Formula for computing MT_MET

Hi Felix

First of all, please use v1.9. When you set MT_MET(X Y); ma5 first calculates vector sum of the 4 momenta of X and Y this you can see in `ANALYSIS_X/Build/SampleAnalyzer/User/Analyzer/user.cpp` and then this "combined vector system" is fed into the function that you referred.

```
const MAfloat32 mt_met(const MALorentzVector& MET) const
{
  // Computing ET sum
  MAfloat64 ETsum = sqrt( momentum_.M()*momentum_.M() +
                       momentum_.Pt()*momentum_.Pt() ) + MET.Pt();

  // Computing PT sum
  MALorentzVector pt = momentum_ + MET;

  MAfloat64 value = ETsum*ETsum - pt.Pt()*pt.Pt();
  if (value<0) return 0;
  else return sqrt(value);
}
```

here `momentum_` is simply combined X+Y 4-vector.

Cheers

—
Jack Y. Araz

> On Apr 21, 2021, at 3:25 PM, Felix Wilsch <email address hidden> wrote:
>
> [EXTERNAL EMAIL]
>
> New question #696672 on MadAnalysis 5:
> https://answers.launchpad.net/madanalysis5/+question/696672
>
> Hi,
>
> I am using MadAnalysis 1.8.45 to cross check some other python analysis code for a LHCO file.
>
> I am plotting the transverse mass of a di-tau system including the missing energy, i.e. MT_MET(ta[1] ta[2]). But the spectrum obtained this way disagrees with the one obtained in my other analysis code.
>
> Therefore, I would like to ask how MT_MET is calculated in MadAnlysis. According to
> https://bugs.launchpad.net/madanalysis5/+bug/1782140
> the formula used to calculate MT_MET is
>
> MT^2 = (sum ET^2) - (sum PT^2) [PDG2018, (47.50)].
>
> However, from the definition of mt_met in the file
> tools/SampleAnalyzer/Commons/DataFomat/ParticleBaseFormat.h
> it appears to me that the quantity computed in this particular case is rather
>
> MT^2 = (ET_ditau^2 + ET_miss^2) – (sum PT^2),
>
> where
>
> ET_ditau^2 = (P_tau1 + P_tau2)^2 + (PT_tau1 + PT_tau2)^2
>
> and not
>
> MT^2 = (ET_tau1^2 + ET_tau2^2 + ET_miss^2) – (sum PT^2).
>
> Many thanks,
>
> Felix
>
>
> --
> You received this question notification because you are an answer
> contact for MadAnalysis 5.

Hi Jack,

Thank you very much for your answer, but in this case the formula you are using seems not correct to me. If I understand correctly, the ETsum should be

ETsum = ET(X) + ET(Y) + MET.Pt()

where ET(X) stands for the ET calculated for the 4-momentum X. However, according to your answer, what is computed with

```
MAfloat64 ETsum = sqrt( momentum_.M()*momentum_.M() +
                       momentum_.Pt()*momentum_.Pt() ) + MET.Pt();
```

is instead the following:

ETsum = ET(X+Y) + MET.Pt()

which is not giving the same result as the first equation.

Do you agree?

Many thanks again.

Cheers,
Felix

Hi Jack,

Thanks again for your answer.
I understand now, that MadAnalysis does calculate the MT for a “vector system” which is of course fine and correct as it is just another way of defining the observable.

My confusion was due to the formula for MT

MT^2 = (sum ET^2) - (sum PT^2) [PDG2018, (47.50)]

given in this original post (https://bugs.launchpad.net/madanalysis5/+bug/1782140). Based on that I did not assume that MadAnalysis is actually looking at the “vector system”.
But now everything is clear.

Thanks again.

Cheers,
Felix

Thanks Jack Y. Araz, that solved my question.