Tight-to-Loose ratio method: QCD Background

[ChrisVer]

I was reading this document from CMS:
https://cds.cern.ch/record/2002036?ln=en
But I have some problems understanding how they calculated the bckg coming from the QCD.
My questions come from Sec.6 Background, so you can jump and have a quick glimpse over it (?).

They used the tight-to-loose ratio by the ABCD method. You have four regions A,B,C,D.
The QCD regions C,D are obtained with applying (tight) or not (loose) isolation criteria on your jets and probably some choice on your discriminant for the analysis variable $p_T^{\tau}/E_T^{miss}$ , I think it should be >1.5 to get the QCD enriched data.
By that it says you can determine the tight-to-loose ratio, which you use as a weight for your signal events at A the QCD template (?) to obtain your background (B).

a) However I don't understand how this method actually works to find the QCD background. What is making the tight-to-loose ratio useful as a weight? I also don't understand what is the QCD template signal.

b) Also why the ratio is called tight-to-loose while in the text they give it as $R_{TTL}= N_C/N_D$ (obviously loose-to-tight).

c) Finally, I don't understand what they are actually trying to say with:

The tight-to-loose ratio is calculated using different $p_T^{\tau}/E_T^{miss}$ thresholds of 1.5, 1.55 and 1.6, the upper threshold was varried from 3 to 4, 5 and 20

Any idea what they are trying to point out with those numbers? The only threshold for $p_T/E_T^{miss}$ I saw was that it should be larger than 1.5 for the C,D region (so they varied this number by 0.05 per time)... but there is no upper threshold written anywhere :/

 

[mfb]

What is making the tight-to-loose ratio useful as a weight?

The easiest assumption is to have the same tight/(non tight) ratio in th QCD region and the signal region. In this case, the event number at B is the event number at A multiplied by this ratio.
The two ratios won't be exactly the same, so you take the difference between the two ratios from MC, apply this as correction on your measured ratio in the QCD region and then apply the corrected ratio to A and B.

b) Also why the ratio is called tight-to-loose while in the text they give it as $R_{TTL}= N_C/N_D$ (obviously loose-to-tight).

Oh, the joys of inconsistent naming. "Loose" itself should be called "loose but not tight".

(c) probably the upper limit of the ratio used for the $p_T/E_T^{miss}$ control regions.

 

[ChrisVer]

Thanks for the answer @mfb
Does that ratio have any physical meaning? can someone extract any physical meaning from Fig 2-right?
I think small ratios would make the signal events less "important", and so they would contribute less to the background? So for example the $2 h^\pm n \gamma ~~(n =0,1,2,...)$ events which have very small tight-to-loose ratio, are subdominant in the "signal"?

The easiest assumption is to have the same tight/(non tight) ratio in th QCD region and the signal region. In this case, the event number at B is the event number at A multiplied by this ratio.
The two ratios won't be exactly the same, so you take the difference between the two ratios from MC, apply this as correction on your measured ratio in the QCD region and then apply the corrected ratio to A and B.

So you say that my explanation is the "easiest" assumption and not the "exact" one...?
Because I think I said that the ratio should be the same for both QCD and Signal regions (obtain it from QCD and apply it to the signal to reach B from A).

 

[mfb]

It is the ratio of isolated to non-isolated taus (or tau candidates). It depends on the isolation definition, so it does not have a direct physical interpretation.

I think small ratios would make the signal events less "important", and so they would contribute less to the background?

Those ratios are for background only. A small D/C ratio would indicate that the isolation selection is very efficient in background rejection.

The overall contributions from the different background components are different, the ratio alone won't tell you where they are relevant.

So you say that my explanation is the "easiest" assumption and not the "exact" one...?

Hmm, looks like they used the easier approach. This is justified if they don't see a difference between the ratios in MC.