1. Jet-jet angular distributions and search for quark substructure in p-p collisions at 1.96 TeV Lee Pondrom, U. of Wisconsin, for the CDF Collaboration XIX International Baldin Seminar September 29-October 4, 2008

2. Tevatron Run2 Collider operations About 5 fb -1 delivered, and 4 fb -1 recorded each by CDF and D0. About 2 fb -1 delivered in calendar 2008. Instantaneous luminosity record 315 E30. Initial pbars 3E12 at 980 GeV. Run to last one or two more years.

3. Tevatron collider operations Store 6434 Monday Sept 22

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

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

6. Typical dijet event display

7. 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/sin 4 (  */2). Rutherford’s formula is flat in  exp(|    2 |) Where  ’s refer to the two leading jets

8. 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 u and d quarks. Color singlet means that some diagrams have no interference term. g²/4  = 1; strength of the interaction ~(ŝ/  ²)² This measurement is not sensitive to the interference term. _ _ _

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

10. treatment of the data Divide the data into four bins in jet-jet invariant mass, using the two highest E T 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.

11. 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.

12. Pythia Angular distributions compared to CDF data

13. Pythia angular distributions compared to CDF data

14. Pythia simulation fits to data a 1  p T 2 +a 2  ŝ

15. Pythia simulation fits to data

16. Pythia Monte Carlo Simulation of quark substructure

18.  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.

19. Dependence of the  ratios vs (mass) 4 on the parameter  Systematic uncertainties included

20. Sensitivity of the slope to the quark substructure parameter  Limit is dominated by systematic uncertaities

21. Systematics There are many adjustable parameters in the comparison of data to Monte Carlo simulation. Is it possible to adjust the Monte Carlo to mask the presence of new physics in the data? The answer is yes. The study of systematics should give the degree of flexibility inherent in the comparison.

22. 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.

23. MRST compared to CTEQ

25. Systematics of the pdf’s MRSTLO ‘high  s ’ and CTEQ5L predict the same angular distributions with no quark substructure. A new method for evaluating uncertainties from the pdf’s, using ‘vectors’ which represent uncertainties coming from the input experimental data. Preliminary studies of the vectors in CTEQ6 indicate small effects on the  ratios.

26. Systematic studies continued Choice of Q 2. Here the angular distributions differ. Vary the mix of ŝ and p T 2 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.

27. Procedure Calculate R for three MC samples: best fit, +1  and -1 , varying the choice of Q 2. Do a simple average =(R 1 +R 2 +R 3 )/3 Calculate R for three data samples:level7 jetEcorrections, +1  and -1 . Again do a simple average =(R 1d +R 2d +R 3d )/3

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

29. 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)).

30. 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.

31. Feldman-Cousins plot

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

33. Feldman Cousins limit contours

34. 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

35. Sensitivity of the slope to the quark substructure parameter  Limit is dominated by systematic uncertaities

36. 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

37. Дополнительный материал

38. 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

39. 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.

40. Additional jet energy uncertainties

41. Conclusion of the plug uncertainty exercise Hardly any visible effect.

42. Hadron level corrections notice how flat the had level distributions are

43. Monte Carlo ratios had/detector

44. Trigger threshold in the Monte Carlo simulation

45. 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.

46. 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.

47. 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.

48. 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.

51. 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 =E Tave and  0 =m jj match Pythia choices

52. Data hadron level corrected compared to Pythia for Q 2 =p T 2 +ŝ

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

54.  =3 TeV Pythia fits to data

55. Nlojet++ angular distributions for two choices of hard scale

56. Nlojet++ compared to Pythia Slightly different pdf’s:CTEQ5L for Pythia and CTEQ6 for Nlojet++ The dependence on the hard scale is much reduced in Nlojet++, where E Tave and m jj have almost the same shapes. The data follow  0 =p T (Pythia), but either choice for  0 works with Nlojet++ This justifies the procedure used earlier,where the variation in Q 2 was limited in systematics

57. Nlojet++ fits to the data-about 50- 50 E Tave and m jj

58. For Nlojet++ define R=  (1->10)/  (10->20)

59. Switch on quark substructure in Pythia.

60. R from Pythia with quark substructure

61.  2 vs  -4 for R(data) using linear fits from Pythia

62. Conclusions Nlojet++ confirms the limited variation of Q 2 in Pythia in systematics studies. Jet energy corrections systematics need another look. Hadron level jet100 data are consistent with nlo QCD predictions. Pythia must be used to extract , and the limit for (u,d,s) quarks will be near 3 TeV.

63. Vertex and MET before cuts

64. Data kinematic distributions

65. More data kinematic distributions

66. 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.

67. Modifications to the default QCD monte carlo mstp(32) Q² flag from 8-pt² to 4-ŝ msel from 1 to 0 allows user to switch on new physics msub(381) to msub(388) standard QCD 2  subprocesses ckin(1)=400. sets  ŝ>400 GeV ckin(3)=90. sets pt>90 GeV/c itcm(5)=1 switches on quark substructure Rtcm(41)=Λ in GeV rtcm(42)=±1 sign of interference term

68. MC cut on CM energy The requirement ckin(1)=400 was made to save MC disk space and execution time. The QCD default runs with ckin(3)=200 give similar mass distributions, but distort the angular distributions, so are not suitable. An overall factor of five is gained in total number of events vs events at high mass.

69. MC pT>90GeV Q²=pT² CTEQ5L

70. Data and Pythia ET and mass

71. Fits of the MC to data 48  bins Data(k)=a 1  p T 2 (k)+a 2  ŝ(k) Mass GeV Events data a1a1 a2a2 ²² 550- 650 1659261.50± 0.04 0.49± 0.04 87.8 650- 750 544041.52± 0.07 0.46± 0.07 28.2 750- 850 161121.40± 0.13 0.54± 0.12 57.9 850- 950 45811.14± 0.17 0.77± 0.17 39.7

72. R ratios vs jet-jet (mass) 4

73. Plot the slope vs 1/  4

74. Q² not correlated with PDF’s

75. Q² dependence study Mass GeV a 1 upa 2 dna 1 dna 2 up ²² 6001.58.411.42.5793 7001.66.331.39.5932 8001.66.31.14.7862 9001.48.43.81.1144

76.  Plots varying the Q² fit

77. Jet energy corrections

78. Angular distributions ±1σ JetEcorr

79. Monte Carlo R ratios for systematics Mass bin GeV R p T ² dn 2  R best fit R p T ² up 2  600 0.994±0.0060.978±0.0080.963±0.007 700 0.849±0.0110.825±0.0130.802±0.012 800 0.846±0.0200.803±0.0230.762±0.021 900 0.829±0.0360.779±0.0420.731±0.036

80. Jet100 data varying jetEcorr for systematics Mass bin GeV Up 1  Level7 jetEcor Down 1  600 1.050±0.0060.967±0.0060.905±0.006 700 0.839±0.0090.817±0.0100.788±0.011 800 0.788±0.0160.766±0.0180.742±0.020 900 0.756±0.0290.711±0.0310.696±0.036

81.  =2TeV Pythia fits to data