1. Photon energy smearing from  events
Glen Cowan, Sudan Paramesvaran,
David Hopkins, Henning Flaecher
Royal Holloway, University of London
EMC Calibration Meeting
6 Sept 2006

2. Context Follows on from resolution studies by David, Henning, Sudan.
Same mmg n-tuples and selection as before, see e.g. David Hopkins
talk 5 April 06 at EMC software meeting:
2 ‘good’ measured tracks
1 ‘good’ measured photon
1 identified m (loose)
Kinematic fit c2 prob > 0.05
184 fb-1 → 1.2 million events

3. Goal of study For the photon in the mmg events we have
Emeas measured by the calorimeter
Efit from the kinematic fit
Histograms of x = Emeas/Efit
found to have high-x tail, especially for higher Eg
Goal: (Roodman, Kocian, ...) try smearing MC photon energies to give better data/MC agreement.

4. Method (1) Scale to same area as data histogram
Try to smear MC so that it looks like data, i.e.,
find a pdf s(z) such that y + z ~ f(x)
Find
For x = y + z

5. Method (2) For x = y + z we have In terms of the histograms this is
where
Find
For a parameterized pdf s(z;q ) we therefore have
original MC
smeared MC
smearing matrix

6. Method (3) Try for smearing pdf: Gaussian Student’s t
For Student’s t, n controls extent of tails
n = ∞ is Gaussian, n = 1 is Cauchy
Use binned ML but for now ignore MC statistical errors,
equivalent to minimizing

7. Gaussian fit Student’s t fit

8. Gaussian fit Student’s t fit

9. Gaussian fit Student’s t fit

10. Gaussian fit Student’s t fit

11. Gaussian fit Student’s t fit

12. Gaussian fit Student’s t fit

13. Gaussian fit Student’s t fit

14. Gaussian fit Student’s t fit

15. Gaussian fit Student’s t fit

16. Gaussian fit Student’s t fit

17. Gaussian fit Student’s t fit

18. Gaussian fit Student’s t fit

19. Gaussian fit Student’s t fit

20. Gaussian fit Student’s t fit

21. Gaussian fit parameters

22. Student’s t fit parameters
For 1.0 < E < 1.5 GeV, →∞
(consistent with Gaussian).

23. Andrew Wagner, 29 Aug 06 Neutrals meeting, showed
similar study with L/R asymmetric Gaussian smearing:

24. Andrew Wagner, 29 Aug 06 Neutrals meeting:

25. From here,
Parameterize the fitted parameters vs energy, (e.g. polynomial),
then for each photon
generate z ~ s(z;q(E)) and replace E → E (1 + z)
Resulting distribution will not be exactly equal to smeared MC
from fit due to several approximations made, but should be close.
To what extent are the tails due solely to EMC response? Are they
in part caused by, e.g., modeling of tracking, backgrounds,...?
Some further steps:
investigate angular dependence, refine E binning,
need more MC data (also use more real data?),
check effect on other quantities, e.g., p0 peak