Dynamical Likelihood Method and CDF Top Mass Measurements Corfu2005 K.Kondo

1. Dynamical Likelihood Method and CDF Top Mass Measurements Corfu2005 K.Kondo CONTENTS Dynamical Likelihood Method (DLM) Differential cross section Transfer function Likelihoodas a function of dynamical parameters Methods of Top Mass Measurement at CDF Template method Matrix element method (Dalitz-Goldstein-D0 type) Quantized DLM (QDLM) TTbar Processes for Top Mass Determination lepton+4jets (l+j), dilepton+2jets (dlep)

2. 2 km Tevatron in Run2 • The Tevatron : pp collider • 6x6 36x36 p and p bunches • 3.5μs  396 ns between xing.

3. The CDF-Ⅱ Detector polar angle  Silicon Tracking Detectors Central Outer Tracker (COT) h = 1.0 Solenoid Coil h = 2.0 EM Calorimeter  h = 2.8 Hadronic Calorimeter Muon Drift Chambers Muon Scintillator Counters Steel Shielding

4. Why Top Quark Mass ?

5. ν W＋ e+ jet t g b b t jet u（ｐ） d jet W－ jet u 時間 t t Production and Decay t Wb; W ln, qq’ ( l = e,m ) t t 2l+2b+MET(5%), l+4j+MET(30%), 6j(44%) Example of l+4j+MET Secondary vertex detection u (p) Key information: MW is well known, b can be tagged.

6. Mtop Measurements at Tevatron (Run1 & 2) • Combined RunI mass: • mt=178.0 ± 4.3 GeV/c2 • was: 174.3 ± 5.1 GeV/c2 • Higgs mass • Best-fit MH 113 GeV/c2 • 95% C.L. : MH < 237 GeV/c2 • Run II measurements • Template • QDLM • M.E. method(D-G type) • mt=172.7 ± 4.3 GeV/c2 • by l+j Template and QDLM l+j dilep

7. Brief History of DLM and Related Methods - History - K.K.: J.Phys.Soc.Jpn57 (1988) 4126, DLM Dalitz-Goldstein: Phys.Rev. D45 (1992) 1531. M.E. method (D-G type) First observation of top at CDF (1994), Template method D0 Collabolation, Run1: Nature 429(2004), Phys.Lett. B617 (2005). M.E. CDF Collaboration, Run2: to be submitted to PRL & PRD. Template & QDLM K.K.: hep-ex/0508035(2005). QDLM (Quantized DLM) - CDF Top Mass Measurements in Run2 - Template Method Metrix Element Method ( Dalitz-Goldstein-D0 type) QDLM for l+4j, dilepton, all-jets channels, and for ttbar resonance search.

8. Ｄｙｎａｍｉｃａｌ　Ｌｉｋｅｌｉｈｏｏｄ　ＭｅｔｈｏｄEvent reconstruction using parton dynamics explicitely Ｍｏｔｉｖａｔｉｏｎ Uncertainties in collider events quarks, gluons → jetsmomentum-energy measurements missing particles → MET parton-jet identification unknown initial state signal-background identification Advantage: Overall pictures of each event is observed. Probabilistic full reconstruction of parton processbased ontheory and observation: Determine dynamical parameters, e.g. M, G, V-A vs. V+A, S/B likelihood,...

9. parton process dynamical parameter Transfer Function path P.D.F. observed beam Posterior probability: Ｃｏｎｃｅｐｔ　of DLM

10. Use of differential cross section Traditional: prior probability DLM: posterior probability integrate (QDLM) QDLM: Each final parton occupies a unit phase space. For a given(c1,…,cn) , integrate by (a,b): I(a*,b*): parton flux factor, ds/dF n(f):Probability for a single quantum state per unit luminosity of the incident beams. Final state density=1

11. 3 Versions of Likelihood Single path likelihood Template: dilep M.E.: QDLM: Multiple paths/events: maximum likelihood search 1. Get max-like mass, , in an event and compare its distribution in multiple events with those of M.C. events of known masses. 2. Joint likelihood function for multiple events

12. Mass measurement by Template M. First Observation of Top Quark at CDF: (Run1) - Template Method - データ T.M.= Simplified DLM ● Definition of likelihood is simplified as Xsec　⇒ Propagator T.F. ⇒Gaussian ● Calibration: compare max- like mass distribution with those of Monte Carlo sample of known masses. トップ対＋ BG data t t + BG Background(BG) バックグラウンド（BG）

13. Event by event likelihood distributionl+j: Template & QDLM (Run2) likelihood Mtop TemplateQDLM 2b-tagged QDLM 1b-tagged

14. Quantization of Transfer Variable Space(QDLM) For a single path, the phase volume and Jacobian- scaled transfer variables are both quantized. QDLM is essentially Jacobian free.

15. Phase space and observables (QDLM) ds/dFn(f) DFn(f) D3np ds/dX D3nX W(Y|X) D3nY ds/dY

16. Resonance “sｒ” for reconstruction

17. dy x Transfer Function derived by M.C. events y, dx • M.C. eventswith the same cuts as applied to data. • Require parton-jet matching (DR<0.4). • Scale invariance of TF • Variable transform x

18. Transfer Functions (ＱDLM) b-jets W-jets

19. Background and TTbar Candidate Events l+j Background Composition and Number of TTbar Candidate Template QDLM Source Expected Background Identified TTbar Candidates Dominant background for l+4j+MET channel (W+QCD jets)

20. ＱDLM: Signal/Background Separationby Likelihood Distributions Parton Level CDF simulation x = Mtop y =–2ln(L) background background Chi2 min. at : input mass: Signal lower mass:Bkgd signal signal:175GeV We expect the background makes likelihood peak down when it is multiplied to signal events.

21. Likelihood for Signal & Background Zjj-like TTbar-like l+jets QDLM Dilepton M.E.

22. Systematic Uncertainty (QDLM/Template) Calibration of jet energy scale using TTbar events themselves (In-situ calib) This is possible by other methods too. Systematic DLM Template DMtop(GeV) DMtop(GeV) Jet Energy Scale 3.0 [~2.5] ISR/FSR 0.6 0.7 PDF 0.5 0.3 Modeling 0.8 0.9 Method 0.5 0.6 Total 3.2 1.3 Template

23. Calibration for measured mass value Why? Propagetor factor of orignal B-W form is assumed: cf. Effective form including higher order effects is in Pythia. Parton-jetmatching is not guaranteed. 1 parton→parton shower→fragmentation→detector→jet(s) Even if a parton and a jet are matched, the topology assignment is not unique. Multiple solutions for unmeasured momenta. Background still remains.

24. Mapping Function vs. Background (QDLM) (9.1 events) Reconstructed Mtop = 171.8 Reconstructed mass with Correctedmass based on various background fracrtion the estimated b.g. fraction

25. Input-output masses after calibration dilep M.E.l+j QDLM Output masses are corrected with the mapping function.

26. Joint mass likelihood Dilepton M.E. l+j QDLM

27. Event max-like Mtop distributions Template QDLM

28. Uncertainty Check by Pseudo-experiments Dilepton M.E. l+j Template

29. Concluding Remarks on DLM • DLM is useful for particle searches as well as for high precision measurements. But there is room for improvement/development. • Parton kinematics determination by DLM, • Identifications of parton-jet, S/B and correct solutions. • Calibration by M.C. generator saves you at any stage of your analysis. • It is amusing to notice that space-time Lagrangian momentum Likelihood

30. Backup slides

31. Procedure of Mass Measurements • Definition of likelihood • Transfer function from parton to obsevable variables • Study of Signal/Background likelihood • Mass determination: (a) Max-like mass for each event, and compare its distribution with that of M-known M.C. events (b) Likelihood as a function of M and take maximum value of joint likelihood of multiple events • Calibration of the reconstructed mass (a)template (b) mapping function • Systematic uncertainties of the mass (a) based on QCD jets (b) from DLM itself

32. Systematic Uncertainty (QDLM)

33. Summaryof QDLM • We assume a single path occupies a unit p.s. DFn*=1. The cross section for the path is given by • The variable space in a single path is • Prior TF is obtained by the MC events satisfying the event selection criteria. Posterior TF is obtained from prior TF and • The likelihood for the k-th path in the i-th event is defined by • The expectation value of the event likelihood is given by • The likelihood of dynamical constant a is =1 const.

34. Conclusion • A precise Mtop measurement provides a good estimate of mass range of Higgs in the Standard Model. • If Higgs is excluded in the estimated mass range, whether found in elsewhere or not, a new physics will immediately start. Hopefully, this happens in ~ 5 years. • DLM will evolve as the standard method of data analysis in H.E. particle physics.

35. Solving problems by likelihood The values of likelihood can be used for process (S vs. B) determination, right topology identification, right solution for missing momentum. By iteration, one gets better estimation of L measurement of dynamical parameter study of kinematics

36. Event selection criteria • Events are energetic • Ht,SumEt • Events are central and spherical • ||< 2.0, aplanarity • Two high ET b-jets • Displaced secondary vertex • Soft lepton inside jet • High energy jets and isolated leptons • missing Et from neutrino in leptonic modes • High Et jets • Possible additional jets from gluon radiation (isr,fsr)

37. Concept of QDLMQuantized phase space and transfer variables parton process theoretical experimental observed beam

38. Normalization of ds/dF as likelihood P(a), l0 : Prior probabilities. [ l0 ] = [L] - 2 We assume Bayes’ Postulate ( Principle of Equidistribution of Ignorance ). Quantities parameters: a variables: x, Lint and Ntot ( depend on a implicitly). true value of a

39. Crosssectionandprobabilitydensityfunction (p.d.f.) Take an example of a = M. f (x;M)= p.d.f. (Axiom No.1 for p.d.f.) ( Dalitz-Goldstein,... ) This is quite reasonable for a general p.d.f., but • Nds/dx depends on the choice of x, while ds/dFn does not. • ds/dFnis a probability per unit beam luminosity. This concept is missing in the general p.d.f. f (x;M).

40. Expectation value of likelihood for an event • Likelihood of from multiple events • Variable transformation from to

41. Discovery of c,b c, bの発見TC-mass parton state = observable

42. Posterior TF x , y : indicates 1-d quantity in this page

43. TTbar 6 jet channel：　parton-jet idetification by Likelihood 戸谷・蛯名 Quark level Observation level

44. Topmass in Tevatron, LHC, ILC Measurements at TeV2, LHC,ILC W mass, Top mass, Weinberg angle →New physics search with higher order corrections Energy scan near the top threshold

45. Why Top Mass (in S.M.) Mt  175 GeV  (vacuum expectation value of Higgs) = 171.274 GeV Special role in EWSB ? Dominant parameter in radiative corrections: quadratic in mt , logarithmic in mH Mt and EW measurements gives MHiggs

46. Blue band