1. K. Goulianos The Rockefeller University Pomeron Intercept and Slope: the QCD connection 12 th Blois Workshop, DESY, Hamburg, Germany 21-25 May2007 intercept slope 12th International Conference on Elastic and Diffractive Scattering Forward Physics and QCD

2. Blois Workshop 2007 DESY, 21-25 May 2007 Pomeron Intercept and Slope: the QCD connection K. Goulianos2 Contents  Introduction  Diffraction in QCD  Pomeron intercept and slope  Cross sections with /no free parameters  Conclusion

3. Blois Workshop 2007 DESY, 21-25 May 2007 Pomeron Intercept and Slope: the QCD connection K. Goulianos3 The Pomeron Trajectory Intercept=1.1 -large- Slope=0.25 -small-

4. Blois Workshop 2007 DESY, 21-25 May 2007 Pomeron Intercept and Slope: the QCD connection K. Goulianos4 A bit of history… Pre-1970: guess a’~1 (as for other trajectories) ~1970:  ’=0.5,   =1 1995:  ’=0.25,   =1.1 In this talk: The QCD connection time Covolan, Montagna, and Goulianos PLB 389 (1995) 176

5. Blois Workshop 2007 DESY, 21-25 May 2007 Pomeron Intercept and Slope: the QCD connection K. Goulianos5 A clue from Diffraction Dissociation  < 0.1 KG, Phys. Rep. 101, 169 (1983) M Why 1/M 2 ?

6. Blois Workshop 2007 DESY, 21-25 May 2007 Pomeron Intercept and Slope: the QCD connection K. Goulianos6 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 rapidity gap

7. Blois Workshop 2007 DESY, 21-25 May 2007 Pomeron Intercept and Slope: the QCD connection K. Goulianos7 Diffractive Rapidity Gaps p p X p pp Particle productionRapidity gap   -ln  ln M X 2 ln s X  dN/d 

8. Blois Workshop 2007 DESY, 21-25 May 2007 Pomeron Intercept and Slope: the QCD connection K. Goulianos8 Another clue: Diffraction and Unitarity  Unitarity problem: Using factorization and std pomeron flux  SD exceeds  T at  Renormalization: Normalize Pomeron flux to unity to eliminate overlapping gaps KG, PLB 358 (1995) 379

9. Blois Workshop 2007 DESY, 21-25 May 2007 Pomeron Intercept and Slope: the QCD connection K. Goulianos9 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. Blois Workshop 2007 DESY, 21-25 May 2007 Pomeron Intercept and Slope: the QCD connection K. Goulianos10 PHENOMENOLOGY Aristotle 450 BC earth water air fire atom Demokritos 1869 periodic table Mendeleyev Plato (427-347 B.C) platonic love 2007 ? candidates superimposed

11. Blois Workshop 2007 DESY, 21-25 May 2007 Pomeron Intercept and Slope: the QCD connection K. Goulianos11 The QCD Connection (see E. Levin, An Introduction to Pomerons,Preprint DESY 98-120) y  Emission spacing controlled by  -strong    : power law rise with energy  s  ’ reflects the size of the emitted cluster, which is controlled by 1 /  s and thereby is related to  y  Forward elastic scattering amplitude assume linear t-dependence

12. Blois Workshop 2007 DESY, 21-25 May 2007 Pomeron Intercept and Slope: the QCD connection K. Goulianos12 Gap probability MUST be normalized to unity! Single Diffraction in QCD 2 independent variables: t color factor gap probability sub-energy x-section

13. Blois Workshop 2007 DESY, 21-25 May 2007 Pomeron Intercept and Slope: the QCD connection K. Goulianos13 Single diffraction (re)normalized  The Pumplin bound is obeyed at all impact parameters Grows slower than s 

14. Blois Workshop 2007 DESY, 21-25 May 2007 Pomeron Intercept and Slope: the QCD connection 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

15. Blois Workshop 2007 DESY, 21-25 May 2007 Pomeron Intercept and Slope: the QCD connection K. Goulianos15 Inclusive vs Diffractive DIS F 2 ~ x  qq KG, “Diffraction: a New Approach,” J.Phys.G26:716-720,2000 e-Print Archive: hep-ph/0001092  P (0)-1 (  q  )/2 Brend Loehr@smallx-2007 Diffractive to ND ratio flat in x and Q2 for fixed 

16. Blois Workshop 2007 DESY, 21-25 May 2007 Pomeron Intercept and Slope: the QCD connection K. Goulianos16  ’ versus    Constant set to  o pp

17. Blois Workshop 2007 DESY, 21-25 May 2007 Pomeron Intercept and Slope: the QCD connection K. Goulianos17 Multigap Diffraction (KG, hep-ph/0205141)  y

18. Blois Workshop 2007 DESY, 21-25 May 2007 Pomeron Intercept and Slope: the QCD connection K. Goulianos18 Multigap Cross Sections Same suppression as for single gap! Gap probabilitySub-energy cross section (for regions with particles) 5 independent variables color factor

19. Blois Workshop 2007 DESY, 21-25 May 2007 Pomeron Intercept and Slope: the QCD connection K. Goulianos19 Diffractive Studies @ CDF   Elastic scatteringTotal cross section SD DDDPESDD=SD+DD  T =Im f el (t=0) OPTICAL THEOREM   GAP

20. Blois Workshop 2007 DESY, 21-25 May 2007 Pomeron Intercept and Slope: the QCD connection K. Goulianos20 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

21. Blois Workshop 2007 DESY, 21-25 May 2007 Pomeron Intercept and Slope: the QCD connection K. Goulianos21 Gap Survival Probability S = Results similar to predictions by: Gotsman-Levin-Maor Kaidalov-Khoze-Martin-Ryskin Soft color interactions

22. Blois Workshop 2007 DESY, 21-25 May 2007 Pomeron Intercept and Slope: the QCD connection K. Goulianos22 Unexpected, not understood Hadron-like  QCD factorisation not OK Dijets in  p at HERA: the puzzle (?) slide imported from diffractive group experimental summary of the HERA/LHC Workshop of March 14, 2007

23. Blois Workshop 2007 DESY, 21-25 May 2007 Pomeron Intercept and Slope: the QCD connection K. Goulianos23 Dijets in  p at HERA : the expectation Factor 0f ~3 suppression expected at W~200 GeV (just as in pp collisions) for both direct and resolved components K. Goulianos, POS (DIFF2006) 055 (p. 8)

24. Blois Workshop 2007 DESY, 21-25 May 2007 Pomeron Intercept and Slope: the QCD connection K. Goulianos24 Conclusion Use:  M 2 – scaling  Non-suppressed 2-gap to 1-gap ratios  Renormalization Build:  QCD theory of diffraction