say you want 20 bins that means each bin will be delta pt = 25 GeV so essentially you will have y axis d\sigma/dpt [pb/25 GeV]. I imagine you want the y-axis in pb/ XXX gev so I would say lumi = 1/1000 because ma5 takes it in fb-1 by default and multiplies the xsec with lumi to get the number of events. So N events per bin is bin efficiency X xsec X 1000 X lumi in fb-1. when you set lumi = 1/1000 you will just get the bin eff X xsec. Note that it will still say events in the y-axis but you can go into the folder and modify the histogram labels as you like, ma5 writes a small python/root script for you to modify the plot if needed.

Cheers


Jack Y. Araz

> On Oct 17, 2020, at 2:30 AM, Alan Hernández <email address hidden> wrote:
>
> New question #693494 on MadAnalysis 5:
> https://answers.launchpad.net/madanalysis5/+question/693494
>
> Dear Madanalysis experts,
>
> I'm trying to plot a differential cross section. I've read the previous questions https://answers.launchpad.net/madanalysis5/+question/680493 and https://answers.launchpad.net/madanalysis5/+question/244358 I think the solution seems to be very obvious, so please forgive me for this basic question but it is not clear for me.
>
> I have generated N=10000 events and I obtain the cross section 599 pb, so the luminosity is 0.016 fb-1,
> then I write
>
> set dat.xsection = 599
> set main.lumi = 0.016
>
> and for example, I want the differential cross section dsigma/d PT(t1), I use
>
> plot PT([t1] ) number_of_bins 0 500
>
> I understand the number_of_bins should be chosen correctly to get a normalization mapping the differential cross section. I also understand that finding the correct number of bins is as easy as multiply or divide but I can not recognize what I should multiply (or divide). I think it is related to the lumi 0.016 fb-1. Where should I begin to understand it? Maybe I'm not understanding the relation between the normalization and the mapping to the units pb/GeV. Sorry again for this question.
>
>
> Thanks in advance
>
> Alan
>
> --
> You received this question notification because you are an answer
> contact for MadAnalysis 5.

Revision history for this message
Alan Hernández (alaban7) said :
#2

Hi Jack!

Thank you so much for your answer! let me see if I got it. To obtain the differential cross section in y-axis in units of pb/GeV it is as easy as choose

plot PT([t1] ) 500 0 500

and when I use set.lumi=.001 I'll get only the cross section instead of the differential cross section, right?

Revision history for this message
Benjamin Fuks (fuks) said :
#3

Hi Alan,

Yes, this will work.

Cheers,

Benjamin

Revision history for this message
Alan Hernández (alaban7) said :
#4

Thanks Jack Y. Araz, that solved my question.