1. pp cross sections at the LHC K. Goulianos FP@LHC, UK 6-8 Dec 2008 1 pp cross sections at the LHC Konstantin Goulianos The Rockefeller University Forward Physics at the LHC Manchester, UK, 6-8 Dec 2008

2. pp cross sections at the LHC K. Goulianos FP@LHC, UK 6-8 Dec 2008 2 Contents  References  Strategy  Renormalization  Cross section @ LHC  Global fit to p ± p,  ± p, K ± p x-sections  Bonus: the ratio of  ' / 

3. pp cross sections at the LHC K. Goulianos FP@LHC, UK 6-8 Dec 2008 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. pp cross sections at the LHC K. Goulianos FP@LHC, UK 6-8 Dec 2008 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

5. pp cross sections at the LHC K. Goulianos FP@LHC, UK 6-8 Dec 2008 5 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

6. pp cross sections at the LHC K. Goulianos FP@LHC, UK 6-8 Dec 2008 6 Renormalization   Flux integral depends on s and s 0  “knee” √s-position determines s 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 Single Diffraction KG-95 Pomeron flux

7. pp cross sections at the LHC K. Goulianos FP@LHC, UK 6-8 Dec 2008 7 The value of s o - a bird’s-eye view “knee” @ 22 ± 1 GeV  s 0 = 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

8. pp cross sections at the LHC K. Goulianos FP@LHC, UK 6-8 Dec 2008 8 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 

9. pp cross sections at the LHC K. Goulianos FP@LHC, UK 6-8 Dec 2008 9 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)

10. pp cross sections at the LHC K. Goulianos FP@LHC, UK 6-8 Dec 2008 10 Global fit to p ± p,  ±, K ± p x-sections  INPUT  RESULTS CMG-96  Use standard Regge theory negligible

11. pp cross sections at the LHC K. Goulianos FP@LHC, UK 6-8 Dec 2008 11 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

12. pp cross sections at the LHC K. Goulianos FP@LHC, UK 6-8 Dec 2008 12 DISCUSSION

13. pp cross sections at the LHC K. Goulianos FP@LHC, UK 6-8 Dec 2008 13 BONUS - the ratio of  '/   The key!

14. pp cross sections at the LHC K. Goulianos FP@LHC, UK 6-8 Dec 2008 14 thank you

15. pp cross sections at the LHC K. Goulianos FP@LHC, UK 6-8 Dec 2008 15 BACKUP - 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)