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Christmas 3rd Report

Liverpool Christmas Meeting17/12/2007

Nicholas Austin

naustin@mail.cern.ch

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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!