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Jet-jet angular distributions Blessing

Investigating quark substructure via angular distributions & MC simulation. Explore sensitivity & systematics in high-mass dijet data. Discover insights on jet energy scale & parton distribution functions.

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Jet-jet angular distributions Blessing

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  1. Jet-jet angular distributions Blessing Lee Pondrom and Yeongdae Shon University of Wisconsin September 18, 2008

  2. Data Sample • 1.1 fb­¹ integrated luminosity • 12 million jet100 triggers • 10 nb constant trigger cross section

  3. Minimal cuts • ||<2 • |Zvertex|<60 cm • Missing ET significance < 5 GeV

  4. QCD 22 angular distributions • The formulas of Combridge for q+qq+q, q+qbarq+qbar, q+qbarg+g, q+gq+g, g+gg+g, and g+gq+qbar give angular distributions which resemble Rutherford’s formula dd~1/sin4(*/2). Rutherford’s formula is flat in exp(|2|) Where ’s refer to the two leading jets

  5. Jet-jet angular distribution and quark substructure • Quark substructure effective contact color singlet Lagrangian of Eichten, et al is: • L = ±(g²/2Λ²(LLLL • Looks just like muon decay. Affects only the quarks. Color singlet means that some diagrams have no interference term. Correct formulas with interference are in CDFR3637. • g²/4 = 1; strength of the interaction ~(ŝ/²)² _ _ _

  6. Effect of quark substructure • The quark substructure Lagrangian is basically isotropic, so the angular distribution near *=, or  is most sensitive to . • The ET distribution also depends on , but is more sensitive to the jet energy scale than the angular distribution in a given mass bin.

  7. treatment of the data • Divide the data into four bins in jet-jet invariant mass, using the two highest ET jets in the event. Do not look for third jets. • Each bin is 100 GeV wide, starting at 550-650 GeV, and ending at 850-950 GeV.

  8. Monte Carlo predicts the expected QCD distributions, and the effects of quark substructure • The MC program used is Pythia. • Pythia generates the QCD event at the ‘hadron level’, without the CDF detector simulation, via a multistep process involving ISR, 22,FSR, and parton fragmentation. • Hadron level events are then subject to the full CDF detector simulation, and analyzed with the same code as data.

  9. Pythia Angular distributions compared to CDF data

  10. Pythia angular distributions compared to CDF data

  11. Pythia simulation fits to dataa1pT2+a2ŝ

  12. Pythia simulation fits to data

  13. Pythia Monte Carlo Simulation of quark substructure

  14. Pythia Monte Carlo Simulation of quark substructure

  15.  Distribution sensitivity to  • A ratio method was used to measure the effect of  on the angular distribution in a given mass bin. • Define R=(1<<10)/(15<<25). • Using Pythia for the  dependence, plot R()/R() versus (mass)4, where R() means no quark substructure.

  16. Dependence of the  ratios vs (mass)4 on the parameter 

  17. To obtain a limit we must understand the systematics • Sensitivity to the choice of the parton distribution functions. We are looking at high mass dijets, searching for quark substructure, so the most important pdf’s are proton valence  valence. • The first study compared CTEQ and MRST.

  18. MRST compared to CTEQ5

  19. Systematics of the pdf’s • MRSTLO ‘high s’ and CTEQ5L predict the same angular distributions with no quark substructure. • There is a new method for evaluating uncertainties from the pdf’s, using ‘vectors’ which represent 1 variation coming from the input experimental data.

  20. Systematic studies continued • Choice of Q2. Here the angular distributions differ. Vary the mix of ŝ and pT2 by 1. • The jet energy scale. Use the utility to vary the jet energy corrections by ±1. The high mass jet-jet cross section depends on the jet energy corrections.

  21. Varying JetEcorr by ±1σ

  22. Procedure • Calculate R for three MC samples: best fit, +1 and -1, varying the choice of Q2. • Do a simple average <R>=(R1+R2+R3)/3 • Calculate R for three data samples:level7 jetEcorrections, +1 and -1. • Again do a simple average <Rd>=(R1d+R2d+R3d)/3

  23. Systematic uncertainties • The systematics are included in the uncertainty in each ratio by summing the deviations from the mean: dR² = i=1,3(Ri-<R>)²/2 for the MC, and similarly for dR²d. • Then the final ratios Rd/R are calculated for each mass bin, and plotted vs (mass)4

  24. Summary • The ratio R=(110)/(1525) shows a linear dependence vs x=(mass)4 , with a slope which increases with increasing . • The data have a slope which is slightly negative: dR/dx = -0.160.08. This result is unphysical. • To set a limit, we use the Feldman Cousins method (PRD 57,3873 (1998)).

  25. Feldman Cousins method • The method is based on physically allowed results versus experimental results, which can be unphysical. • The uncertainties must be known, but not the result. • For a set of allowed results, generate all possible outcomes, using the uncertainties.

  26. Procedure • Eight input slopes were chosen, in steps of .05, between 0 and 0.4. • For each input slope, the output was obtained by Gaussian variation using the known uncertainties, including systematics • 20,000 ‘psuedo-experiments’ were performed for each input. • The resulting curves are normalized to one.

  27. Results of the pseudo-experiments

  28. Feldman Cousins renormalization • The next step is to renormalize the curves, by finding the maximum in each vertical tower, giving a box in x and y. • Then each box in that y row is divided by the maximum. • This gives step 2.

  29. Renormalized plot

  30. Final limits • By integration, 95% and 68% confidence contours can be extracted from this plot.

  31. Feldman Cousins limit contours

  32. Limits from the plot • From the intersection of the measured slope with the confidence level contours, we conclude: • Slope<0.24 95% confidence • Slope<0.06 68% confidence • Expected slope limit for zero slope result (based on these experimental uncertainties) slope<0.35

  33. Conclusions • To interpret these slopes as lower limits on the quark substructure parameter , we must rely on Pythia Monte Carlo simulation, which gives the sensitivity of the slope of the angular distribution ratio to . • 95% confidence >2.4 TeV • 68% confidence >3.5 TeV • 95% confidence expected result >2.2 TeV

  34. Requested material • Three topics are covered. Not part of the blessing. • 1. Extra jetEnergy uncertainty in the plug • 2. Hadron level corrections from Pythia • 3. Trigger threshold at 100 GeV in the Monte Carlo

  35. Check of the effect of the extra plug uncertainties • The normal level7 jetEcorrections package was run on 5M data jet100 events • The supplied uncertainty formula was applied only to those jets (1.1<|det|<2.1) • Central jets were not affected.

  36. Additional jet energy uncertainties

  37. Conclusion of the plug uncertainty exercise • Hardly any visible effect.

  38. Hadron level correctionsnotice how flat the had level distributions are

  39. Monte Carlo ratios had/detector

  40. Trigger threshold in the Monte Carlo simulation

  41. Monte Carlo trigger • The conclusion here is that, while the  distribution of the Monte Carlo in the 550-650 GeV mass bin does not exactly match the data, and the resulting 2 is bad, the discrepancy is not due to the trigger turn on. • There are small discrepancies in all of the plots, and each bin in  has over 1000 events.

  42. Дополнительныйматериал

  43. CTEQ6 and the vectors • Only CTEQ6 has the vectors. Earlier versions, like the default CTEQ5L used here, do not. • There are 40 vectors, in pairs up and down. They are linearly independent • It is not obvious which vectors affect specific pdf’s – like up quarks.

  44. CTEQ6 and the vectors cont’d • Preliminary studies with the full Pythia Monte Carlo, but without the CDF detector simulation, show that the vector effect is small. • Conclusion: The lack of knowledge of the pdf’s is not an important contributor to the systematic uncertainty.

  45. This is the analysis for which blessing is requested • The following slides were requested after the June 12 presentation. • Correction of the data to the hadron level is necessary to compare to NLOJet++, a subject which we prefer to postpone at the present time. The analysis for preblessing compares data as taken with fully simulated Monte Carlo.

  46. Further studies with Nlojet++ • NLO QCD C++ code written by Zoltan Nagy (arXiv:hep-ph/0110315) • Downloadable from CERN • Born+nlo calculations with 5E9 events • Three partons in the final state, pairs clustered in cone 0.7 merged to one ‘jet’. • Hard scale 0=ETave and 0=mjj match Pythia choices

  47. Data hadron level corrected compared to Pythia for Q2=pT2 +ŝ

  48. Pythia fit to the data corrected to the hadron level.

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