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Photon energy smearing from events. Glen Cowan , Sudan Paramesvaran, David Hopkins, Henning Flaecher Royal Holloway, University of London. EMC Calibration Meeting 6 Sept 2006. Context. Follows on from resolution studies by David, Henning, Sudan.
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Photon energy smearing from events Glen Cowan, Sudan Paramesvaran, David Hopkins, Henning Flaecher Royal Holloway, University of London EMC Calibration Meeting 6 Sept 2006
Context Follows on from resolution studies by David, Henning, Sudan. Same mmgn-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
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.
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
Method (2) For x = y + z we have where In terms of the histograms this is Find For a parameterized pdf s(z;q ) we therefore have original MC smeared MC smearing matrix
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
Gaussian fit Student’s t fit
Gaussian fit Student’s t fit
Gaussian fit Student’s t fit
Gaussian fit Student’s t fit
Gaussian fit Student’s t fit
Gaussian fit Student’s t fit
Gaussian fit Student’s t fit
Gaussian fit Student’s t fit
Gaussian fit Student’s t fit
Gaussian fit Student’s t fit
Gaussian fit Student’s t fit
Gaussian fit Student’s t fit
Gaussian fit Student’s t fit
Gaussian fit Student’s t fit
Student’s t fit parameters For 1.0 < E < 1.5 GeV, →∞ (consistent with Gaussian).
Andrew Wagner, 29 Aug 06 Neutrals meeting, showed similar study with L/R asymmetric Gaussian smearing:
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
