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

2. LISHEP 2009, Brazil, Jan 19-24 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

3. LISHEP 2009, Brazil, Jan 19-24 DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 3 References http://physics.rockefeller.edu/dino/my.html CDF PRD 50, 5518 (1994)  el @ 1800 & 546 GeV CDF PRD 50, 5535 (1994)  D @ 1800 & 546 GeV CDF PRD 50, 5550 (1994)  T @ 1800 & 546 GeV KG-PR Physics Reports 101, No.3 (1983) 169-219 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

4. LISHEP 2009, Brazil, Jan 19-24 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

5. LISHEP 2009, Brazil, Jan 19-24 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

6. LISHEP 2009, Brazil, Jan 19-24 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

7. LISHEP 2009, Brazil, Jan 19-24 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

8. LISHEP 2009, Brazil, Jan 19-24 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

9. LISHEP 2009, Brazil, Jan 19-24 DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 9  T sd (s  ∞) and ratio of  '/   arXiv:0812.4464v1[hep-ph] submitted to PLB  Constant set to  o pp

10. LISHEP 2009, Brazil, Jan 19-24 DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 10 The value of s o - a bird’s-eye view “knee” @ 22 ± 1 GeV  s o = 1 ± 0.2 GeV KG-95 √s (GeV)  Cool [KG]FNAL1420 Albrow ISR23.326.9 o ArmitageISR23.327.4  error in knee position: ± 1 GeV

11. LISHEP 2009, Brazil, Jan 19-24 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 

12. LISHEP 2009, Brazil, Jan 19-24 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

13. LISHEP 2009, Brazil, Jan 19-24 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)

14. LISHEP 2009, Brazil, Jan 19-24 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

15. LISHEP 2009, Brazil, Jan 19-24 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

16. LISHEP 2009, Brazil, Jan 19-24 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)

17. LISHEP 2009, Brazil, Jan 19-24 DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 17 DISCUSSION

18. LISHEP 2009, Brazil, Jan 19-24 DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 18 thank you