Diffractive, Elastic, and Total pp Cross Sections at the LHC Konstantin Goulianos The Rockefeller University

LISHEP 2009, Brazil, Jan DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 2 Contents  References  Single diffraction  Renormalization  triple-Pomeron coupling  ratio of  '   Total cross section  the SUPERBALL cross section  cross section from a global fit  The elastic cross section  Discussion

LISHEP 2009, Brazil, Jan DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 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) KG-95 PLB 358, 379 (1995) Renormalization Erratum: PLB 363, 268 (1995) CMG-96 PLB 389, 176 (1996)Global fit to p ± p,  ±, K ± p

LISHEP 2009, Brazil, Jan DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 4 Single diffraction  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 KG-95 Pomeron-proton x-section Pomeron flux p2p2 p1p1 P

LISHEP 2009, Brazil, Jan DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 5 Standard Regge theory Parameters:  s o, s o ' and g(t)  set s o ‘ = s o (universal) P  g(t)  g(0) ≡ g PPP see KG-PR  determine s o and g PPP – how? KG-95

LISHEP 2009, Brazil, Jan DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 6 The triple-Pomeron coupling in QCD Experimentally: KG&JM, PRD 59 (114017) 1999 Color factor: gluon fraction quark fraction

LISHEP 2009, Brazil, Jan DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 7 Renormalization   Flux integral depends on s and s 0  “knee” √s-position determines the s sb value where flux becomes unity  get s o   s   s  = -2  s/s = -4 (  √s)/√s  get error in s o from error in √s-knee  T sd renormalized KG-95 Pomeron flux s sb =22 GeV p1p1 p2p2 P

LISHEP 2009, Brazil, Jan DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 8  The Pumplin bound is obeyed at all impact parameters grows slower than s  Renormalization and Pumplin bound

LISHEP 2009, Brazil, Jan DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 9  T sd (s  ∞) and ratio of  '/   arXiv: v1[hep-ph] submitted to PLB  Constant set to  o pp

LISHEP 2009, Brazil, Jan DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 10 The value of s o - a bird’s-eye view 22 ± 1 GeV  s o = 1 ± 0.2 GeV KG-95 √s (GeV)  Cool [KG]FNAL1420 Albrow ISR o ArmitageISR  error in knee position: ± 1 GeV

LISHEP 2009, Brazil, Jan DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 11 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 

LISHEP 2009, Brazil, Jan DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 12  Froissart-Martin bound: (s in GeV 2 )  For m 2 = m  2   / m 2 ~ 10 4 mb – very large!  But if m 2 = s o = (mass) 2 of a large SUPER glue BALL, a ln 2 s behavior ala Froissart-Martin an be reached at a much lower s-value, s sb,   Determine s sb and s o from  T SD  Show that √s sb < 1.8 TeV  Show that at √s = 1.8 TeV Reggeon contributions are negligible  Get cross section at the LHC from The total cross section

LISHEP 2009, Brazil, Jan DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 13 The SUPERBALL  T  Froissart-Martin bound  Valid above “knee” at √s = 22 GeV and therefore at √s = 1.8 TeV  Use superball mass  m 2 = s o = (1±0.2) GeV 2  At √s 1.8 TeV Reggeon contributions are negligible (CMG-96))  compatible with CGM-96 global fit result of 114 ± 5 mb (see next 2 slides)

LISHEP 2009, Brazil, Jan DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 14 Global fit to p ± p,  ±, K ± p x-sections  INPUT  RESULTS CMG-96  Use standard Regge theory negligible

LISHEP 2009, Brazil, Jan DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 15 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

LISHEP 2009, Brazil, Jan DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 16 The elastic cross section  Optical theorem: obtain imaginary part of the amplitude from  T  Dispersion relations: obtain real part of the amplitude from  T  Add Coulomb amplitude  Get differential elastic cross section and  -value  T optical theorem Im f el (t=0) dispersion relations Re f el (t=0)

LISHEP 2009, Brazil, Jan DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 17 DISCUSSION

LISHEP 2009, Brazil, Jan DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 18 thank you