Detection of Z Gauge Bosons in the Di-muon Decay Mode

Transcription

1 Detection of Z Gauge Bosons in the Di-muon Decay Mode Robert Cousins, Jason Mumford and Slava Valuev University of California, Los Angeles CMS Physics Meeting June, CMS Physics Meeting June,

2 Introduction Z bosons appear in many models beyond SM. Z µ + µ is on list to be studied extensively for Physics TDR: Detailed signal and background studies, with the use of most complex available tools (full simulation, full reconstruction, etc.). As close to reality as possible (background uncertainties, detector misalignment, calibration and B field uncertainties, etc.). Strategy for physics as a function of luminosity. Main Z physics goals: Understand discovery potential and optimize the search strategy main observable: M µ+µ. This analysis Work out algorithms to distinguish among models (incl. graviton) and study properties, once discovered Work in progress main observables: A FB on- and off-peak, y, σ Br, Γ. CMS Physics Meeting June,

3 References This analysis is discussed in more detail in: Analysis note CMS A /. Talks at SUSY/BSM meetings, December and 7 March. Talk at PRS meeting, May. Talks on related subjects by UCLA group (see other references therein): Status of a Study of High-Mass Muon Pairs from Drell-Yan and Z (PRS/µ meeting, Sept. ; US-CMS physics meeting, 8 Oct. ). A Look at Track Quality Variables Inside Kalman Filter Fits to Tracker and Muon Hits (PRS/µ meeting, 8 Feb. ). Status of Z' Background Study for Data Challenge (PRS/µ meeting, April ). Status of a Study of High-Mass Muon Pairs from Drell-Yan, Z', and Gravitons (SUSY/BSM meeting, 7 May ). Root-Based Muon Analysis - A Users Perspective (Analysis Micro-Workshop, July ). Progress in Fitting High-Momentum Muons in ORCA (PRS/µ and SUSY/BSM meetings, -7 Sept. ). Modus Operandi for Z Analysis (EMU meeting, January ). Status of a Study of Simulated and Reconstructed Z Events in CMS (Workshop on Muons at the LHC and Tevatron, April ). CMS Physics Meeting June,

4 Z µ + µ : signal and backgrounds Z s arise in many models: Z SSM in sequential standard model (benchmark toy model); Z = Z ψ cosθ E + Z χ sinθ E in E and/or SO() models: Z ψ, Z χ and Z η (θ E = 7.78 o ); Z LRM and Z ALRM in left-right symmetric models; etc. Limits on the mass: Current: -8 GeV; Expected by LHC start-up: TeV. Br(Z µ + µ ): -8% (if no exotic decay channels are open) CMS Physics Meeting June, PYTHIA cross-sections; no added K-factors dσ/dm (fb/ GeV) BR tt DY M µµ (GeV) Dominant (and irreducible) background: Drell-Yan production of muon pairs pp γ/z µ + µ. Other sources: ZZ, WZ, WW, ttbar, bb-bar, etc. (studied as part of setting up DC) TeV Z SSM di-bosons

5 Generation and reconstruction Monte Carlo samples: couplings from literature, generated with PYTHIA. Z SSM, Z ψ, Z η, Z χ, Z LRM, Z ALRM at, and TeV decaying to µ + µ ( events each); Drell-Yan µ + µ pairs above.,.,,., and TeV ( events each). Simulation and reconstruction: CMSIM, ORCA (no pile-up) apply L and HLT requirements (p T and η thresholds et al., except for isolation); use MuonAnalysis package as an analysis framework; use L-seeded Global Muon Reconstructor (GMR) for muon identification; for off-line reconstruction, refit the GMR-found hits using an optimized combination of tracker-plus-first-muon-station and tracker-only fits (Truncated Muon Reconstructor, TMR) see three next slides. CMS Physics Meeting June,

6 Some possible track fitting methods Tracker plus full muon system ( Global Muon Reconstructor, GMR) Parameter measurement at inner surface of tracker from backward part of Kalman filter fit to tracker and muon hits (default fitting method). for more information. Tracker only Tracker System Measure here Forward filter Muon System Backward filter Use only tracker hits for Kalman filter. Take measurement from innermost tracker surface. Available as reconstruction option in ORCA (implementation by. eumeister). Iron CSC, DT Use scaled final forward values to initialize backward filter Tracker System Muon System Tracker plus first muon station Use tracker and hits from first muon station which contains hits. Tracker System Muon System CMS Physics Meeting June,

7 Optimization of high-p T muon track fitting Different fitting methods offer certain features: GMR current default for muons, uses all muon hits. Tracker only smallest p T -resolution tails, smallest RMS in barrel, and (currently) best pulls. Tracker plus first muon station best fitted p T -resolution sigma of the methods considered. Fits can be compared to choose fit method track-by-track. Kalman filter variables can be used as criteria for replacing bad fits. Currently use tracker-plus-first-muon-station fit, but replace it by tracker-only fit if it has much better probability of χ given degrees of freedom (about % of all tracks). ( Truncated Muon Reconstructor, TMR) (See J. Mumford s talks at PRS/µ meetings in February and September for more details.) CMS Physics Meeting 7 June,

8 Z SSM ( TeV) vs Drell-Yan background Default GMR Opp-sign dimuon mass Optimized Opp-sign dimuon mass Events/ GeV/ fb- GMR Events/ GeV/ fb- TMR mu+ mu- mass ORCA.. Digis MuonAnalysis package ote: Optimization algorithm was tuned on different sample. CMS Physics Meeting 8 June, mu+ mu- mass TMR has narrower signal, perhaps reduced background tails.

9 Event selection Both µ + and µ should be within < η. and pass the trigger: Acceptance efficiency: raises from about 8% at TeV to more than 9% at very high M µµ (Figure below); L/HLT trigger efficiency: about 98% at TeV, about 9% at TeV. Acceptance.8... M µ + µ - (GeV) Require that there are at least two µ s of opposite charge sign. o background-rejection cuts. Overall efficiency: 7-7% (- TeV). CMS Physics Meeting 9 June,

10 Fitting procedure Generate ensembles of MC experiments: number of events in each experiment fluctuates according to Poisson distribution with a mean of σ Br ( Ldt) ε; appropriately add Drell-Yan contribution from lower masses. In each experiment, fit M µµ values using an unbinned maximum likelihood: p( M µµ ) = s s ps ( M µµ ; m, Γ ) + pb ( M µµ ) tot tot p s (signal pdf) is a convolution of a Breit-Wigner with a Gaussian smearing; p b (background pdf) is an exponential, with the slope parameter determined from fits to Drell-Yan events. Up to three free parameters: signal fraction ( s / tot ), signal mean (m ), and signal FWHM (Γ). o constraints on the absolute background level: fit assumes only background shape is known. CMS Physics Meeting June,

11 Example: Z ψ at TeV, Ldt =. fb - - Events/ GeV/. fb True (PYTHIA) mass Reconstructed (optimized) mass Z DY Z DY - Events/ GeV/. fb σ m =.9% on-fluctuating mass spectra: (stat. much larger than expected) generated and reconstructed - Events/ GeV/. fb µ µ mass Reconstructed dilepton mass Entries S L = 7. Mean. RMS µ µ mass µ µ mass Reconstructed dilepton mass Events/ GeV/. fb Entries 7 Mean..8. S L =. RMS µ µ mass ( TeV: just above expected CDF/D mass reach; Ldt =. fb - : a few days of LHC low-luminosity running) Realistic mass spectra: two typical MC experiments B-only fit S+B fit CMS Physics Meeting June,

12 Fit results: m and Γ Signal mean mass: close to true value, small spread. Measured with precision of % (at high masses and discovery limit) or better umber of experiments TeV Z ψ,. fb Entries Mean 998. RMS 9.9 Underflow Overflow χ / ndf.7 / 8 Prob.997 Constant.9 ±. Mean 998. ±.9 Sigma 8.98 ±.7 TeV Z ψ, Ldt =. fb - Mean mass = 998 GeV; RMS = 9 GeV 9 9 m (GeV) Entries Mean 9 RMS 8.7 Underflow Overflow χ / ndf.7 / 9 Prob.78 Constant. ±.9 Mean 9 ±. Sigma 8. ± m (GeV) (Still have to account for the radiative tail in the mass distribution in the fits) umber of experiments TeV Z SSM, fb Signal Γ: hard to reconstruct (FWHM dominated by resolution smearing) - TeV Z SSM, Ldt = fb - Mean mass = 9 GeV; RMS = 8 GeV CMS Physics Meeting June,

13 Significance estimators (I) Discussed in detail in V. Bartsch and G. Quast, CMS I /9 Use likelihood-ratio estimator S L to calculate significance of an observed signal : = ln( L L ), where S L S + B B L S+B is the maximum likelihood from the signal-plus-background fit (p), L B is the maximum likelihood from the background-only fit (p b ). Justification: In the large-statistics limit, S L is expected to follow a χ -distribution with ndof equal to the difference in the number of free parameters between S+B and B-only hypotheses (theorem proved by S.S. Wilks in 98). If ndof is one, then distribution of S L is a standard Gaussian. Therefore, S L gives the probability (expressed in number of σ s) that the pure background fakes a signal (i.e. significance). CMS Physics Meeting June,

14 Significance estimators (II) For comparison with S L, also try a few other commonly used ( counting ) estimators: S =, S S S c c c cl = S S = ( = B S S + + B B, (proposed by S. Bityukov and. Krasnikov) ln ( S + B + ) exp( )). S B B Usual convention: S > is necessary to establish a discovery (probability of.9-7 that the pure background would mimic a signal) ), S and B number of signal and background events within m ±σ. S CMS Physics Meeting June,

15 Significance estimators: MC study Important caveat: Wilks theorem is valid in the largestatistics limit, whereas we are in the small-statistics regime eed to check that the tails of S L distribution for the background-only sample are those of the normal Gaussian Perform a (large) number of background-only MC experiments to obtain the distributions of various definitions of S given above. Calculate the probability (p-value) of observing a value of S greater than S crit (how often a false discovery would be claimed for a certain choice of S crit ). See how well this probability agrees with area in the tail of a Gaussian distribution. CMS Physics Meeting June,

16 Background to TeV Z ( fb - ) Sc Background-only mass fits: significance S B Sc_rec Entries Mean. RMS.7 Underflow Overflow ScL S cl ScL_rec Entries Mean.7 RMS.77 Underflow Overflow,, MC experiments < evt > above. TeV: < evt > within m ± σ m :. Sc S c Sc_rec Entries Mean.997 RMS.7 Underflow Overflow Sc S c Sc_rec Entries Mean.9 RMS.89 Underflow Overflow Fix both m and Γ to true values (see Wilks theorem) SL S L SL_rec Entries Mean.7 RMS.77 Underflow Overflow Observed: S L > : events S L > : 8 events S L > : events too many events at large S c Expected for a Gaussian: Above σ: events Above σ:. events Above σ:. events CMS Physics Meeting June,

17 Significance estimators: MC study Check p-values for a few other integrated luminosities and signal mass points: in these cases tail of S L distribution is always consistent with that of a Gaussian; all other S estimators may overestimate or underestimate the probability of a false discovery. Also check distributions of S for signal-plus-background fits: S c >> S L, S c ~ S L for all masses, luminosities, Z models; S L is always symmetric and Gaussian-like. Significance estimator S L performs as desired for Z mass reach studies (low background, small statistics regime). Similarly good performance of S L was seen by Bartsch and Quast in H µ studies, in a different sig/bknd regime. CMS Physics Meeting 7 June,

18 Z ψ at TeV,. fb - : significance Sc.8... s b Sc_rec Entries Mean. RMS.7 Underflow Overflow χ / ndf. / Prob.788 Constant. ±. Mean. ±. Sigma. ±.79 ScL.. ScL_rec Entries Mean. RMS.7 Underflow Overflow χ / ndf 7.9 / Prob.799 Constant. ±.7 Mean. ±. Sigma.77 ±. Fix both m and Γ to true values to calculate S L.8... Sc... ( Sc_rec Entries Mean.8 RMS. Underflow Overflow χ / ndf 7.79 / Prob.7 Constant. ±. Mean.8 ±. Sigma. ±. s b + ) b.. Sc Sc_rec Entries Mean.79 RMS.79 Underflow Overflow χ / ndf.7 / 7 Prob.887 Constant. ±.9 Mean.8 ±. Sigma.77 ±.8 s s S cl + b S c >> S L S c < S L S c S L (in agreement with other Z models, masses, luminosities tried) SL.... SL_rec Entries Mean.9 RMS.7 Underflow Overflow χ / ndf 7.9 / Prob.7 Constant.7 ±. Mean.9 ±. Sigma.9 ±. S L For. fb -, average S L is more than for all the Z models considered. TMR reconstruction of high-p T muons gives ~ % higher S L (% at TeV, % at TeV). S L scales very nicely with. Ldt CMS Physics Meeting 8 June,

19 Z µ + µ : CMS discovery potential ) - Int. luminosity (fb Z µ + - µ : σ significance curves ORCA.. no pile-up Z ψ Z Z η χ Z LRM Z SSM Z ALRM Z µ + µ mass reach: > TeV with. fb -.7. TeV with fb TeV with fb - (if GMR is used, GeV less with fb - and GeV less with fb - ) - - Z mass (TeV).B.: no syst. uncertainties Perfect alignment, calibration, B field; Background shape, functional forms of pdf s, mass resolution perfectly known. CMS Physics Meeting 9 June,

20 A critical look Main weak point: systematic uncertainties are not taken into account. Arising from imperfect knowledge of the detector: alignment, magnetic field, calibration, etc. In the fitting procedure: background shape, functional forms of pdf s, mass resolution, etc. Some other items to be improved/checked: Brem photons. ot used in the reconstruction of muon momentum; residual radiative tail not accounted for in the fits. Software. Set of PYTHIA, CMSIM and ORCA is. years old. Event rates. Given by PYTHIA; need to check K-factors. Pile-up. eglected; effect is expected to be small, but not proven. How does this study compare with the previous ones? CMS Physics Meeting June,

21 Previous studies of CMS discovery potential (I) Estimates of the CMS potential to discover Z were previously reported by four groups/individuals. In chronological order: C.E. Wulz: (CMS-T/9-7 and DPF/DPB Snowmass (99)) Tools: PYTHIA version available at that time; muon momentum smeared using parameterization by W. Ko and J. Rowe (CMS T/9-). Criterion for Z discovery: more than signal (di-muon plus di-electron) events in the mass peak. Conclusion: it will be possible to discover Z bosons up to a mass of about TeV with an integrated luminosity of fb - (in a combined analysis of Z µ + µ and Z e + e channels). D. Bourilkov: (CMS I-/ and CER-YR--) Study mainly dedicated to Drell-Yan production of lepton pairs at LHC. Tools: PYTHIA; no further details given. Conclusion: Z resonances with masses up to ~ - TeV can be probed at LHC. CMS Physics Meeting June,

22 Previous studies of CMS discovery potential (II) JIR group (V. Palichik, S. Shmatov et al.): (hep-ph/, talks at CMS physics ( April ) and SUSY/BSM meetings (7 May ); presented at Physics at LHC, Prague ) Tools: PYTHIA; muon momentum smeared using parameterization by W. Ko and J. Rowe. Criterion for Z discovery: S c > and at least signal events under the mass peak. Conclusions: Z mass reach is in the range between. and TeV for an integrated luminosity of fb -, and between. and TeV for a luminosity of fb - (for a set of Z models similar to one we studied). ETH group (M. Dittmar et al.): (Phys. Lett. B8 (), talk at SUSY/BSM meeting (7 Sept. )) Study focused on observables other than M µ+µ. Tools: PYTHIA; no details given on how the stated mass reach was obtained. Conclusion: reconfirm the known Z boson LHC discovery potential, to reach masses up to about TeV for a luminosity of fb -. CMS Physics Meeting June,

23 Comparison with previous studies This study has two main advantages: Full simulation and reconstruction of signal and background; therefore, takes into account: Trigger and track-finding inefficiencies; Charge misassignment; Details of detector acceptance; Momentum and mass resolution, etc. Appropriate statistical techniques to quantify the mass reach. We believe it gives somewhat more justifiable estimates of CMS discovery potential in Z µ + µ channel, while still suffering from the lack of systematic errors. CMS Physics Meeting June,

24 Summary We have set up a procedure for studying and quantifying the Z mass reach. Main points: Full simulation (CMSIM) and reconstruction (ORCA) as input; Unbinned M.L. fits exploring signal and background shapes only; Likelihood-ratio significance estimator, shown to perform as desired. We have obtained mass reach estimates in Z µ + µ channel, with systematic uncertainties yet to be accounted for: More than σ significance above TeV at the earliest stages of datataking; Average σ significance at a mass of.7-.7 TeV (depending on the model) with an integrated luminosity of fb -. Plan to evaluate systematic uncertainties and their impact, and improve/check other items mentioned earlier. CMS Physics Meeting June,

25 Acknowledgements We would like to thank all the members of CMS who contributed to the software packages used in this study. We are particularly grateful to: orbert eumeister, for his assistance and numerous useful discussions on reconstruction-related issues. Our referees (Marcos Cerrada, Marcella Diemoz, and Stefano Lacaprara), for careful reading of the note and helpful comments and questions. CMS Physics Meeting June,

26 Backup slides follow CMS Physics Meeting June,

27 Background to TeV Z ( fb - ) Sc Background-only mass fits: significance S B Sc_rec Entries Mean. RMS.7 Underflow Overflow 89 ScL S cl ScL_rec Entries Mean.88 RMS. Underflow Overflow 8,, MC experiments < evt > above TeV: 7. < evt > within m ± σ m : Sc S c Sc_rec Entries Mean.879 RMS.99 Underflow Overflow Sc S c Sc_rec Entries Mean. RMS.79 Underflow Overflow too many events in the tails SL S L SL_rec Entries Mean.8 RMS. Underflow Overflow Observed: S L > : events S L > : events S L > : events Expected for a Gaussian: Above σ: events Above σ:. events Above σ:. events CMS Physics Meeting 7 June,

28 Example at TeV: Z SSM at fb - True (PYTHIA) mass Reconstructed (optimized) mass Events/ GeV/ fb- 8 Z Events/ GeV/ fb- 8 σ m =.7% DY Z DY on-fluctuating mass spectra: (stat. much larger than expected) generated and reconstructed mu+ mu- mass Reconstructed dilepton mass mu+ mu- mass Reconstructed dilepton mass Events/ GeV/ fb-.. S L =. Entries Mean RMS. Events/ GeV/ fb S L =. Entries Mean 9 RMS 8.8 Realistic mass spectra: two typical MC experiments. mu+ mu- mass.8... mu+ mu- mass B-only fit S+B fit CMS Physics Meeting 8 June,

29 Z SSM at TeV, fb - : significance Sc Entries Mean 7.9 RMS 8.9 Underflow Overflow χ / ndf 9.7 / 9 Prob.98 Constant.7 ±. Mean 8 ±.797 Sigma 8. ±. Sc s b ( Entries Mean 7.89 RMS.977 Underflow Overflow χ / ndf. / Prob. Constant. ±.79 Mean 7. ±.7 Sigma.998 ±. s b + ) b Sc SL Entries Mean.89 RMS.7 Underflow Overflow χ / ndf.7 / Prob. Constant 9.8 ±. Mean.7 ±. Sigma.99 ±.7 s S L Entries Mean 8.98 RMS.8 Underflow Overflow χ / ndf.877 / 8 Prob.777 Constant.9 ±.8 Mean ±.8 Sigma.7 ±. s + b Fix both m and FWHM to true values to calculate S L S c >> S L S c < S L S c ~ S L for all Z models, masses, luminosities tried Bartsch and Quast also found that S c badly overestimates true S CMS Physics Meeting 9 June,

30 Z at TeV: S L significance L dt Z SSM Z ψ Z η Z χ Z LRM Z ALRM fb - OPT fb - GMR fb - OPT For fb -, S is more than for most of the Z models considered; For fb -, S is less than for all models; S L scales nicely with L int TMR reconstruction of high-p T muons helps (~ % gain). CMS Physics Meeting June,

31 Example at TeV: Z ψ at fb - Events/ GeV/ fb- True (PYTHIA) mass Z DY.. 7 mu+ mu- mass Reconstructed dilepton mass Events/ GeV/ fb S L =. Entries Mean RMS 7. Reconstructed (optimized) mass Events/ GeV/ fb- Events/ GeV/ fb mu+ mu- mass Reconstructed dilepton mass.8. DY σ m = 8.% Z S L =.7 Entries Mean RMS 7 on-fluctuating mass spectra: (stat. much larger than expected) generated and reconstructed Background flattens out with mass; how well can it be controlled? Realistic mass spectra: two typical MC experiments mu+ mu- mass.. 7 mu+ mu- mass B-only fit S+B fit CMS Physics Meeting June,

32 Z at TeV: S L significance L dt Z SSM Z ψ Z η Z χ Z LRM Z ALRM fb - OPT fb - GMR fb - OPT For fb -, S is less than for all Z models considered; For fb -, S is still less than for most of the models; Again, TMR reconstruction results in a higher S (by ~ %). CMS Physics Meeting June,