Diffractive x-sections and event final states at the LHC Konstantin Goulianos The Rockefeller University / Diffraction Day 7 May 2010 CERN

K. Goulianos D-day 7 May 2010 CERNDiffractive x-sections and event final states at the LHC 2 Describe a phenomenology based on pre-LHC results and use it to:  make predictions for LHC  suggest measurements to confirm / modify parameters  suggest scheme to be implemented in MC simulations  propose method to measure luminosity Current MC generators: unreliable for extrapolations to LHC  MC tuning  based on multi-parameter tuning of ill-defined event topologies  Solution: use nested x-sections Contents  define diffractive x-section event topologies  nested diffractive gaps  describe in terms of proton pdf’’s and QCD color factors  normalize to guarantee unitarity  renormalization model OUTLINE

K. Goulianos D-day 7 May 2010 CERNDiffractive x-sections and event final states at the LHC 3 REMARKS  MC generators inadequate:  e.g. PYTHIA and PHOJET predictions of diffractive processes disagree with each other and with data.  Diffractive factorization at HERA? Breakdown observed in, e.g. Vector mesons:  vs. W, b-slopes of t-distributions Dijets: E T jet dependence, resolved vs. direct components,...  RENORM model: describes both p(pbar)-p and  p  Luminosity measurement: requires a known x-section  suggest SD – well defined and slowly varying

K. Goulianos D-day 7 May 2010 CERNDiffractive x-sections and event final states at the LHC 4 Diffractive pp(pp) CDF Single Diffraction dissociation (SD) Double Diffraction dissociation (DD) Double Pomeron Exchange (DPE)  Central Diffraction Single + Double Diffraction (SDD) SD SDD   Elastic scatteringTotal cross section  T =Im f el (t=0) OPTICAL THEOREM   gap nested gap Use nesting until no diffractive gap fits in √s'

K. Goulianos D-day 7 May 2010 CERNDiffractive x-sections and event final states at the LHC 5 Definitions  dN/d  M p p’ rap-gap  =-ln  0 p M ,t,t p p p’ ln M 2 ln s particles M 2 scaling: no price paid for increasing diffractive gap size

K. Goulianos D-day 7 May 2010 CERNDiffractive x-sections and event final states at the LHC 6 M 2 scaling KG&JM, PRD 59 (1999)  factorization breaks down to ensure M 2 scaling - why? Regge 1  Independent of s over 6 orders of magnitude in M 2 !  d  dM 2 | t=-0.05 independent of s over 6 orders of magnitude ! data

K. Goulianos D-day 7 May 2010 CERNDiffractive x-sections and event final states at the LHC 7  T SD (pp & pp) Factor of ~8 (~5) suppression at √s = 1800 (540) GeV  suppressed relative to Regge KG, PLB 358, 379 (1995) 1800 GeV 540 GeV M ,t,t p p p’  T SD mb √s=22 GeV

K. Goulianos D-day 7 May 2010 CERNDiffractive x-sections and event final states at the LHC 8 Gap probability MUST be normalized to unity! Single Diffraction 2 independent variables: t color factor gap probability sub-energy x-section

K. Goulianos D-day 7 May 2010 CERNDiffractive x-sections and event final states at the LHC 9 Single diffraction (re)normalized  Pumplin bound obeyed at all impact parameters Grows slower than s 

K. Goulianos D-day 7 May 2010 CERNDiffractive x-sections and event final states at the LHC 10 Unitarity and Renormalization  Two free parameters: s 0 and g PPP  Obtain product g PPP s 0  from  SD  Renormalized Pomeron flux determines s 0  Get unique solution for g PPP Pomeron-proton x-section Pomeron flux  gap probability Set to unity – determines g PPP and s 0 KG, PLB 358 (1995) 379

K. Goulianos D-day 7 May 2010 CERNDiffractive x-sections and event final states at the LHC 11 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)

K. Goulianos D-day 7 May 2010 CERNDiffractive x-sections and event final states at the LHC 12 Multi-gap Diffraction (KG, hep-ph/ )  y

K. Goulianos D-day 7 May 2010 CERNDiffractive x-sections and event final states at the LHC 13 Multi-gap Cross Sections Same suppression as for single gap! Gap probabilitySub-energy cross section (for regions with particles) 5 independent variables color factor

K. Goulianos D-day 7 May 2010 CERNDiffractive x-sections and event final states at the LHC 14 Rapidity Gaps in Fireworks

K. Goulianos D-day 7 May 2010 CERNDiffractive x-sections and event final states at the LHC 15 Gap survival probability S =

K. Goulianos D-day 7 May 2010 CERNDiffractive x-sections and event final states at the LHC 16 Diffractive Structure Function CDF H1 momentum fraction of parton in “Pomeron” – note quotes Using preliminary pdf’s from same suppression as in soft diffraction – why? Breakdown of QCD factorization

K. Goulianos D-day 7 May 2010 CERNDiffractive x-sections and event final states at the LHC 17 Diffractive Tevatron p jet reorganize jet

K. Goulianos D-day 7 May 2010 CERNDiffractive x-sections and event final states at the LHC 18 F D JJ ( , Q 2 Tevatron

K. Goulianos D-day 7 May 2010 CERNDiffractive x-sections and event final states at the LHC 19 SD/ND dijet ratio vs. x CDF <  < Flat  dependence for  < 0.5 CDF Run I

K. Goulianos D-day 7 May 2010 CERNDiffractive x-sections and event final states at the LHC 20 Diffractive HERA e Q2Q2 ** p jet  reorganize J. Collins: factorization holds (but under what conditions?) e **  t p IP Pomeron exchangeColor reorganization Results favor color reorganization

K. Goulianos D-day 7 May 2010 CERNDiffractive x-sections and event final states at the LHC 21 Dijets in  p at HERA DIS 2008 talk by W. Slomiński, ZEUS  % apparent rise when E T jet 5  10 GeV  due to suppression at low E T jet !!!

K. Goulianos D-day 7 May 2010 CERNDiffractive x-sections and event final states at the LHC 22 Vector meson production (Pierre Marage, HERA-LHC 2008)  left - why different  vs. W slopes?  more room for particles  right - why smaller b-slope in  *p?  same reason

K. Goulianos D-day 7 May 2010 CERNDiffractive x-sections and event final states at the LHC 23 Unexpected, not understood QCD factorisation not OK Dijets in  p at HERA – 2007 Hadron-like  e Q2Q2 ** p jet  reorganize Direct vs. resolved  the reorganization diagram predicts:  suppression at low Z | P jets, since larger  is available for particles  same suppression for direct and resolved processes

K. Goulianos D-day 7 May 2010 CERNDiffractive x-sections and event final states at the LHC 24  SD and ratio of  ' 

K. Goulianos D-day 7 May 2010 CERNDiffractive x-sections and event final states at the LHC 25 The total x-section √s F =22 GeV SUPERBALL MODEL

K. Goulianos D-day 7 May 2010 CERNDiffractive x-sections and event final states at the LHC 26 Strategy and Conclusion   T from SUPERBALL model  optical theorem  Im f el ( t=0 )  dispersion relations  Re f el ( t=0 )  differential  SD from RENORM  use nested pp multiplicities for pomeron-proton collisions at √s‘ For a phenomenological approach see: K. Goulianos, Phys. Lett. B 193 (1987) 151 pp  T optical theorem Im f el (t=0) dispersion relations Re f el (t=0) STRATEGY CONCUSION more to come…