1. Diffraction, saturation, and pp cross-sections at the LHC Diffraction, saturation and pp cross sections at the LHC Konstantin Goulianos The Rockefeller University Moriond QCD and High Energy Interactions La Thuile, March 20-27, 2011 (member of CDF and CMS) 

2. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 2 CONTENTS  Introduction  Diffractive cross sections  The total, elastic, and inelastic cross sections  Monte Carlo strategy for the LHC  Conclusions

3. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 3 Two reasons: one fundamental / one practical.  fundamental  practical: underlying event (UE), triggers, calibrations  the UE affects all physics studies at the LHC Why study diffraction?  T optical theorem Im f el (t=0) dispersion relations Re f el (t=0) Diffraction measure  T &  -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   T NEED ROBUST MC SIMULATION OF SOFT PHYSICS

4. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 4 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 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  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

5. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 5 Diffractive gaps definition: gaps not exponentially suppressed p p X p Particle productionRapidity gap   -ln  ln M X 2 ln s X No radiation

6. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 6 Diffractive pbar-p studies @ CDF   Elastic scatteringTotal cross section SD DDDPESDD=SD+DD  T =Im f el (t=0) OPTICAL THEOREM   GAP

7. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 7 Basic and combined diffractive processes a 4-gap diffractive process gap SD DD

8. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 8 Regge theory – values of s o & g? Parameters:  s 0, s 0 ' and g(t)  set s 0 ‘ = s 0 (universal IP )  determine s 0 and g PPP – how? KG-1995: PLB 358, 379 (1995 )

9. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 9 A complication …  Unitarity!  d  /dt  sd grows faster than  t 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

10. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 10  T SD vs  T (pp & pp) Factor of ~8 (~5) suppression at √s = 1800 (540) GeV KG, PLB 358, 379 (1995) 1800 GeV 540 GeV M ,t,t p p p’ √s=22 GeV  RENORMALIZATION MODEL CDF Run I results TT TT  suppressed relative to Regge for √s>22 GeV

11. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 11 Gap probability  (re)normalize to unity Single diffraction renormalized – (1) 2 independent variables: t color factor gap probability sub-energy x-section KG  EDS 2009: http://arxiv.org/PS_cache/arxiv/pdf/1002/1002.3527v1.pdf KG  CORFU-2001: hep-ph/0203141

12. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 12 Single diffraction renormalized – (2) color factor Experimentally: KG&JM, PRD 59 (114017) 1999 QCD:

13. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 13 Single diffraction renormalized - (3) set to unity  determine s o

14. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 14 Single diffraction renormalized – (4)  Pumplin bound obeyed at all impact parameters grows slower than s 

15. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 15 M 2 distribution: data KG&JM, PRD 59 (1999) 114017  factorization breaks down to ensure M 2 scaling Regge 1 Independent of s over 6 orders of magnitude in M 2  M 2 scaling  d  dM 2 | t=-0.05 ~ independent of s over 6 orders of magnitude ! data

16. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 16 Scale s o and triple-pom coupling  Two free parameters: s o and g PPP  Obtain product g PPP s o  from  SD  Renormalized Pomeron flux determines s o  Get unique solution for g PPP Pomeron-proton x-section Pomeron flux: interpret as gap probability  set to unity: determines g PPP and s 0 KG, PLB 358 (1995) 379 S o =3.7±1.5 GeV 2 g PPP =0.69 mb -1/2 =1.1 GeV -1

17. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 17 Saturation “glueball” at ISR? See M.G.Albrow, T.D. Goughlin, J.R. Forshaw, hep-ph>arXiv:1006.1289 Giant glueball with f 0 (980) and f 0 (1500) superimposed, interfering destructively and manifesting as dips (???) √s o

18. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 18 Multigap cross sections, e.g. SDD Same suppression as for single gap! Gap probabilitySub-energy cross section (for regions with particles) 5 independent variables color factor KG, hep-ph/0203141

19. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 19 SDD in CDF: data vs NBR MC http://physics.rockefeller.edu/publications.html  Excellent agreement between data and NBR (MinBiasRockefeller) MC

20. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 20 Multigaps: a 4-gap x-section

21. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 21 The total x-section √s F =22 GeV SUPERBALL MODEL 98 ± 8 mb at 7 TeV 109 ±12 mb at 14 TeV http://arxiv.org/ abs/1002.3527

22. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 22 Total inelastic cross section ATLAS measurement of the total inelastic x-section Renormalization model The  el is obtained from  t and the ratio of el/tot

23. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 23  SD and ratio of  ' 

24. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 24 Diffraction in PYTHIA -1 some comments:  1/M 2 dependence instead of (1/M 2 ) 1+   F-factors put “by hand” – next slide  B dd contains a term added by hand - next slide

25. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 25 Diffraction in PYTHIA -2 note:  1/M 2 dependence  e 4 factor Fudge factors:  suppression at kinematic limit  kill overlapping diffractive systems in dd  enhance low mass region

26. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 26 CMS: observation of Diffraction at 7 TeV An example of a beautiful data analysis and of MC inadequacies No single MC describes the data in their entirety

27. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 27 Monte Carlo Strategy for the LHC   T  from SUPERBALL model  optical theorem  Im f el ( t=0 )  dispersion relations  Re f el ( t=0 )   el   inel  differential  SD  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 “  T optical theorem Im f el (t=0) dispersion relations Re f el (t=0) MONTE CARLO STRATEGY

28. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 28 Monte Carlo algorithm - nesting 'c'c t Profile of a pp inelastic collision  y‘ <  y' min EXIT  y‘ >  y' min generate central gap repeat until  y' <  y' min ln s' evolve every cluster similarly gap no gap final state from MC w /no-gaps

29. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 29 SUMMARY  Introduction  Diffractive cross sections  basic:SD p, SD p, 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 – use “nesting” derived from ND and QCD color factors

30. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 30 BACKUP

31. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 31 RISING X-SECTIONS IN PARTON MODEL (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

32. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 32 Gap survival probability S =

33. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 33 Diffraction in MBR: dd in CDF http://physics.rockefeller.edu/publications.html renormalized gap probabilityx-section

34. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 34 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

35. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 35 Dijets in  p at HERA from RENORM Factor of ~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)

36. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 36 Saturation at low Q 2 and small-x figure from a talk by Edmond Iancu

37. K. Goulianos Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC 37 The end