1. 1 Christmas 3 rd Report Liverpool Christmas Meeting 17/12/2007 Nicholas Austin naustin@mail.cern.ch

2. 2 ttbarH Analysis TDR Method Fake Rate Method Official CSC code results Improvement of Reconstruction of W  l SCT Endcap C Efficiency Calculation Original idea and method Problems with backtracking The all new improved method Topics

3. 3 ttbarH Higgs Analysis

4. 4 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. ProcessCross-Section ttjj474 pb gg  ttbb8.1 pb qq  ttbb0.5 pb gg  Z/  /W  ttbb 0.9 pb M H (GeV)  inc (pb) BR(H->bb) 1000.840.82 1100.660.79 1200.520.70 1300.420.56 1400.340.37 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.

5. 5 The TDR Method (1)Preselection At least 1 isolated lepton (e or  ) with P T (e)>25GeV or P T (  )>20GeV and |  |  2.5 At least 6 jets with P T >20GeV and |  |<5, 4 of which must be tagged as b-jets (2) Reconstruction of two W decays If >1 lepton choose highest P T. Reconstruct neutrino 4-mom m (assume M =0 so E =|p |). Identify P x and P y with P miss x and P miss y Calculate P z by constaining the invariant mass of the l system to M W  0,1,2 solutions. Build List of all light jet pairs (i.e. those not tagged as b-jets) Keep all pairs with m jj = m W ± 25 GeV and rescale so m jj = m W

6. 6 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 l b-jjb combinations, the one that minimises The top quark masses are identified with the invariant masses of the lnb and the jjb systems  2 = (m l b – m t ) 2 + (m jjb – m t ) 2 Tails of distribution dominated by events with incorrect pairing  require rec top masses to lie in range M t ± 20GeV (4) Higgs Reconstruction Assign remaining two b quarks to the Higgs decay If more than one choose two with highest P T

7. 7 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… N events (ttjj event reconstructed as ttH event) = N pass (N events (2 light jets in event are mistagged as b jets)) N events (2 light jets in event are mistagged as b jets) ~ N events (All) * P(2 light jets in event are mistagged as b jets) P(2 light jets in event are mistagged as b jets) =  i  j(!=i) P(q i mistagged as a b) * P(q j 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…

8. 8 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, q 1,q 2 Select combinations of 2 jets that are then selected as fake B jets Calculate Event Rate for each combination: fWeight = fFakeBProb[q 1 ] * fFakeBProb[q 2 ] 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!

9. 9 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

10. 10 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. M H Reconstruction Signal ttH ttjj + ttcc ttbb Sum

11. 11 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.

12. 12 The TDR Method: Official CSC Group Code

13. 13 Reconstruction of W  l and the calculation of P z This gives a quadratic equation in P z : (P z ) 2 –  P z ) +  = 0 Which is parameterised as:

14. 14 Quadratic equation in P z 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 P z = P l 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 P z is re-calculated giving one solution. “Sliding W Mass Solution” This makes use of the fact that M W 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 E T and lepton momentum. When  is calculated to be negative M W is increased so that upon recalculation the quadratic in P z yields one solution. The amount M W 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 M W 2 = 2(P T E l sin  l – p x p l x – p y p l y ) This gives P z = P T / tan  l

15. 15 “Delta=0 solution” cf “Set P z =P l z solution”

16. 16 “Sliding M W Mass solution”

17. 17 Negative Delta Solutions S/B Summary

18. 18 SCT EndCap C Efficiency Calculation (SCT_BackTrackEffTool)

19. 19 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

20. 20 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 (x extrap,y extrap ) RDO hit = centre of a strip that has detected the cosmic particle, (x rdo,0) Using similar triangles: W = (Wmax + Wmin) / 2 r = W*L / (Wmax – Wmin) dist = X rdo * (1 + Y extrap /r) - X extrap

21. 21 SCT Efficiency Road Width Calculation – Original Method – Results 1 Disk 0 Side 0 Disk 0 Side 1 Outer RingMiddle Ring 2 distributions! Why?

22. 22 SCT Efficiency Road Width Calculation – Original Method – Extrapolation of Truth Track Vs RDO Hits Disk 0 Side 0 Disk 0 Side 1 Outer RingMiddle Ring Just to show what we should expect in a perfect detector!

23. 23 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 RingMiddle Ring Relative position of extrapolated truth tracks wrt position of extrapolated TRT track Disk 0 Side 0Disk 0 Side 1

24. 24 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

25. 25 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.

26. 26 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…

27. 27 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.

28. 28 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 RingMiddle Ring

29. 29 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

30. 30 MERRY CHRISTMAS AND A HAPPY NEW YEAR!