Diffractive and total pp cross sections at the LHC and beyond Konstantin Goulianos The Rockefeller University Otranto (Lecce), Italy Hotel Baia dei Turchi September , 2010 DIFFRACTION 2010 International Workshop on Diffraction in High-Energy Physics

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 2 CONTENTS  Introduction  Diffractive cross sections  The total cross section  Ratio of pomeron intercept to slope  Conclusions

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 3 Diffractive pp/pp Processes   Elastic scatteringTotal cross section SD DDDPESDD=SD+DD  T =Im f el (t=0) OPTICAL THEOREM   GAP

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 4 Basic and combined (“nested”) diffractive processes multi-gap “nested” process

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 5 The problem: the Regge theory description violates unitarity at high s  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

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 6 Standard Regge Theory Parameters:  s 0, s 0 ' and g(t)  set s 0 ‘ = s 0 (universal IP)  g(t)  g(0) ≡ g PPP  KG-1995  determine s 0 and g PPP – how? KG-1995: PLB 358, 379 (1995 )

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 7 Global fit to p ± p,  ±, K ± p x-sections  INPUT  RESULTS CMG-1996 PLB 389, 176 (1996) Regge theory eikonalized negligible

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 8 Renormalization  the key to diffraction in QCD

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 9 Diffractive gaps definition: gaps not exponentially suppressed p p X p Particle productionRapidity gap   -ln  ln M X 2 ln s X No radiation

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 10  T SD (pp & pp) - data Factor of ~8 (~5) suppression at √s = 1800 (540) GeV  suppressed relative to Regge for √s>22 GeV KG, PLB 358, 379 (1995) 1800 GeV 540 GeV M ,t,t p p p’  T SD mb √s=22 GeV  RENORMALIZATION MODEL CDF Run I results

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 11 M 2 distribution: data KG&JM, PRD 59 (1999)  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

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 12 Gap probability  (re)normalize to unity Single diffraction renormalized – (1) 2 independent variables: t color factor gap probability sub-energy x-section EDS 2009: CORFU-2001: hep-ph/

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 13 Single diffraction renormalized – (2) color factor Experimentally: KG&JM, PRD 59 (114017) 1999 QCD:

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 14 Single diffraction renormalized - (3) set to unity  determine s o

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 15 Single diffraction renormalized – (4)  Pumplin bound obeyed at all impact parameters Grows slower than s 

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 16 Scale s o and triple-pom coupling  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: 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

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 17 Multigap diffraction KG, hep-ph/  y

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 18 Multigap cross sections Same suppression as for single gap! Gap probabilitySub-energy cross section (for regions with particles) 5 independent variables color factor

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 19 Gap survival probability S =

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 20 The total x-section √s F =22 GeV SUPERBALL MODEL 98 ± 8 mb at 7 TeV 109 ±12 mb at 14 TeV

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 21 Born Eikonal  T at LHC from CMG global fit   LHC √s=14 TeV: 122 ± 5 mb Born, 114 ± 5 mb eikonal  error estimated from the error in  given in CMG-96 caveat: s o =1 GeV 2 was used in global fit! Compare with SUPERBALL  (14 TeV) = 109 ± 6 mb

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 22  SD and ratio of  ' 

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 23 Monte Carlo Strategy for the LHC   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 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 “  T optical theorem Im f el (t=0) dispersion relations Re f el (t=0) MONTE CARLO STRATEGY

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 24 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 DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 25 SUMMARY  Froissart bound  Valid above the “knee” at √s = 22 GeV in  T SD vs. √s and therefore valid at √s = 1.8 TeV of the CDF measurement  Use superball scale s 0 (saturated exchange) in the Froissart formula, where s 0 = 3.7±1.5 GeV 2 as determined from setting the integral of the Pomeron flux to unity at the “kneee” of s√s = 22 GeV  m 2 = s 0 = (3.7±1.5 GeV 2  At √s 1.8 TeV Reggeon contributions are negligible (see global fit)   compatible with CGM-96 global fit result of 114 ± 5 mb   t = (98 ± 8) mb at 7 TeV – wait and see!

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 26 BACKUP

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 27 Diffractive Tevatron p jet reorganize jet

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 28 F D JJ ( , Q 2 Tevatron

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 29 SD/ND dijet ratio vs. x CDF <  < Flat  dependence for  < 0.5 CDF Run I

K. Goulianos DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 30 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 DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 31 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 DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 32 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 DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 33 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 DIFF. 2010, 09/10-15 Otranto, ITALY Diffractive and total x-sections at LHC and beyond 34 The end