Diffractive and Total pp cross sections at LHC K. Goulianos EDS 2009, June 29-July 3 1 Diffractive and Total pp Cross Sections at LHC Konstantin Goulianos The Rockefeller University 13th International Conference on Elastic & Diffractive Scattering (13th "Blois Workshop") CERN, 29th June - 3rd July 2009

Diffractive and Total pp cross sections at LHC K. Goulianos EDS 2009, June 29-July 3 2 Contents  References  Strategy  Unitarity and renormalization  Cross LHC  Global fit to p ± p,  ± p, K ± p x-sections  The ratio of  ' /    Discussion

Diffractive and Total pp cross sections at LHC K. Goulianos EDS 2009, June 29-July 3 3 References CDF PRD 50, 5518 (1994)  1800 & 546 GeV CDF PRD 50, 5535 (1994)  1800 & 546 GeV CDF PRD 50, 5550 (1994)  1800 & 546 GeV KG-PR Physics Reports 101, No.3 (1983) Diffractive interactions of hadrons at high energies KG-95 PLB 358, 379 (1995); Erratum: PLB 363, 268 (1995) Renormalization of hadronic diffraction CMG-96 PLB 389, 176 (1996) Global fit to p ± p,  ± and K ± p cross sections KG-09 arXiv: v2 [hep-ph] 26 March 2009 Pomeron intercept and slope: the QCD connection

Diffractive and Total pp cross sections at LHC K. Goulianos EDS 2009, June 29-July 3 4  Froissart bound (s in GeV 2 )  For m 2 = m  2   /m 2 ~ 10 4 mb – large!  If m 2 = s o = (mass) 2 of a large SUPER glue BALL, the bound can be reached at a much lower s-value, s F,   Determine s F and s 0 from  T SD  Show that √s F < 1.8 TeV  Show that at √s = 1.8 TeV Reggeon contributions are negligible  Get cross section at the LHC as Strategy

Diffractive and Total pp cross sections at LHC K. Goulianos EDS 2009, June 29-July 3 5 Standard Regge Theory Parameters:  s 0, s 0 ' and g(t)  set s 0 ‘ = s 0 (universal IP)  g(t)  g(0) ≡ g PPP see KG-PR  determine s 0 and g PPP – how? (KG-95)

Diffractive and Total pp cross sections at LHC K. Goulianos EDS 2009, June 29-July 3 6 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

Diffractive and Total pp cross sections at LHC K. Goulianos EDS 2009, June 29-July 3 7 Renormalization   Flux integral depends on s and s 0  “knee” √s-position determines s-value where flux becomes unity  get s o  get error in s o from error in √s-knee  s   s  = -2  s/s = -4 (  √s)/√s Single Diffraction KG-95 Pomeron flux

Diffractive and Total pp cross sections at LHC K. Goulianos EDS 2009, June 29-July 3 8 The value of s o - a bird’s-eye view 22 ± 1 GeV  s 0 = 1 ± 0.2 GeV KG-95 √s (GeV)  Cool [KG]FNAL1420 Albrow ISR o ArmitageISR  error in knee position: ± 1 GeV KG-95  riple-Pomeron coupling:

Diffractive and Total pp cross sections at LHC K. Goulianos EDS 2009, June 29-July 3 9 The value of s o - limited edition CDF shape of renormalized  SD E396  use CDF points to fix the level of renormalized curve  use E396 points to fix the level of the Regge curve  both curves are somewhat high in this plot  adjusting height leads to the same “knee” position shape of Regge s 

Diffractive and Total pp cross sections at LHC K. Goulianos EDS 2009, June 29-July 3 10 The SUPERBALL cross-section  Froissart bound  Valid above “knee” at √s = 22 GeV and therefore at √s = 1.8 TeV  Use superball mass  m 2 = s 0 = (1±0.2) 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 (see next slides)

Diffractive and Total pp cross sections at LHC K. Goulianos EDS 2009, June 29-July 3 11 Global fit to p ± p,  ±, K ± p x-sections  INPUT  RESULTS CMG-96  Use standard Regge theory negligible

Diffractive and Total pp cross sections at LHC K. Goulianos EDS 2009, June 29-July 3 12 Born Eikonal  T at LHC from 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) = 113 ± 6 mb

Diffractive and Total pp cross sections at LHC K. Goulianos EDS 2009, June 29-July 3 13 Extra: the ratio of  '/   The key! KG-09

Diffractive and Total pp cross sections at LHC K. Goulianos EDS 2009, June 29-July 3 14 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 mass s 0 (saturated dressed proton mass) in the Froissart- Martin formula, where s 0 is determined from setting the integral of the Pomeron flux to unity at √s = 22 GeV  m 2 = s 0 = (1±0.2) 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

Diffractive and Total pp cross sections at LHC K. Goulianos EDS 2009, June 29-July 3 15 thank you

Diffractive and Total pp cross sections at LHC K. Goulianos EDS 2009, June 29-July 3 16 DISCUSSION