JER mapping

A mapping is needed to transpose from p_T^\text{gen} to p_T^\text{rec} after fitting the resolution for a given [\eta^\text{rec}, p_T^\text{gen}] bin.
Some information is shared, obtained from colleagues on the implementation of such mapping.

To begin with, we make TH1Fs with the p_T^\text{rec} distribution and the jet response p_T^\text{rec}/p_T^\text{gen} for each [\eta^\text{rec}, p_T^\text{gen}] bin. Examples of histograms inside the output root file:

KEY: TH1F JetPt_JetEta0.348to0.435_RefPt90to120;1  
KEY: TH1F RelRsp_JetEta0.348to0.435_RefPt90to120;1  

KEY: TH1F JetPt_JetEta0.348to0.435_RefPt120to150;1  
KEY: TH1F RelRsp_JetEta0.348to0.435_RefPt120to150;1  

and so on for all other remaining [\eta^\text{rec}, p_T^\text{gen}] bins (RefPt = p_T^\text{gen}, JetPt = p_T^\text{rec}, RelRsp is the Response). The code related for this task can be found here.

Then given the above root file we make a loop over all histograms for each \eta^\text{rec} bin in order to:
Take mean via TH1F::GetMean() of JetPt_JetEta0.348to0.435_RefPt90to12 histogram and the mean of the RelRsp_JetEta0.348to0.435_RefPt90to120.
We then make a point in a graph via TGraphErrors::SetPoint(point, mean_JetPt, 1/median_RelRSP).
We repeat this for all p_T^\text{gen} bins and we create a TGraphErrors with 1/median(response) vs \langle p_T^\text{rec}\rangle (1/median is taken for the sake of their studies, in our case we should plot the quantity of interest, the plain median).
We repeat for all other \eta^\text{rec} bins. The code that performs this task can be found here, for example in L213-314.

So since initially you have response vs p_T^\text{gen} you go to the median(response) or the inverse of it as a function of \langle p_T^\text{rec}\rangle.