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

Blois Workshop 2007 DESY, 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

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

Blois Workshop 2007 DESY, 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

Blois Workshop 2007 DESY, 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 ?

Blois Workshop 2007 DESY, 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

Blois Workshop 2007 DESY, 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 

Blois Workshop 2007 DESY, 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

Blois Workshop 2007 DESY, May 2007 Pomeron Intercept and Slope: the QCD connection K. Goulianos9 M 2 -scaling KG&JM, PRD 59 (1999) Factorization breaks down so as to ensure M 2 -scaling! renormalization 1  Independent of S over 6 orders of magnitude in M 2 !

Blois Workshop 2007 DESY, 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 ( B.C) platonic love 2007 ? candidates superimposed

Blois Workshop 2007 DESY, May 2007 Pomeron Intercept and Slope: the QCD connection K. Goulianos11 The QCD Connection (see E. Levin, An Introduction to Pomerons,Preprint DESY ) 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

Blois Workshop 2007 DESY, 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

Blois Workshop 2007 DESY, 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 

Blois Workshop 2007 DESY, 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

Blois Workshop 2007 DESY, 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: ,2000 e-Print Archive: hep-ph/  P (0)-1 (  q  )/2 Brend Diffractive to ND ratio flat in x and Q2 for fixed 

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

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

Blois Workshop 2007 DESY, 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

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

Blois Workshop 2007 DESY, 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

Blois Workshop 2007 DESY, 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

Blois Workshop 2007 DESY, 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

Blois Workshop 2007 DESY, 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)

Blois Workshop 2007 DESY, 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