-- FrankGolf - 23 Jun 2008

This is a collection of notes summarizing my MET study.

Projects:

Notes

• The following notes may be helpful:
  1. All code may be found on cmslpc at ~fgolf/work/met_compare/CMSSW_1_6_11/src/Analyzers/StandAloneNtupleMaker/
  2. Ntuple making code may be found in interface/ and src/ with .cfg files in test/
  3. Ntuples themselves may be found in data/
  4. Analysis code and output root files may be found in data/
  5. Plot making tools may be found in data/
  6. Plots themselves may be found in plots/

Variables

• The following variables may require some definition:
  1. tot9 is the sum of energy deposited in the ecal+hcal in an area covered by 3x3 hcal towers
  2. ratio is the fraction tot9/p, where p is the magnitude of the track momentum measured at the vertex
  3. met is the raw MET calculated as a vector sum of calo towers
  4. metmu is the MET corrected for muons
  5. met_corr0 is the MET corrected, using the response function, for all tracks with p > 1. GeV
  6. met_corr1 is the MET corrected, using the response function, for all tracks with p > 1. GeV and corrected, using RF = 0, for all tracks with p < 1. GeV

Plots Legend

• Plots use the following color scheme
  • Black is raw MET
  • Red is MET corrected for muons only
  • Green is corrected MET w/ pt cutoff 0 Gev
  • Blue is corrected MET w/ pt cutoff 1 Gev
  • Magenta is corrected MET w/ pt cutoff 2 Gev
  • Cyan is corrected MET w/ pt cutoff 5 Gev

Response Functions

• Two response functions (RF) were derived.
• Both were obtained from same sample of 135k single pions.
• Both response functions require pions with abs(eta) < 2.4 and pt < 102.
• Both response function only use tracks with nhits > 8, nchisq < 5, and d0 < 0.01
• Calculated as ensemble average of tot9/p.
• RF is a 2D function : RF = RF(pt, eta)
• Response function 1 (RF1) uses raw readout of ecal and hcal over area spanned by 3x3 hcal towers (data/response_function.root)
• Response function 2 (RF2) corrects for negative readouts using : *cal = ( *cal9 > 0 ) ? *cal9 : 0; (data/response_function2.root)

Track Based Correction

• Correct MET on a track-by-track basis
• Correct MET in components
  • met_x = met_x + (avg energy deposited in calo)_x - track px
  • met_y = met_y + (avg energy deposited in calo)_y - track py
• met_x = MET * cos( met_phi )
• met_y = MET * sin( met_phi )
• avg energy deposited in calo = p * RF
• track_px = pt * cos( phi )
• track_py = pt * sin( phi )
• So, the idea here is to remove the amount of energy a given track deposits on average in the calo, determined using the RF, and replace it with the full track momentum

Muons

• Muons are corrected using RF = 0

Pass One

• Run over a small sample of Z->mumu events.
• Sample has 678 events with two reconstructed muons in the final state.
• Good starting sample since it has a well defined final state : MET ~ 0 (deviations due to any transverse momentum Z has if it recoils against another particle)
• Identify muons by matching mus_d0 to the d0 of the tracks in the track collection.
• Do not make any attempt to deal with electrons.
• Use RF1
• Figure of merit is number of events with MET > x. Here use x = 30 GeV .
• Used ntuple data/standalone.root
• Examine two classes of implementations

Quality Cuts

• Apply RF1 to those tracks that pass (looser) quality cuts : nhits > 6. & nchisq < 4 & d0 < 0.05
• Only apply to tracks in kinematical window of RF1 : abs(eta) < 2.4 & pt < 102.

• N-1 plot of track d0 (nchisq < 4 & nhits > 6)
  

• N-1 plot of track nchisq (d0 < 0.05 & nhits > 6)
  

• N-1 plot of track nhits (nchisq < 4 & d0 > 0.05)
  

Implementation One

• Correct tracks, using RF1, passing quality cuts with additional requirement pt > y, where y is element of set {0, 1, 2, 5}
• Do not correct tracks passing quality cuts with pt < y
• Used code data/rfonly.h and data/rfonly.C

• Corrected MET (overlay, log scale)
  

Black line is raw MET. After muons are corrected (red line), we see distribution shift left and events migrate from tail to bulk. Further morphing occurs as track based correction is applied (eg. Blue line, 1 GeV pt cutoff).

• Corrected MET (overlay, log scale)
  

Cleaner version of the above plot showing raw MET (black), MET corrected for muons only (red), and (blue) MET corrected for tracks w/ pt > 1, no correction below cut. Illustrates more clearly the improvement after each stage.

• Table showing number of events after each stage with MET > 30 GeV

Cut	# Events
raw	112
muons	75
0	43
1	42
2	50
5	54

• Cumulative MET (overlay)
  

Fraction of events with MET < x. This gives further confirmation of the interpretation above. At each stage, more events more into the bulk of the distribution so that a larger fraction of events are found at low x in the corrected sample compared to the uncorrected one.

• Quality Factor
  

Quality factor refers to the ratio of the number of events with MET > x between two different samples. Here, the denominator is the corrected MET with pt cut of 1 GeV while the numerator is MET corrected for muons only.

Implementation Two

• Correct tracks, using RF1, passing quality cuts with additional requirement pt > y, where y is element of set {0, 1, 2, 5}
• Correct tracks passing quality cuts with pt < y using RF1 = 0
• Used code data/rffull.h and data/rffull.C

• Corrected MET (overlay, log scale)
  

Black line is raw MET. After muons are corrected (red line), we see distribution shift left and events migrate from tail to bulk. Further morphing occurs as track based correction is applied (eg. Blue line, 1 GeV pt cutoff).

• Corrected MET (overlay, log scale)
  

Cleaner version of the above plot showing raw MET (black), MET corrected for muons only (red), and (blue) MET corrected for tracks w/ pt > 1, no correction below cut. Illustrates more clearly the improvement after each stage.

• Table showing number of events after each stage with MET > 30 GeV

Cut	# Events
raw	112
muons	75
0	43
1	42
2	49
5	43

• Cumulative MET (overlay)
  

Fraction of events with MET < x. This gives further confirmation of the interpretation above. At each stage, more events more into the bulk of the distribution so that a larger fraction of events are found at low x in the corrected sample compared to the uncorrected one.

• Quality Factor
  

Quality factor refers to the ratio of the number of events with MET > x between two different samples. Here, the denominator is the corrected MET with pt cut of 1 GeV while the numerator is MET corrected for muons only.

As we can see, there are not significant differences between the two implementations expect for the 5 GeV pt cutoff which is expected since this would lead to ignoring a large number of tracks in the first implementation. As a result, for future passes, only the 1 GeV cut in the second implementation will be used.

Pass Two

• Run over a sample of W->munu events.
• Require at least one reconstructed muon in the final state.
• Will provide us with a check on the results of the first pass - if we were merely shifting the MET by an overall additive or multiplicative factor, it will show up here.
• Identify muons by matching mus_d0 to the d0 of the tracks in the track collection.
• Do not make any attempt to deal with electrons.
• Use RF1
• Figure of merit is number of events with MET > x. Here use x = 30 GeV .
• Compare efficiency of W->munu to rejection of Z->mumu
• Used ntuple data/standalone_wmu.root
• Used code data/rf1wmu.h and data/rf1wmu.C

Results

• Corrected MET (overlay, log scale)
  

Significant shift in bulk of distribution between raw MET and MET corrected for muons. This is expected given the physics involved. Little change after applying response function. This is reasonable since most of the events are in the 0-jet bin (will discuss more below).

• Cumulative MET (overlay)
  

Reemphasizes conclusions drawn above. Correcting for muons results in significant change in MET. Additional track based correction causes no significant shift in MET distribution.

• Quality Factor
  

Ratio of number of events with MET > x. Denominator is track based corrected MET. Numerator is MET corrected for muons only.

• The track based correction does not have a signficant impact on the MET distrubtion. We can now produce an efficiency/rejection plot to verify the efficacy of our correction.

• Signal vs. Background
  

There is some gain in sig/bkgd. For example, at a signal efficiency of 0.9, track based correction decreases acceptance of background by a factor of 1.4.

Pass Three

• Run over a small sample of Z->mumu events.
• Implement and verify several improvements
• Replace muon id by d0 matching with track indices from muon collection
• Remove electrons from set of corrected tracks
• Recalculate response function corrected for negative calo responses
• Used ntuple data/standalone2.root but run on first 678 events only (to compare to results from previous two passes)
• Used code data/rf2.h and data/rf2.C

Muon Implementation

• In passes one and two, muons were identified by matching the d0 of each muon in the collection to the d0 of a track in the track collection. This new implementation will use a new method whereby the track index is obtained directly from the muon collection.
• Two implementations appear to be identical. Verified. From here on out we will use track indices from the muon collection.

Electron Implementation

• Currently correct for all tracks that pass quality cuts and are not muons.
• Want to remove those tracks that are "electrons" since they deposit nearly all of their energy in the ecal
• Will identify tracks to remove by finding those objects in the reco::PixelMatchedGsfElectronCollection w/ abs(hadOverEm) < hoe_cut
• Will try several different cuts and compare results : hoe_cut = 0.03, 0.05, 0.1

• els_hadOverEm (Z->mumu)
  

Ratio of hadronic energy to electromagnetic energy for reco::GsfPixelMatchedElectronCollection.

• els_hadOverEm (Z->mumu)
  

Ratio of hadronic energy to electromagnetic energy for "real" electrons from Z->ee. This distribution shows us what h/e is for such electrons, thereby allowing us to determine appropriate cuts to remove fakes from the Z->mumu sample above.

hoe_cut = 0.03

• Corrected MET (overlay, log scale)
  

Cut	# Events
raw	112
muons	75
1	42

• Cumulative MET (overlay)
  

• Quality Factor
  

So, it appears that removing electrons had no effect on the MET distribution - the number of events in the tail remains unchanged.

hoe_cut = 0.05

• Corrected MET (overlay, log scale)
  

Cut	# Events
raw	112
muons	75
1	43

• Cumulative MET (overlay)
  

• Quality Factor
  

So, it appears that removing electrons had little effect on the MET distribution - the number of events in the tail is not statistically different.

hoe_cut = 0.10

• Corrected MET (overlay, log scale)
  

Cut	# Events
raw	112
muons	75
1	44

• Cumulative MET (overlay)
  

• Quality Factor
  

So, it appears that removing electrons had little effect on the MET distribution - the number of events in the tail is not statistically different. If we compare the three corrections overlayed :

• Corrected MET (3 ele corrections, overlayed, log scale)
  

• Quality Factor (3 ele corrections, overlayed)
  

For these two plots, green is hoe_cut = 0.03, magenta is hoe_cut = 0.05, and cyan is hoe_cut = 0.10. There are no noticeable differences between the three implementations on the Z->mumu sample. The next step is to run the same implementations on a Z->ee sample and compare signal to background.

hoe_cuts on Z->ee

We will now implement the same set of hoe_cuts on a Z->ee sample and use the above results for Z->mumu to do a signal to background comparison between them. Below is an overlay plot of the raw MET, MET corrected for muons, and three different implementations of the MET corrections with hoe cuts of 0.03, 0.05, 0.10. The code used can be found at data/rf1zee.h and data/rf1zee.C. The ntuple run on was data/standalone_zee.root and the output at data/rf1zee.root.

• Corrected MET (3 ele corrections, overlayed, log scale)
  

Raw MET is black. MET corrected for muons is in red. The three implementations of the MET corrections (0.03, 0.05, 0.10) appear in green, blue, and magenta, respectively.

Cut	# Events
raw	49
muons	48
0.03	24
0.05	26
0.10	24

There appears to be very little difference between the two implementations, on the order of 1%. The final results appear roughly independent of the choice of hoe we make. In order to be as inclusive as possible at this stage, we will use the loosest cut from here on out - hoe = 0.1.

RF Implementation

• We will now study the new response function where negative readouts of the ecal and hcal have been zeroed
• Response function used will be data/response_function2.root
• Muons will be corrected but no attempt will be made to deal with electrons as I a final decision on which hoe_cut to use has not been made yet
• Ntuple used will be data/standalone_wee.root
• Code used will be modified version of data/rf2.h and data/rf2.C where electron cuts are turned off
• Output stored in data/rf2_rf2.root

• Corrected MET (RF2, overlayed)
  

Cut	# Events
raw	112
muons	75
1	41

• Cumulative MET (RF2, overlayed)
  

• Quality Factor (RF2)
  

Comparing the two response functions (muons in red, RF1 in magneta, RF2 in cyan):

• Corrected MET (2 RFs, overlayed, log scale)
  

• Quality Factor (2 RFs, overlayed)
  

Pass Four

• Run over small samples of Z->mumu and Z->munu events
• Put it all together - track based correction, muon correction, electron removal, improved RF

Z->mumu run

• Corrected MET (overlayed, log scale)
  

Correction	# Events
raw	112
muons	75
tracks	42

• Cumulative MET (overlayed)
  

• Quality Factor
  

Track based correction improves upon muon-only correction by factor 1.79.

W->munu run

• Corrected MET (overlayed, log scale)
  

Correction	# Events
raw	73
muons	487
tracks	458

• Cumulative MET (overlayed)
  

• Quality Factor
  

Track based correction trails the muon-only correction by factor 0.94.

Combined Results

Putting the two runs together we derive the following signal to background results.

• Signal vs. Background
  

Pass Five

• Perform a run on small Z->mumu and Z->munu samples
• Compare performace of our RF and the KGB RF
• Ntuple used is data/standalone2.root
• Code is data/rfkgb.h and data/rfkgb.C
• Output is data/rfkgb.root
• Plots found in plots/rfkgb/

Z->mumu run

• Corrected MET (overlayed, log scale)
  

Raw MET is in black, MET corrected for muons only in red, our correction is in green, KGB correction in blue.

Correction	# Events
raw	112
muons	75
our	42
kgb	36

• Cumulative MET (overlayed)
  

• Quality Factor
  

After performing this, several deficiencies in our implementation were made apparent. I have not been checking to see if outerEta and outerPhi are valid (i.e. are well defined and not default -999). Also, I have been ignoring tracks that do not pass quality cuts! This could be hurting us significantly.

W->munu run

• Corrected MET (overlayed, log scale)
  

Raw MET is in black, MET corrected for muons only in red, our correction is in green, KGB correction in blue.

Correction	# Events
raw	73
muons	487
our	458
kgb	457

• Cumulative MET (overlayed)
  

• Quality Factor
  

Combined Results

Putting the two runs together we derive the following signal to background results.

• Signal vs. Background