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Diffractive and total pp cross sections at the LHC and beyond

Diffractive and total pp cross sections at the LHC and beyond. Konstantin Goulianos The Rockefeller University http://physics.rockefeller.edu/dino/myhtml/conference.html. DIFFRACTION 2010 International Workshop on Diffraction in High-Energy Physics.

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Diffractive and total pp cross sections at the LHC and beyond

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  1. Diffractive and total pp cross sections at the LHC and beyond Konstantin Goulianos The Rockefeller University http://physics.rockefeller.edu/dino/myhtml/conference.html DIFFRACTION 2010 International Workshop on Diffraction in High-Energy Physics Otranto (Lecce), ItalyHotel Baia dei Turchi September 10 - 15, 2010

  2. CONTENTS • Introduction • Diffractive cross sections • The total cross section • Ratio of pomeron intercept to slope • Conclusions Diffractive and total x-sections at LHC and beyond

  3. Diffractive pp/pp Processes sT=Im fel (t=0) Elastic scattering Total cross section f f OPTICAL THEOREM GAP h h DD DPE SDD=SD+DD SD Diffractive and total x-sections at LHC and beyond

  4. Basic and combined (“nested”) diffractive processes multi-gap “nested” process Diffractive and total x-sections at LHC and beyond

  5. The problem: the Regge theory description violates unitarity at high s • ds/dt ssd grows faster than st as s increases  unitarity violation at high s (similarly for partial x-sections in impact parameter space) • the unitarity limit is already reached at √s~ 2 TeV Diffractive and total x-sections at LHC and beyond

  6. Standard Regge Theory KG-1995:PLB 358, 379 (1995) • Parameters: • s0, s0' and g(t) • set s0‘ = s0 (universal IP) • g(t)  g(0) ≡ gPPP KG-1995 • determine s0 and gPPP – how? Diffractive and total x-sections at LHC and beyond

  7. Global fit to p±p, p±, K±p x-sections Global fit to p±p, p±, K±p x-sections CMG-1996 PLB 389, 176 (1996) Regge theory eikonalized • INPUT • RESULTS negligible Diffractive and total x-sections at LHC and beyond

  8. Renormalization the key to diffraction in QCD Diffractive and total x-sections at LHC and beyond

  9. X ln s f Particle production Rapidity gap ln MX2 -ln x h Diffractive gapsdefinition: gaps not exponentiallysuppressed p p p X No radiation Diffractive and total x-sections at LHC and beyond

  10. p’ p x,t p M sTSD(pp & pp) - data  suppressed relative to Regge for √s>22 GeV Factor of ~8 (~5) suppression at √s = 1800 (540) GeV sTSDmb  RENORMALIZATION MODEL KG, PLB 358, 379 (1995) 540 GeV 1800 GeV CDF Run I results √s=22 GeV Diffractive and total x-sections at LHC and beyond

  11. M2 distribution: data  ds/dM2|t=-0.05 ~ independent of s over 6 orders of magnitude! KG&JM, PRD 59 (1999) 114017 Regge data 1 Independent of s over 6 orders of magnitude in M2 • M2 scaling  factorization breaks down to ensure M2 scaling Diffractive and total x-sections at LHC and beyond

  12. t 2 independent variables: color factor Single diffraction renormalized – (1) CORFU-2001: hep-ph/0203141 EDS 2009: http://arxiv.org/PS_cache/arxiv/pdf/1002/1002.3527v1.pdf sub-energy x-section gap probability Gap probability  (re)normalize to unity Diffractive and total x-sections at LHC and beyond

  13. color factor Single diffraction renormalized – (2) Experimentally: KG&JM, PRD 59 (114017) 1999 QCD: Diffractive and total x-sections at LHC and beyond

  14. Single diffraction renormalized - (3) set to unity  determine so Diffractive and total x-sections at LHC and beyond

  15. Grows slower than se  Pumplin bound obeyed at all impact parameters Single diffraction renormalized – (4) Diffractive and total x-sections at LHC and beyond

  16. Scale so and triple-pom coupling Pomeron flux: interpret as gap probability set to unity: determines gPPP and s0 KG, PLB 358 (1995) 379 Pomeron-proton x-section • Two free parameters: s0 and gPPP • Obtain product gPPP•s0e / 2 from sSD • Renormalized Pomeron flux determines s0 • Get unique solution for gPPP gPPP=0.69 mb-1/2=1.1 GeV -1 So=3.7±1.5 GeV2 Diffractive and total x-sections at LHC and beyond

  17. Multigap diffraction KG, hep-ph/0203141 f y Diffractive and total x-sections at LHC and beyond

  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! Diffractive and total x-sections at LHC and beyond

  19. S = Gap survival probability Diffractive and total x-sections at LHC and beyond

  20. The total x-section √sF=22 GeV SUPERBALL MODEL 98 ± 8 mb at 7 TeV 109 ±12 mb at 14 TeV Diffractive and total x-sections at LHC and beyond

  21. Born Eikonal sT at LHC from CMG global fit • s @ LHC √s=14 TeV: 122 ± 5 mb Born, 114 ± 5 mb eikonal  error estimated from the error in e given in CMG-96 Compare with SUPERBALLs(14 TeV) = 109± 6 mb caveat: so=1 GeV2 was used in global fit! Diffractive and total x-sections at LHC and beyond

  22. sSD and ratio of a'/e Diffractive and total x-sections at LHC and beyond

  23. sT optical theorem Im fel(t=0) dispersion relations Re fel(t=0) Monte Carlo Strategy for the LHC MONTE CARLO STRATEGY • sT  from SUPERBALL model • optical theorem  Im fel(t=0) • dispersion relations  Re fel(t=0) • differential sSD from RENORM • use nested pp final states for pp collisions at the IP ­ p sub-energy √s‘ Strategy similar to that employed in the MBR (Minimum Bias Rockefeller) MC used in CDF based on multiplicities from: K. Goulianos, Phys. Lett. B 193 (1987) 151 pp “A new statistical description of hardonic and e+e− multiplicity distributions “ Diffractive and total x-sections at LHC and beyond

  24. Dijets in gp at HERAfrom RENORM K. Goulianos, POS (DIFF2006) 055 (p. 8) Factor of ~3 suppression expected at W~200 GeV (just as in pp collisions) for both direct and resolved components Diffractive and total x-sections at LHC and beyond

  25. SUMMARY • Froissart bound • Valid above the “knee” at √s = 22 GeV in sTSD vs. √s and therefore valid at √s = 1.8 TeV of the CDF measurement • Use superball scale s0 (saturated exchange) in the Froissart formula, where s0= 3.7±1.5 GeV2as determined from setting the integral of the Pomeron flux to unity at the “kneee” of s√s = 22 GeV  m2 = s0 = (3.7±1.5 GeV2 • At √s 1.8 TeV Reggeon contributions are negligible (see global fit) • compatible with CGM-96 global fit result of 114 ± 5 mb • st= (98 ± 8) mb at 7 TeV – wait and see! Diffractive and total x-sections at LHC and beyond

  26. BACKUP Diffractive and total x-sections at LHC and beyond

  27. Diffractive dijets @ Tevatron jet p jet reorganize Diffractive and total x-sections at LHC and beyond

  28. FDJJ(x,b,Q2) @ Tevatron Diffractive and total x-sections at LHC and beyond

  29. SD/ND dijet ratio vs. xBj@ CDF CDF Run I 0.035 < x < 0.095 Flat x dependence for b < 0.5 Diffractive and total x-sections at LHC and beyond

  30. jet x p p x,t IP g* Q2 g* e reorganize e Diffractive DIS @ HERA J. Collins: factorization holds (but under what conditions?) Pomeron exchange Color reorganization Results favor color reorganization Diffractive and total x-sections at LHC and beyond

  31. Vector meson production (Pierre Marage, HERA-LHC 2008) • left - why different s vs. W slopes?  more room for particles • right - why smaller b-slope in g*p?  same reason Diffractive and total x-sections at LHC and beyond

  32. Dijets in gp at HERA - 2008 DIS 2008 talkby W.Slomiński, ZEUS • 20-50 % apparent rise when ETjet 510 GeV  due to suppression at low ETjet !!! Diffractive and total x-sections at LHC and beyond

  33. jet x Hadron-like g p g* Q2 e reorganize Dijets in gp at HERA – 2007 Direct vs. resolved • the reorganization diagram predicts:  suppression at low Z|Pjets, since larger Dh is available for particles  same suppression for direct and resolved processes QCD factorisation not OK Unexpected, not understood Diffractive and total x-sections at LHC and beyond

  34. The end Diffractive and total x-sections at LHC and beyond

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