1 christmas 3 rd report liverpool christmas meeting 17/12/2007 nicholas austin [email protected]
TRANSCRIPT
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• ttbarH Analysis
•TDR Method
• Fake Rate Method
• Official CSC code results
• Improvement of Reconstruction of Wl
• SCT Endcap C Efficiency Calculation
• Original idea and method
• Problems with backtracking
• The all new improved method
Topics
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ttbarH Higgs Analysis
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The ttH Channel: Signal and Backgrounds
Associative Higgs Production with a tt pair (ttH)
Look for events with a final state of
• one isolated lepton
• missing energy
• 6 jets (4 of which are tagged as b-jets).
Hoped that a Higgs signal might be reconstructed as a peak in the invariant jet-jet mass spectrum of tagged b-jets from such events.
Process Cross-Section
ttjj 474 pb
ggttbb 8.1 pb
qqttbb 0.5 pb
ggZ//Wttbb 0.9 pb
MH (GeV)
inc (pb) BR(H->bb)
100 0.84 0.82
110 0.66 0.79
120 0.52 0.70
130 0.42 0.56
140 0.34 0.37
Largest background results from misidentifying light jets as b jets. (Sometimes also charm).
Reducible with the use of good b-tagging algorithms
Small Irreducible QCD background producing a continuum of ttbb final states.
Even smaller Irreducible Electroweak background produces resonances at masses corresponding to the intermediate particle.
• Also a large combinatorial background associated with incorrectly pairing two out of the four b-jets in the signal events themselves.
• TDR Method designed to remove this by completely reconstructing the two top quarks in the event.
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The TDR Method(1) Preselection
• At least 1 isolated lepton (e or ) with PT(e)>25GeV or PT()>20GeV and ||2.5
• At least 6 jets with PT>20GeV and ||<5, 4 of which must be tagged as b-jets
(2) Reconstruction of two W decays
• If >1 lepton choose highest PT.
• Reconstruct neutrino 4-momm (assume M=0 so E=|p|).
• Identify Px and P
y with Pmissx and Pmiss
y
• Calculate Pz by constaining the invariant
mass of the l system to MW
0,1,2 solutions.
• Build List of all light jet pairs (i.e. those not tagged as b-jets)
• Keep all pairs with mjj = mW ± 25 GeV and rescale so mjj = mW
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The TDR Method Continued(3) Reconstruction of the two top quarks
• Ambiguities arise when pairing the two W bosons with two of the four jets (and hence assignment of the remaining two jets to the Higgs decay) Combinatorial Background.
• Reduced by selecting from all lb-jjb combinations, the one that minimises
• The top quark masses are identified with the invariant masses of the lnb and the jjb systems2 = (mlb – mt)2 + (mjjb – mt)2
• Tails of distribution dominated by events with incorrect pairing require rec top masses to lie in range Mt ± 20GeV
(4) Higgs Reconstruction
• Assign remaining two b quarks to the Higgs decay
• If more than one choose two with highest PT
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The Fake Rate Method for Backgrounds• Found that background datasets (v11) gave very low statistics.
• Estimating the shapes of the background distributions is impossible.
• Introduce Fake Rate Method with ttX dataset.
• When running over the ttX dataset, the events that will make it into the final reconstructed higgs mass plot will consist of ttbb events, ttjj events and ttcc events.
• Consider first the light jets. Simply…
• Nevents(ttjj event reconstructed as ttH event) = Npass(Nevents(2 light jets in event are mistagged as b jets))
• Nevents(2 light jets in event are mistagged as b jets) ~ Nevents(All) * P(2 light jets in event are mistagged as b jets)
• P(2 light jets in event are mistagged as b jets) = ij(!=i) P(qi mistagged as a b) * P(qj mistagged as a b)
• ttjj events will either be tagged
• correctly - in which case no fake higgs event will be reconstructed
• incorrectly - in which case a fake higgs event may be reconstructed.
• Using this probabilistic method now all ttjj events can be used to estimate the shape of the background…
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PreSelection
• If jet is tagged as a light jet, assign it a probability that it could be reconstructed as a fake b:
• if it is really a b jet, P(fake b) = 0
• if it is really a light jet, P(fake b) = P(light jet could be mistagged as a b jet)
• If jet is tagged as a b jet:
• if it is really a light jet, P(fake b) = 1
• LOOP over all Light Pairs in the event, q1,q2
• Select combinations of 2 jets that are then selected as fake B jets
Calculate Event Rate for each combination: fWeight = fFakeBProb[q1] * fFakeBProb[q2]
Hadronic W Reconstruction
Two Top Quarks Reconstructed
Higgs Reconstruction:
Histogram is filled with the Inv Mass of the remaining two jets, weighted by fWeight
Leptonic W Reconstruction
The Fake Rate Method for Backgrounds
NB. We are now using all ttjj events. Not just those that would have been mistagged as a b, but also those that are actually tagged correctly Better Statistics!
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Fake Rates• For light jets (u,d,s), the event weight needed is
• P(light jet is mistagged as a b jet) = N(true light jets mistagged as a b jet) N(true light jets)
• CARL… • Looked at dijet sample to see what fraction of truth light jets are mistagged as b jets• Parameterised this as a quartic function of log(Pt(jet)) in bins of eta
• Functions in PT are then interpolated between the different bins in eta
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Fake Rates• Similar methods used to estimate ttcc and ttbb background using
P(charm jet is mistagged as a b jet) = N(true charm jets mistagged as a b jet) N(all true charm jets)
P(b jet is correctly tagged as a b jet) = N(correctly tagged b jets) N(all true b jets)
• Events classified by truth information.
MH Reconstruction
Signal ttH
ttjj + ttcc
ttbb
Sum
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The TDR Method: Official CSC Group Code
• Works in the same way as my analysis code, but uses v12 datasets
• Does not use fake rate method. Backgrounds estimated using CSC datasets
• These are lacking in statistics. Future: plan to incorporate fake rate method in this analysis structure.
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The TDR Method: Official CSC Group Code
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Reconstruction of Wl and the calculation of Pz
• This gives a quadratic equation in Pz: (P
z)2 – Pz) + = 0
• Which is parameterised as:
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• Quadratic equation in Pz gives 0,1,2 solutions depending on the sign of = 2 – 4.
• What do we do if <0?
• Ignore these events? Waste!
• Official code sets Pz = Pl
z when the quadratic fails to give a solution.
• Is there a better way? I was asked to look at two possible methods…
• “Delta = 0 Solution”
• When is calculated to be negative it is simply set to zero and Pz is re-calculated giving
one solution.
• “Sliding W Mass Solution”
• This makes use of the fact that MW is not a fixed number when measured in the detector – it has a natural width, plus a broadened mass spectra due to the detector measurement resolution of missing ET and lepton momentum.
• When is calculated to be negative MW is increased so that upon recalculation the quadratic in P
z yields one solution.
• The amount MW has to be increased by to give one solution can be found analytically by solving the equation =0.
• The new mass needed is given by MW2 = 2(P
TElsinl – pxpl
x – pypl
y)
• This gives Pz = P
T / tanl
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“Delta=0 solution” cf “Set Pz=Pl
z solution”
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“Sliding MW Mass solution”
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Negative Delta Solutions S/B Summary
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SCT EndCap C Efficiency Calculation
(SCT_BackTrackEffTool)
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SCT Endcap C Efficiency Calculation
• It is important to understand the efficiencies of the modules in the SCT endcaps.
• Done for barrel, but I am the only person working on this with cosmics for endcap C
• Work is ongoing in calculating these SCT efficiencies for the SR1 cosmic tests carried out on endcap C.
• Current work is focused on the optimisation of the roadwidth used in this efficiency calculation
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SCT Efficiency Road Width Calculation – Original Method
• Extrapolate TRT tracks into the SCT.
• Compare intersections of the extrapolated tracks with SCT modules with ‘RDO hits’.
• Plot distance/residual between the ‘hit strip’ in the SCT module and the extrapolated track position.
Extrap Hit at (xextrap,yextrap)
RDO hit = centre of a strip that has detected the cosmic particle, (xrdo,0)
Using similar triangles:W = (Wmax + Wmin) / 2r = W*L / (Wmax – Wmin)dist = Xrdo * (1 + Yextrap/r) - Xextrap
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SCT Efficiency Road Width Calculation – Original Method – Results 1
Disk 0 Side 0
Disk 0 Side 1
Outer Ring Middle Ring
2 distributions! Why?
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SCT Efficiency Road Width Calculation – Original Method – Extrapolation of Truth Track Vs RDO Hits
Disk 0 Side 0
Disk 0 Side 1
Outer Ring Middle Ring
Just to show what we should expect in a perfect detector!
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SCT Efficiency Road Width Calculation – Original Method – Extrapolation of TRT Track Vs Extrapolation of Truth Track
Disk 0 Side 0
Disk 0 Side 1
Outer Ring Middle Ring
Relative position of extrapolated truth tracks wrt position of extrapolated TRT track
Disk 0 Side 0 Disk 0 Side 1
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Comparisons of the directions of the TRT track and the Truth Track
Direction of Truth Track
Direction of Reconstructed TRT Track
Shifted in Eta
Shifted in Py
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Problems with Back Tracking
• Orientation of straws in the TRT gives a very bad resolution
• Poor measurement of direction
• Especially bad for cosmic rays and backtracking
• Cosmic rays come from up above, not the interaction point.
• Backtracking starts with the TRT information and works towards the SCT.
• To constrain position of cosmic rays you need at least 2 SCT space points!
Relative position of extrapolated truth tracks wrt position of extrapolated TRT track
Residuals: Extrapolated TRT tracks with 2+ SP’s
• Low Statistics
• These results are biased…space points used in track fitting may be in modules for which we are measuring the residual.
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Removing the Bias
• Must remove space points from active disk – i.e. the disk we are extrapolating to.
• Remove space point from active disk, refit track and then extrapolate this.
• As we require a minimum of 2 SCT space points to get a good refit and we are going to remove one, we need to first select tracks with 3+ space points.
Problems• Very few tracks to start with that have 3+ space points.
• Only 2 space points is working on the limit more would be good!
• Backtracking algorithm that originally made tracks is internal and buried deep in athena. Therefore can’t use it to refit the tracks. Must use a track fitter.
• Refit of track seldom works (tried two different fitters)
• The few times the refit does work it is quite different to the original track and does not extrapolate into the module we would extrapolate to No residual!
• No statistics
• Decided to give up on this method…
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New Method: Standalone SCT Tool using SCT Space Points
• Consider tracks with 3+ SCT spacepoints
• Use original track to find modules it passes through (will change this so that it loops over all modules in a disk – removing all TRT dependence)
• Loop over disks
• Find all SCT space points NOT in active disk
• Loop over pairs of these spacepoints, extrapolating the line they make wrt each other to the module of interest in the active disk
• Compare extrapolated positions with RDO strip hits
• Still has some bias
• if more than one SP in same disk
• if say one cosmic track has 3 space points outside the active disk, then there are 3 possible choices of pairs, and 3 residuals plotted for the same event.
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New Method: Standalone SCT Tool using SCT Space Points
Advantages
• It works!!!
• It’s standalone, could be employed for tests with no TRT information.
• Quick and easy.
Disk 0 Side 0
Disk 0 Side 1
Outer Ring Middle Ring
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Next in SCT Endcap C Efficiency Calculation
• At a glance - Roadwidth ~ 5-10mm
• Remove Bias
• Make completely SCT standalone
• Calculate efficiencies using measured road width
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MERRY CHRISTMAS AND
A HAPPY NEW YEAR!