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Pomeron Intercept and Slope: the QCD connection

This presentation discusses the QCD connection of the Pomeron Intercept and Slope, covering diffraction in QCD, cross-sections, and unitarity. Key topics include historical perspectives, particle production, and dijets at HERA. The Pomeron Trajectory intercept and slope values are examined in relation to QCD mechanisms and diffraction processes.

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Pomeron Intercept and Slope: the QCD connection

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

  2. Contents • Introduction • Diffraction in QCD • Pomeron intercept and slope • Cross sections with/no free parameters • Conclusion Pomeron Intercept and Slope: the QCD connection K. Goulianos

  3. The Pomeron Trajectory Intercept=1.1 -large- Slope=0.25 -small- Pomeron Intercept and Slope: the QCD connection K. Goulianos

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

  5. M x< 0.1 A clue from Diffraction Dissociation KG, Phys. Rep. 101, 169 (1983) Why 1/M2 ? Pomeron Intercept and Slope: the QCD connection K. Goulianos

  6. POMERON p-p Interactions Non-diffractive: Color-exchange Diffractive: Colorless exchange with vacuum quantum numbers rapidity gap Incident hadrons acquire color and break apart Incident hadrons retain their quantum numbers remaining colorless Pomeron Intercept and Slope: the QCD connection K. Goulianos

  7. xp p p p X X ln s f Particle production Rapidity gap ln MX2 -ln x dN/dh h h Diffractive Rapidity Gaps Pomeron Intercept and Slope: the QCD connection K. Goulianos

  8. Another clue: Diffraction and Unitarity • Unitarity problem: Using factorization and std pomeron flux sSD exceeds sT at • Renormalization: Normalize Pomeron flux to unity to eliminate overlapping gaps KG, PLB 358 (1995) 379 Pomeron Intercept and Slope: the QCD connection K. Goulianos

  9. renormalization 1 M2-scaling KG&JM, PRD 59 (1999) 114017  Independent of S over 6 orders of magnitude in M2 ! Factorization breaks down so as to ensure M2-scaling! Pomeron Intercept and Slope: the QCD connection K. Goulianos

  10. 450 BC 1869 Aristotle Demokritos Mendeleyev earth water air fire atom periodic table Plato (427-347 B.C) platonic love PHENOMENOLOGY ? 2007 candidates superimposed Pomeron Intercept and Slope: the QCD connection K. Goulianos

  11. f y Emission spacing controlled by a-strong  sT: power law rise with energy ~1/as (see E. Levin, An Introduction to Pomerons,Preprint DESY 98-120) f assume linear t-dependence y Forward elastic scattering amplitude The QCD Connection a’ reflects the size of the emitted cluster, which is controlled by 1 /as and thereby is related to e Pomeron Intercept and Slope: the QCD connection K. Goulianos

  12. t 2 independent variables: color factor Single Diffraction in QCD sub-energy x-section gap probability Gap probability MUST be normalized to unity! Pomeron Intercept and Slope: the QCD connection K. Goulianos

  13. Grows slower than se  The Pumplin bound is obeyed at all impact parameters Single diffraction (re)normalized Pomeron Intercept and Slope: the QCD connection K. Goulianos

  14. Color factor: Pomeron intercept: lg=0.20 lq=0.04 lR=-0.5 The Factors k and e Experimentally: KG&JM, PRD 59 (114017) 1999 CTEQ5L fg=gluon fraction fq=quark fraction Pomeron Intercept and Slope: the QCD connection K. Goulianos

  15. aP(0)-1 (eq+l)/2 eq Diffractive to ND ratio flat in x and Q2 for fixed x Inclusive vs Diffractive DIS KG, “Diffraction: a New Approach,” J.Phys.G26:716-720,2000 e-Print Archive: hep-ph/0001092 Brend Loehr@smallx-2007 F2 ~ x-l Pomeron Intercept and Slope: the QCD connection K. Goulianos

  16. a’ versus e • Constant set to sopp  Pomeron Intercept and Slope: the QCD connection K. Goulianos

  17. Multigap Diffraction (KG, hep-ph/0205141) f y Pomeron Intercept and Slope: the QCD connection K. Goulianos

  18. 5 independent variables color factor Gap probability Sub-energy cross section (for regions with particles) Multigap Cross Sections Same suppression as for single gap! Pomeron Intercept and Slope: the QCD connection K. Goulianos

  19. Diffractive Studies @ CDF sT=Im fel (t=0) Elastic scattering Total cross section f f OPTICAL THEOREM GAP h h DD DPE SDD=SD+DD SD Pomeron Intercept and Slope: the QCD connection K. Goulianos

  20. Agreement with renormalized Regge predictions DD SDD DPE • One-gap cross sections are suppressed • Two-gap/one-gap ratios are Central and Two-Gap CDF Results Pomeron Intercept and Slope: the QCD connection K. Goulianos

  21. S = Gap Survival Probability Results similar to predictions by: Gotsman-Levin-Maor Kaidalov-Khoze-Martin-Ryskin Soft color interactions Pomeron Intercept and Slope: the QCD connection K. Goulianos

  22. Dijets in gp at HERA: the puzzle (?) slide imported from diffractive group experimental summary of the HERA/LHC Workshop of March 14, 2007 Hadron-like g QCD factorisation not OK Unexpected, not understood Pomeron Intercept and Slope: the QCD connection K. Goulianos

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

  24. Conclusion Use: • M2 – scaling • Non-suppressed 2-gap to 1-gap ratios • Renormalization Build: • QCD theory of diffraction Pomeron Intercept and Slope: the QCD connection K. Goulianos

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