1. Diffraction at Tevatron p p  p p p p  p (p) + X p p  p (p) + j j p p  p p + j j

3. Color Singlet Exchange

5. Hard Color Singlet Studies jet    QCD color-singlet signal observed in ~ 1 % opposite-side events ( p ) Publications DØ: PRL 72, 2332(1994) CDF: PRL 74, 885 (1995) DØ: PRL 76, 734 (1996) Zeus: Phys Lett B369, 55 (1996) (7%) CDF: PRL 80, 1156 (1998) DØ: PLB 440, 189 (1998) CDF: PRL 81, 5278 (1998) H1: hep-ex/0203011 (sub. to Eur Phys J C) Newest Results  Color-Singlet fractions at  s = 630 & 1800 GeV  Color-Singlet Dependence on: , E T,  s (parton-x)

6. DØ Detector EM Calorimeter L0 Detector beam (n l0 = # tiles in L0 detector with signal 2.3 < |  | < 4.3) Central Gaps EM CalorimeterE T > 200 MeV|  | < 1.0 Forward Gaps EM Calorimeter E > 150 MeV2.0 < |  | < 4.1 Had. CalorimeterE > 500 MeV3.2 < |  | < 5.2) Central Drift Chamber (n trk = # charged tracks with |  | < 1.0) End Calorimeter Central Calorimeter (n cal = # cal towers with energy above threshold) Hadronic Calorimeter

7. Measurement of f s Count tracks and EM Calorimeter Towers in |  | < 1.0 E T >30 GeV f S 1800 = 0.94  0.04 stat  0.12 sys % jet    Negative binomial fit to “QCD” multiplicity f S = color-singlet fraction =(N data - N fit )/N total (Includes correction for multiple interaction contamination. Sys error dominated by background fitting.) High-E T sample (E T > 30 GeV,  s = 1800 GeV)

8. 630 vs. 1800 Multiplicities Jet E T > 12 GeV, Jet |  | > 1.9,  > 4.0 R 1800 = 3.4  1.2 Opposite-Side DataSame-Side Data 1800 GeV: 630 Gev: n cal n trk f S 1800 (E T =19.2 GeV) = 0.54  0.06 stat  0.16 sys % f S 630 (E T = 16.4 GeV) = 1.85  0.09 stat  0.37 sys % 630

9. Color Singlet Models If color-singlet couples preferentially to quarks or gluons, fraction depends on initial quark/gluon densities (parton x) larger x  more quarks Gluon preference: perturbative two-gluon models have 9/4 color factor for gluons  Naive Two-Gluon model (Bj)  BFKL model: LLA BFKL dynamics Predictions: f S (E T ) falls, f S (  ) falls (2 gluon) / rises (BFKL) Quark preference:  Soft Color model: non-perturbative “rearrangement” prefers quark initiated processes (easier to neutralize color)  Photon and U(1): couple only to quarks Predictions: f S (E T ) & f S (  ) rise

10. Model Fits to Data Using Herwig 5.9 Soft Color model describes data  s = 1800 GeV

11. Survival Probability Assumed to be independent of parton x (E T,  ) Originally weak  s dependence Gotsman, Levin, Maor Phys. Lett B 309 (1993) Subsequently recalculated GLM hep-ph/9804404 Using soft-color model (uncertainty from MC stats and model difference) with

12. Modifications to Theory  BFKL: Cox, Forshaw (manhep99-7) use a non- running  s to flatten the falling E T prediction of BFKL (due to higher order corrections at non-zero t)  Soft Color: Gregores subsequently performed a more careful counting of states that produce color singlets to improve prediction.

13. Hard Single Diffraction -4.0 -1.6  3.0 5.2 Measure min multiplicity here -5.2 -3.0 -1.  1. 3.0 5.2 OR FGap fractions (central and forward) at  s = 630 & 1800 GeV  Single diffractive  distribution Phys Lett B 531 52 (2002) Measure multiplicity here

14. 630 vs. 1800 Multiplicities  s = 1800 GeV:  s = 630 GeV:

15. Event Characteristics 1800 Forward Jets Solid lines show show HSD candidate events Dashed lines show non-diffractive events Less jets in diffractive events Jets are narrower and more back-to-back Diffractive events have less overall radiation Gap fraction has little dependence on average jet E T

16. Comparison to MC f visible =  gap · f predicted   gap *Add diffractive multiplicity from MC to background data distribution *Fit to find percent of signal events extracted  Find predicted rate POMPYT x 2 / PYTHIA *Apply same jet  cuts as data, jet E T >12GeV *Full detector simulation * Model pomeron exchange in POMPYT26 (Bruni & Ingelman) * based on PYTHIA * define pomeron as beam particle * Use different structure functions

18. Pomeron Structure Fits  Demand data fractions composed of linear combination of hard and soft gluons, let overall  s normalization and fraction of hard and soft at each energy be free parameters  If we have a  s independent normalization then the data prefer : –1800: hard gluon 0.18±0.05( stat )+0.04-0.03( syst ) –630: hard gluon 0.39±0.04( stat )+0.02-0.01( syst ) –Normalization: 0.43±0.03( stat )+0.08-0.06( syst ) with a confidence level of 56%.  If the hard to soft ratio is constrained the data prefer: –Hard gluon: 0.30±0.04( stat )+0.01-0.01( syst ) –Norm. 1800: 0.38±0.03( stat )+0.03-0.02( syst ) –Norm. 630: 0.50±0.04( stat )+0.02-0.02( syst ) with a confidence level of 1.9%.  To significantly constrain quark fraction requires additional experimental measurements.  CDF determined 56% hard gluon, 44% quark but this does not describe our data without significant soft gluon or 100% quark at 630

19. Where  is the momentum fraction lost by the proton *Can use calorimeter only to measure *Weights particles in well-measured region *Can define for all events *  calculation works well * not dependent on structure function or center-of- mass energy *Collins (hep-ph/9705393)  true =  calc · 2.2± 0.3  Calculation

20.  distribution for forward and central jets using (0,0) bin  p p =   0.2 for  s = 630 GeV  s = 1800 GeV forward central  s = 630 GeV forward central Single Diffractive  Distributions

22. CDF Diffractive W CDF used asymmetry to extract diffractive component of the W signal 1)TOPOLOGY -lepton favors the hemisphere opposite the rapidity gap -compare multiplicity for region on same side of lepton vs opposite side 2)CHARGE -proton(uud) pomeron(qq) gives twice as many W + as W - -W + production is associated with gaps in p direction (and W - with p) Drawback: Asymmetry approach reduces statistical power of data

23. CDF Diffractive W CDF {PRL 78 2698 (1997)} measured R W = 1.15 ± 0.55% where R W = Ratio of diffractive/non-diffractive W a significance of 3.8 

24. DØ Central W Multiplicity Peak at (0,0) indicates diffractive W-boson Signal: 68 of 8724 events in (0,0) bin n cal L0 n L0 n cal  -1.1 0 1.1 3.0 5.2  Minimum side n cal n L0 DØ Preliminary

25. W Event Characteristics Standard W Events Diffractive W Candidates E T =37.12 E T =35.16 E T =36.08 M T =70.64 M T =70.71 Electron E T Neutrino E T Transverse Mass DØ Preliminary E T =35.27

26. W/Z Data Results Sample Diffractive Probability Background All Fluctuates to Data Central W (1.08 + 0.19 - 0.17)% 1 x 10 -14 7.7  Forward W (0.64 + 0.18 - 0.16)% 6 x 10 -8 5.3  All W (0.89 + 0.19 – 0.17)% 3 x 10 -14 7.7  Z (1.44 + 0.61 - 0.53)% 5 x 10 -6 4.4  *Observed clear Diffractive W and Diffractive Z signals *Measured Diffractive W/All W and Diffractive Z/All Z DØ Preliminary

27. Rate Comparison Correct MC for gap efficiency 20-30% for quark and hard gluon (soft gluon fractions <0.02%) FINAL GAP FRACTION Sample Data Quark Hard Gluon Cen W (1.08 + 0.21 - 0.19)% (4.1  0.8)% (0.15  0.02)% For W (0.64 + 0.19 - 0.16)% (7.2  1.3)% (0.25  0.04)% Z (1.44 + 0.62 - 0.54)% (3.8  0.7)% (0.16  0.02)% NOTE: Observe well-known normalization problem for all structure functions, also different dependence on  for data and MC, as in dijet case DØ Preliminary

28. Demand gap on one side, measure multiplicity on opposite side Gap Region 2.5<|  |<5.2 Double Gaps at 1800 GeV |Jet  | 15 GeV DØ Preliminary

29. Demand gap on one side, measure multiplicity on opposite side Gap Region 2.5<|  |<5.2 Double Gaps at 630 GeV |Jet  | 12 GeV DØ Preliminary

30. Tevatron Summary  Measurements at two CM energies with same detector adds critical new information for examining pomeron puzzle –The higher rates at 630 were not widely predicted before the measurements  Pioneering work in Central Rapidity Gaps –Modifications to theory based on data have occured  Hard Single Diffraction –Many processes observed and studied including Diffractive W (diffraction is not low p T process) –Discrepancy in shape and normalization of  distribution confirms factorization breakdown –Results imply a non-pomeron based model should be considered  Hard Double Pomeron –Observation of interesting new process –Confirms factorization breakdown

31. Conclusion  Diffraction is a complex subject!  Much new experimental and theoretical work with promise of new more precise data to aid understanding Many open questions:  Are the hard and soft Pomeron distinct objects?  How to combine perturbative and non- perturbative concepts?  How to extract unique parton distribution densities from HERA and Tevatron data?  How to understand gap survival probability?  Is there a particle-like pomeron?