Top Quark Mass Measurement with the Matrix Element Method at D0

1. Top Quark Mass Measurementwith theMatrix Element Method at D0 t Petra Haefner

2. Why measure the Top Mass? The 3 “H“ HIGGS • indirect constraints on mass of Higgs boson possible HEAVY (~ 171 GeV) ! • only (known) fermion with mass near electro-weak scale Hadronisation • only quark that does not hadronise • direct mass measurement based on decay products possible Petra Haefner Scientific American, June 2003

3. How does Top decay? branching ratio t  Wb ~ 100 % as |Vtb| >> |Vts|,|Vtd| topology determined by W decays branching ratio W  light q ~ 2/3, W  l+ ~ 1/3  difficult to identify consider only decays to l= e, alljets (44%) largest branching fraction huge backgrounds lepton+jets (30%) good statistics lower backgrounds dilepton (5%) very low statistics cleanest signature Petra Haefner

4. What do we measure? • lepton+jets signature • 1 energetic, isolated lepton (e / ) • 4 energetic jets • 2 b jets (might contain soft lepton) • 2 light jets (u,d,s,c) • missing transverse energy (1 ) • event kinematics • 2 solutions for  pz (along beam axis) • otherwise fully determined kinematics • 24 possible jet-parton assignments (permutations) • consider all 2*24 solutions for including btagging • analysis challenges • calibration: whole detector needs to be understood • jet parton matching: many possible assignments, b-tagging helps • systematic uncertainties: relative energy calibration “easy“, overall jet energy scale (jes / bjes) difficult but important Petra Haefner

5. How do we measure? Template Method (classical approach) take all 2x24 permutations into account choose kinematic fit with smallest 2 fill histogram with reconstructed top mass compare to simulated distributions of different mtop correct permutation only in ~40% of events! all events are weighted equally Matrix Element Method (developed at D0 Run I) calculate probability Pi(mt) for every event to be a top decay take information from all 24 permutations into account combine probabilities of all permutations & events get total probability P(mt) for the whole sample measure mt as most likely one all permutations contribute events are weighted according to their information content Petra Haefner

6. Topological Signal Probability • probability for a given permutation xevt in an event to be a top decay • certain top mass mt, jes scale factor sjes & bjes factor sbjes assumed • incoming: leading order parton density function (PDF) • production: leading order matrix element (ME) for diff. cross section • outgoing: jet transfer functions& muon transfer function for detector response • normalized to total cross section for ttbar production (within detector acceptance) Petra Haefner

7. Past, Present & Future • D0 Run I • first ME top mass measurement • only mt hypotheses varied • D0 Run II, 370 pb-1 • 2D grid of hypotheses in the mt - jes - plane used • measure mt & jes simultaneously • sjes constraint by the W mass in the matrix element • D0 Run IIa, 1.2 fb-1 • 3D grid of hypotheses in the mt - jes - bjes space • probes mt & jes & bjes in one go • sbjes contraint by the balance of the ttbar system • We need O(n3) times the computing power compared to Run I! Petra Haefner

8. Computing Power Needs • we do not need (a lot of) disk space • input files ~ 1 MB, output files ~ 800 MB (per calibration point) • 10 GB for full parton level test • we do not need (a lot of) memory • normal memory use ~ 200 kB • we NEED CPU!!! • 0.5 s/prb, 13 mt * 13 jes * 13 bjes * 24 perms * 1500 evts *13 calib points • 1 028 196 000 probabilities 140 000 CPU hours • this was done in 4 weeks at Gridka (for 7 calibration points) GOOD NEWS • most time consuming part in the probability calculation is the TF evaluation (2 double Gauss * 4 jets) • this was done 4 q * 13 jes * 13 bjes = 676 times / event • changed bjes scheme from jes*bjes to bjes‘ • only (2 q *13 jes + 2 * bjes) evaluations of TF left • instead of 676 TF calculations we only need 52 now! • computing time cut by a factor of 10 • instead of 4 weeks we need ~ 3 days for a full parton level test now!!! Petra Haefner

9. Improvements with b-tagging • l+jets channel has 2 light and 2 b jets • backgrounds (W+jets, MultiJet) contain hardly any b-jets • requiring b-tags can improve sample purity • b-tagging information helps to find “good“ jet permutations • combinations that map jets with tags to b-quarks have higher probability to be the correct combination • so far: • sample separated into 0 , 1 , 2 tags subsamples • 1 , 2 tags samples have larger top fraction, but low statistics • this analysis: • make use of b-tagging NN output (certified for 12 operating points) • include tagging probability for c quarks properly (Wcs) • use probability for certain quark permutation to give observed NN outputs Petra Haefner

10. b-Tagging Probability • for each jet, calculate P(op[i],Fake), P(op[i],c) & P(op[i],b) • for every jet permutation use flavor of associated quark • for every permutation multiply tagging probabilities of all 4 jets • for every event add probabilities of all permutations Fake Fake mean diff c c Petra Haefner b b

11. Jet Permutations example: jtnn(jet1) = 0.99 op = 11 jtnn(jet2) = 0.58 op = 6 jtnn(jet3) = 0 op = -1 jtnn(jet4) = 0.12 op = 0 perm 1: P(j1,11,b) * P(j2,6,b) * P(j3,-1,F) * P(j4,0,F) 0.35 * 0.05 * 0.9*0.02 = 0.000315 perm 24: P(j1,11,F) * P(j2,6,F) * P(j3,-1,b) * P(j4,0,b) 0.001 * 0.006 * 0.35 * 0.02 = 0.000000042 Petra Haefner

12. Ensemble Tests • proof of principle: do 3D fit and b-tagging probabilities work? • event pool of ~ 1500 smeared parton level events • draw 1000 ensembles of 100 events each (redrawing allowed) • fit mt, jes, bjes in every ensemble (i.e. find points of minimum log likelihood / maximum probability) • plot results of these 1000 pseudo-experiments • calculate mean, pull, pull width • combine all calibration points into calibration curves (vs. mt, jes, bjes) 5 calibration points w/ 1000 ens 1000 ens w/ 100 evts 1 ens w/ 100 evts Petra Haefner

13. Signal only, mt Calibration • signal only • no background probabilities included • jes = bjes = 1.0 • several generated top masses (160, 170, 175, 180) • mt, jes, bjes fit • reconstructed mt is divided by generated mt mt jes bjes Petra Haefner

14. Signal + Background, with pbkg • ttbar & W+4jets events • signal & backgr. prbs included • no jes / bjes dependence assumed in pbkg • jes = bjes = 1.0 • mt = 170 GeV • increasing background fraction • mt, jes, bjes fit • reconstructed mt is divided by generated mt Petra Haefner

15. Summary & Outlook • Parton Level Ensemble Tests • signal only tests show that 3D fit works • including b-tagging improves sample purity and expected error • signal + background tests show good agreement with expectation • tests with Wbbjj still need to be done • D0 MC & Data • ensemble tests with full D0 simulation (signal: Pythia, bkg: Alpgen) • no perfect results expected due to simplified model of reality • full MC ensemble tests for deriving calibration curves • correct for small biases when applying technique to data • use full Run IIa data set (~1.2 fb-1) for mass measurement • Good News • gained a factor of 10 in CPU time due to code optimisation • need 4 hours per job instead of 40 h so far! Petra Haefner

16. World Average March 2007 mt = 170.9 ±1.1 (stat) ±1.5 (syst) GeV/c2 Petra Haefner

17. Signal only, jes Calibration Petra Haefner

18. Signal only, bjes Calibration Petra Haefner

19. Signal only, jes&bjes varied Petra Haefner

20. Signal + Background, no pbkg Petra Haefner

21. Ensemble Tests incl. btagging • signal only • no background probabilities included • jes = bjes = 1.0 • true mt: 170 GeV • left: btagging prbs not included • right: with btagging prbs included • errors are reduced by btagging 2.49 2.23 0.021 0.018 Petra Haefner 0.042 0.036

22. Calibration Points for jes, bjes 0.892 0.810 manual jes offset: • scale all jets according to jes manual bjes offset: • scale bjets according to bjes • true mt: 170 GeV • btagging prbs included • left: jes = 0.9 • right: bjes = 0.8 0.017 0.027 Petra Haefner -0.003 0.97 0.30 0.88