Introduction

Jason found in a study described here that using a pT dependent correction for the response of the MC to thrown gammas improved agreement between data and MC.  This was based on data that Hal presented at the analysis meeting.  A copy of the talk can be found here.  Hal found a strong eta dependence as well as pT dependence.  Jason's correction was based on one set of eta points (believe eta=1.85).  I wanted to check two things:

1)If a redefintion of the correction would help and

2)If an eta-dependent correction would help

Method

I got 3 sets of small MC samples from Hal: eta=1.16, 1.30 and 1.85.  The first eta point had 4 pT points while the last 2 each had 7.  At each point I made a histogram of:

Response = (pT_true -pT_reco)/pT_reco.

Then I fit the response histogram to find the MPV.  I plot the MPV as a function of the mean pT_reco at that point for each eta sample.

The lower eta points show a turnover at low pT.  This made finding a common fit function for the response difficult.  I ignored this turn over and fit to :

F = p0/(pT_reco-p1)+p2

which fit pretty well over the range pT>3 GeV or so.

Next I looked at how the 3 fit parameters varied with eta and obtained fits of p0,p1,p2 as a function of eta.  The result is:

P0 = -1.097*Eta + 3.069
P1 = 34.589*Eta + -68.742
P2 = -0.125*Eta + 0.393
 

The correction is then pT_corr = pT_reco*(1+F(pT_reco,eta))

I applied this correction and repeated the study.  Plots before and after are below.  The correction does a good job for the higher pT range. 

Plots

Response as a function of pT_reco before the correction is applied.

Response as a function of pT_reco after the correction is applied.  The line is a straight line fit.

Comments

I think it would be useful to have more events at each of the points, and perhaps a range of points around eta=1.4-1.7, to see if the turnover is real.  If it is might need to investiage a different fit function above and below some eta range.

Updated Plot

Keith generated more points at eta=1.59.  Below I have the new Reponse vs. pT_reco curve.  In this case I'm plotting the mean of the response instead of the MPV.  This is why the turnover at low pT_reco in low eta bins went away - I think we need more stats to check this.  But regardless of if I plot the mean or MPV, when we have a point out near pT_reco = 60, the response shoots up again.  This is really weird.