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Predicting and measuring the total inelastic cross section at the LHC

Predicting and measuring the total inelastic cross section at the LHC. Konstantin Goulianos The Rockefeller University. Valparaiso, Chile   May 19-20, 2011. Contents. 1 ) Introduction gaps 2) Predicting the total s : s t

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Predicting and measuring the total inelastic cross section at the LHC

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  1. Predicting and measuring the total inelastic cross section at the LHC Konstantin Goulianos The Rockefeller University Valparaiso, Chile   May 19-20, 2011

  2. Contents 1) Introduction gaps 2) Predicting the total s: st 3) Predicting the total-elastic s: sel total-inelastic s: sinel = st-sel 4) Measuring the “visible”-inelastic s: sinelvis 5) Extrapolating to measured-inelastic s:sinelmeas 6) A Monte Carlo algorithm for the LHC - nesting The total inelastic pp cross section at LHCK. Goulianos

  3. Sec. 1 1) Introduction gaps diffraction, saturation and pp cross sections at LHC • http://physics.rockefeller.edu/dino/myhtml/talks/HEP2006.pdf • http://physics.rockefeller.edu/dino/myhtml/talks/moriond11_dino.pdf 2) Predicting the total sst 3) Predicting the total-elastic ssel  total-inelastic ssinel = st-sel 4) Measuring the “visible”-inelastic ssinelvis 5) Extrapolating to measured-inelastic ssinelmeas 6) A Monte Carlo algorithm for the LHC nesting The total inelastic pp cross section at LHCK. Goulianos

  4. sT optical theorem Im fel(t=0) dispersion relations Re fel(t=0) Why study diffraction? • Two reasons: one fundamental / one practical. • fundamental • practical: underlying event (UE), triggers, calibrations, acceptance, … the UE affects all physics studies at LHC measure sT & r-value at LHC: check for violation of dispersion relations  sign for new physics Bourrely, C., Khuri, N.N., Martin, A.,Soffer, J., Wu, T.T http://en.scientificcommons.org/16731756 • saturation  sT Diffraction NEED ROBUST MC SIMULATION OF SOFT PHYSICS The total inelastic pp cross section at LHCK. Goulianos

  5. MC simulations:Pandora’s box was unlocked at the LHC! • Presently available MCs based on pre-LHC data were found to be inadequate for LHC • MCs disagree in the way they handle diffraction • MC tunes: the “evils of the world” were released from Pandora’s box at the LHC … but fortunately, hope remained in the box  a good starting point for this talk! Pandora's box is an artifact in Greek mythology, taken from the myth of Pandora's creation around line 60 of Hesiod's Works And Days. The "box" was actually a large jar (πιθος pithos) given to Pandora (Πανδώρα) ("all-gifted"), which contained all the evils of the world. When Pandora opened the jar, the entire contents of the jar were released, but for one – hope. Nikipedia The total inelastic pp cross section at LHCK. Goulianos

  6. CMS: observation of Diffraction at 7 TeV (an early example of MC inadequacies) • No single MC describes the data in their entirety The total inelastic pp cross section at LHCK. Goulianos

  7. X ln s f Particle production Rapidity gap ln MX2 Dh≈-ln x h Diffractive gapsdefinition: gaps not exponentiallysuppressed p p p X No radiation The total inelastic pp cross section at LHCK. Goulianos

  8. Diffractive pbar-p 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 The total inelastic pp cross section at LHCK. Goulianos

  9. Basic and combineddiffractive processes gap DD SD a 4-gap diffractive process The total inelastic pp cross section at LHCK. Goulianos

  10. Regge theory – values of so & g? KG-1995:PLB 358, 379 (1995) • Parameters: • s0, s0' and g(t) • set s0‘ = s0 (universal IP ) • determine s0 and gPPP –how? The total inelastic pp cross section at LHCK. Goulianos

  11. A complication …  Unitarity! • 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 The total inelastic pp cross section at LHCK. Goulianos

  12. p’ p x,t p M Sigma-SD vs sigma-total sTSDvssT (pp & pp)  suppressed relative to Regge for √s>22 GeV sT sT Factor of ~8 (~5) suppression at √s = 1800 (540) GeV  RENORMALIZATION MODEL KG, PLB 358, 379 (1995) 540 GeV 1800 GeV CDF Run I results √s=22 GeV The total inelastic pp cross section at LHCK. Goulianos

  13. t 2 independent variables: color factor Single diffraction renormalized – (1 of/4) KG  CORFU-2001: hep-ph/0203141 KG  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 The total inelastic pp cross section at LHCK. Goulianos

  14. color factor Single diffraction renormalized – (2 of/4) Experimentally: KG&JM, PRD 59 (114017) 1999 QCD: The total inelastic pp cross section at LHCK. Goulianos

  15. Single diffraction renormalized - (3 of/4) set to unity  determine so The total inelastic pp cross section at LHCK. Goulianos

  16. grows slower than se  Pumplin bound obeyed at all impact parameters Single diffraction renormalized – (4 of/4) The total inelastic pp cross section at LHCK. Goulianos

  17. 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 The total inelastic pp cross section at LHCK. Goulianos

  18. 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: so and gPPP • Obtain product gPPP•soe / 2 from sSD • Renormalized Pomeron flux determines so • Get unique solution for gPPP gPPP=0.69 mb-1/2=1.1 GeV -1 So=3.7±1.5 GeV2 The total inelastic pp cross section at LHCK. Goulianos

  19. Saturation “glueball” at ISR? Giant glueball with f0(980) and f0(1500) superimposed, interfering destructively and manifesting as dips (???) √so See M.G.Albrow, T.D. Goughlin, J.R. Forshaw, hep-ph>arXiv:1006.1289 The total inelastic pp cross section at LHCK. Goulianos

  20. Saturation at low Q2 and small-x figure from a talk by Edmond Iancu The total inelastic pp cross section at LHCK. Goulianos

  21. DD at CDF: comparison with MBR http://physics.rockefeller.edu/publications.html gap probability x-section renormalized The total inelastic pp cross section at LHCK. Goulianos

  22. 5 independent variables color factor Gap probability Sub-energy cross section (for regions with particles) Multigap cross sections, e.g. SDD KG, hep-ph/0203141 Same suppression as for single gap! The total inelastic pp cross section at LHCK. Goulianos

  23. SDD in CDF: data vs MBR MC http://physics.rockefeller.edu/publications.html • Excellent agreement between data and NBR (MinBiasRockefeller) MC The total inelastic pp cross section at LHCK. Goulianos

  24. Multigaps: a 4-gap x-section The total inelastic pp cross section at LHCK. Goulianos

  25. S = Gap survival probability The total inelastic pp cross section at LHCK. Goulianos

  26. sSD and ratio of a'/e The total inelastic pp cross section at LHCK. Goulianos

  27. Sec. 2 1) Introduction gaps 2) Predicting the total sst 3) Predicting the total-elastic ssinel •  total-inelastic ssinel = st-sel 4) Measuring the “visible”-inelastic ssinelvis 5) Extrapolating to measured-inelastic s sinelmeas 6) A Monte Carlo algorithm for the LHC nesting The total inelastic pp cross section at LHCK. Goulianos

  28. http://arxiv.org/abs/1002.3527 The total x-section √sF=22 GeV SUPERBALL MODEL 98 ± 8 mb at 7 TeV 109 ±12 mb at 14 TeV The total inelastic pp cross section at LHCK. Goulianos

  29. Sec. 3 1) Introduction gaps 2) Predicting the total sst 3) Predicting the total-elastic ssinel •  total-inelastic ssinel = st-sel 4) Measuring the “visible”-inelastic ssinelvis 5) Extrapolating to measured-inelastic s sinelmeas 6) A Monte Carlo algorithm for the LHC nesting The total inelastic pp cross section at LHCK. Goulianos

  30. Global fit to p±p, p±, K±p x-sections PLB 389, 176 (1996) Regge theory eikonalized • INPUT el/tot slowly rising • RESULTS negligible The total inelastic pp cross section at LHCK. Goulianos

  31. The total-inelastic cross section Small extrapolation to 7 TeV sel=(sel/st)●st The total inelastic pp cross section at LHCK. Goulianos

  32. 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! The total inelastic pp cross section at LHCK. Goulianos

  33. Secs. 4 & 5 1) Introduction gaps 2) Predicting the total sst 3) Predicting the total-elastic ssinel •  total-inelastic ssinel = st-sel 4) Measuring the “visible”-inelastic ssinelvis 5) Extrapolating to measured-inelastic s sinelmeas 6) A Monte Carlo algorithm for the LHC nesting The total inelastic pp cross section at LHCK. Goulianos

  34. Visible/total inelastic cross sections ATLAS Pre-Moriond 2011 ATLAS-CONF-2011-002 Feb. 6 2011  with pythia (phojet) extrapolation Post-Moriond 2011 arXiv:1104.023v1 CMS (DIS-2011), also post-Moriond 2011 visible svtxinel=59.9±0.1(stat)±1.1(syst)±2.4(Lumi) (range due to uncertainty in MC extrapolation) Prediction: stinel=71±6 mb The total inelastic pp cross section at LHCK. Goulianos

  35. Sec. 6 1) Introduction gaps 2) Predicting the total sst 3) Predicting the total-elastic ssinel •  total-inelastic ssinel = st-sel 4) Measuring the “visible”-inelastic ssinelvis 5) Extrapolating to measured-inelastic s sinelmeas 6) A Monte Carlo algorithm for the LHC nesting The total inelastic pp cross section at LHCK. Goulianos

  36. Diffraction in PYTHIA – (1 of/3) • some comments: • 1/M2 dependence instead of (1/M2)1+e • F-factors put “by hand” – next slide • Bdd contains a term added by hand - next slide The total inelastic pp cross section at LHCK. Goulianos

  37. Diffraction in PYTHIA – (2 of/3 • note: • 1/M2 dependence • e4 factor • Fudge factors: • suppression at kinematic limit • kill overlapping diffractive systems in dd • enhance low mass region The total inelastic pp cross section at LHCK. Goulianos

  38. Diffraction in PYTHIA – (3 of/3) The total inelastic pp cross section at LHCK. Goulianos

  39. 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) • sel • sinel • differential sSD from RENORM • use nesting of final states (FSs) for pp collisions at the IP­p 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 “ The total inelastic pp cross section at LHCK. Goulianos

  40. Monte Carlo algorithm - nesting Profile of a pp inelastic collision gap gap no gap t h'c evolve every cluster similarly ln s' final state from MC w/no-gaps Dy‘ > Dy'min Dy‘ < Dy'min generate central gap EXIT repeat until Dy' < Dy'min The total inelastic pp cross section at LHCK. Goulianos

  41. SUMMARY • Introduction • Diffractive cross sections • basic: SDp, SDp, DD, DPE • combined: multigap x-sections • ND  no-gaps: final state from MC with no gaps • this is the only final state to be tuned • The total, elastic, and inelastic cross sections • Monte Carlo strategy for the LHC – “nesting” derived from ND and QCD color factors The total inelastic pp cross section at LHCK. Goulianos

  42. BACKUP BACKUP The total inelastic pp cross section at LHCK. Goulianos

  43. 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 RISING X-SECTIONS IN PARTON MODEL a’ reflects the size of the emitted cluster, which is controlled by 1 /as and thereby is related to e The total inelastic pp cross section at LHCK. Goulianos

  44. 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 The total inelastic pp cross section at LHCK. Goulianos

  45. Diffraction in MBR: DPE in CDF http://physics.rockefeller.edu/publications.html • Excellent agreement between data and MBR  low and high masses are correctly implemented The total inelastic pp cross section at LHCK. Goulianos

  46. The end the end The total inelastic pp cross section at LHCK. Goulianos

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