2. K. Goulianos The Rockefeller University Renormalized Diffractive Parton Densities and Exclusive Production Diffraction 2006 Milos island, Greece, 5-10 September 2006

3. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos2 Contents  Introduction  Phenomenology  Experiment confronts phenomenology  Exclusive Production

4. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos3 p-p Interactions Diffractive: Colorless exchange with vacuum quantum numbers Non-diffractive: Color-exchange Incident hadrons retain their quantum numbers remaining colorless Incident hadrons acquire color and break apart POMERONPOMERON Goal: develop a QCD based phenomenology for diffraction rapidity gap

5. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos4 Diffractive Rapidity Gaps p p X p pp Particle productionRapidity gap   -ln  ln M X 2 ln s X

6. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos5 Diffraction Dissociation  < 0.1 KG, Phys. Rep. 101, 169 (1983)

7. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos6 Factorization and scaling in soft single diffraction  Total SD cross section  factorization breakdown  M 2 -scaling  controls level of breakdown  dN/d 

8. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos7 Total Single Diffractive Cross Section  Unitarity problem: Using factorization and std pomeron flux  SD exceeds  T at  Renormalization: Normalize the Pomeron flux to unity KG, PLB 358 (1995) 379

9. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos8 M 2 -scaling KG&JM, PRD 59 (1999) 114017 Factorization breaks down so as to ensure M 2 -scaling! renormalization 1  Independent of S over 6 orders of magnitude in M 2 !

10. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos9 Double Diffraction Dissociation  entral rapidity gaps  How does one apply Pomeron flux renormalization in this case?  Need generalized renormalization!

11. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos10 PHENOMENOLOGY Aristotle 450 BC earth water air fire atom Demokritos 1869 periodic table Mendeleyev Plato (427-347 B.C) platonic love 2006

12. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos11 Elastic and Total Cross Sections QCD expectations y  Elastic cross section: forward scattering amplitude The exponential rise of  T (  y’) is due to the increase of wee partons with  y’ (see E. Levin, An Introduction to Pomerons,Preprint DESY 98-120) y  Total cross section: power law rise with energy  s

13. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos12 Gap probability MUST be normalized to unity! Single Diffraction 2 independent variables: t color factor gap probability sub-energy x-section

14. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos13 Single diffraction (re)normalized  The Pumplin bound is obeyed at all impact parameters Grows slower than s 

15. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos14 The Factors  and  Experimentally: KG&JM, PRD 59 (114017) 1999 g =0.20 q =0.04 R =-0.5 f g =gluon fraction f q =quark fraction Color factor: Pomeron intercept: CTEQ5L

16. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos15 Multigap Diffraction (KG, hep-ph/0205141)  y

17. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos16 Multigap Cross Sections Same suppression as for single gap! Gap probabilitySub-energy cross section (for regions with particles) 5 independent variables color factor

18. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos17 Diffractive Studies @ CDF   Elastic scatteringTotal cross section SD DDDPESDD=SD+DD  T =Im f el (t=0) OPTICAL THEOREM   GAP

19. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos18 Central and Two-Gap CDF Results  One-gap cross sections are suppressed  Two-gap/one-gap ratios are Agreement with renormalized Regge predictions DDSDDDP E

20. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos19 Gap Survival Probability S = Results similar to predictions by: Gotsman-Levin-Maor Kaidalov-Khoze-Martin-Ryskin Soft color interactions

21. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos20 Lessons from Soft Diffraction  M 2 – scaling  renormalization  Non-suppressed 2-gap to 1-gap ratios  Pomeron: composite object made up from underlying proton pdf’s subject to QCD color constraints

22. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos21 HARD DIFFRACTION  Diffractive structure function  factorization breakdown - how?  Restoring factorization  Diffractive fractions  dN/d  JJ, W, b, J/ 

23. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos22 The diffractive structure function at the Tevatron is suppressed by a factor of ~10 relative to expectation from pdf’s measured by H1 at HERA Similar suppression factor as in soft diffraction relative to expectations from Regge theory and factorization! Diffractive Structure Function: Breakdown of QCD Factorization CDF H1  = momentum fraction of parton in Pomeron Using preliminary pdf’s from

24. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos23 Restoring Factorization @ Tevatron R(SD/ND) R(DPE/SD) DSF from two/one gap: factorization restored!

25. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos24 F D JJ (  ) from ZEUS-LPS Data Fit including charm data Fit without charm data ZEUS H1 From: M. Arneodo, HERA/LHC workshop, CERN, 11-13 Oct 2004 Flat after subtracting Reggeon contribution

26. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos25 Hard Diffractive Fractions @ CDF All ratios ~ 1%  ~ uniform suppression ~ FACTORIZATION ! Fraction: SD/ND ratio at 1800 GeV  dN/d  1.45 (0.25)J/  0.62 (0.25)b 0.75 (0.10)JJ 1.15 (0.55)W % Fraction (+/-)

27. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos26 Diffractive Structure Function: Q 2 dependence E T jet ~ 100 GeV ! Small Q 2 dependence in region 100 < Q 2 < 10,000 GeV 2  Pomeron evolves as the proton!

28. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos27 Diffractive Structure Function: t- dependence  No diffraction dips  No Q2 dependence in slope from inclusive to Q 2 ~10 4 GeV 2 Fit d  /dt to a double exponential:  Same slope over entire region of 0 < Q 2 < 4,500 GeV 2 across soft and hard diffraction!

29. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos28 Diffractive DIS @ HERA e Q2Q2 ** p jet  reorganize J. Collins: factorization holds (but under what contitions?) e **  t p IP Pomeron exchangeColor reorganization

30. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos29 Inclusive vs Diffractive DIS KG, “Diffraction: a New Approach,” J.Phys.G26:716-720,2000 e-Print Archive: hep-ph/0001092 H1, ICHEP2006 total error

31. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos30 Diffractive Dijets @ Tevatron p jet reorganize jet

32. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos31 F D JJ ( , Q 2 ) @ Tevatron

33. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos32 SD/ND Dijet Ratio vs x Bj @ CDF 0.035 <  < 0.095 Flat  dependence

34. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos33 Gap Between Jets

35. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos34 valence quarks antiproton x=x= Hard Diffraction in QCD proton deep sea Derive diffractive from inclusive PDFs and color factors antiproton valence quarks p p

36. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos35 Diffractive Higgs @ LHC   D (LHC) ~ P(gap) x  ND (Tevatron) ~ 0.1 x 1 pb = 100 fb Inclusive production H p pp p H p pp p Exclusive DPE Higgs production pp  p H p : 3-10 fb (KMR) Inclusive DPE Higgs production pp  p+X+ H +Y+p : 50-200 fb (others) Exclusive production   excl ~  incl x 0.02~ 2 fb OTHER THEORETICAL PREDICTIONS Back of the envelope calculation Fraction of 2/all particle multiplicity

37. Diffraction 2006, Milos, Greece, Sep 05-10Renormalized Diffractive Parton Densities K. Goulianos36 Diffraction is an interaction between low-x partons subject to color constraints SUMMARY