1. K. Goulianos The Rockefeller University Pomeron Intercept and Slope: are they related? Small-x and Diffraction, FERMILAB, 27-31 March 2007 intercept slope

2. Small-x and diffraction Fermilab, 27-31 March 2007 Pomeron Intercept and Slope: are they related? K. Goulianos2 Contents  Introduction  Diffraction in QCD  Pomeron intercept and slope  Cross sections with /no free parameters  Conclusion

3. Small-x and diffraction Fermilab, 27-31 March 2007 Pomeron Intercept and Slope: are they related? K. Goulianos3 The Pomeron Trajectory Intercept=1.1 -large- Slope=0.25 -small-

4. Small-x and diffraction Fermilab, 27-31 March 2007 Pomeron Intercept and Slope: are they related? K. Goulianos4 Historical perspective first guess: a’~1 (as for other trajectories) ~1970:  ’=0.5,   =1 ~1994:  ’=0.25,   =1.1 In this talk: are  ’ and  o related? A toy estimate of the ratio  ’/  o time

5. Small-x and diffraction Fermilab, 27-31 March 2007 Pomeron Intercept and Slope: are they related? K. Goulianos5 A clue from Diffraction Dissociation  < 0.1 KG, Phys. Rep. 101, 169 (1983) M Why 1/M 2 ?

6. Small-x and diffraction Fermilab, 27-31 March 2007 Pomeron Intercept and Slope: are they related? 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. Small-x and diffraction Fermilab, 27-31 March 2007 Pomeron Intercept and Slope: are they related? 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. Small-x and diffraction Fermilab, 27-31 March 2007 Pomeron Intercept and Slope: are they related? K. Goulianos8 Single Diffraction and Unitarity: more clues  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. Small-x and diffraction Fermilab, 27-31 March 2007 Pomeron Intercept and Slope: are they related? 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. Small-x and diffraction Fermilab, 27-31 March 2007 Pomeron Intercept and Slope: are they related? 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. Small-x and diffraction Fermilab, 27-31 March 2007 Pomeron Intercept and Slope: are they related? 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. Small-x and diffraction Fermilab, 27-31 March 2007 Pomeron Intercept and Slope: are they related? 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. Small-x and diffraction Fermilab, 27-31 March 2007 Pomeron Intercept and Slope: are they related? K. Goulianos13 Single diffraction (re)normalized  The Pumplin bound is obeyed at all impact parameters Grows slower than s 

14. Small-x and diffraction Fermilab, 27-31 March 2007 Pomeron Intercept and Slope: are they related? 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. Small-x and diffraction Fermilab, 27-31 March 2007 Pomeron Intercept and Slope: are they related? K. Goulianos15  ’ versus    Constant set to  o pp

16. Small-x and diffraction Fermilab, 27-31 March 2007 Pomeron Intercept and Slope: are they related? K. Goulianos16 Multigap Diffraction (KG, hep-ph/0205141)  y

17. Small-x and diffraction Fermilab, 27-31 March 2007 Pomeron Intercept and Slope: are they related? K. Goulianos17 Multigap Cross Sections Same suppression as for single gap! Gap probabilitySub-energy cross section (for regions with particles) 5 independent variables color factor

18. Small-x and diffraction Fermilab, 27-31 March 2007 Pomeron Intercept and Slope: are they related? K. Goulianos18 Diffractive Studies @ CDF   Elastic scatteringTotal cross section SD DDDPESDD=SD+DD  T =Im f el (t=0) OPTICAL THEOREM   GAP

19. Small-x and diffraction Fermilab, 27-31 March 2007 Pomeron Intercept and Slope: are they related? K. Goulianos19 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. Small-x and diffraction Fermilab, 27-31 March 2007 Pomeron Intercept and Slope: are they related? K. Goulianos20 Gap Survival Probability S = Results similar to predictions by: Gotsman-Levin-Maor Kaidalov-Khoze-Martin-Ryskin Soft color interactions

21. Small-x and diffraction Fermilab, 27-31 March 2007 Pomeron Intercept and Slope: are they related? K. Goulianos21 Conclusion Use:  M 2 – scaling  Non-suppressed 2-gap to 1-gap ratios  Renormalization phenomenology Build:  QCD theory of diffraction