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Diffractive, Elastic, and Total pp Cross Sections at the LHC

Diffractive, Elastic, and Total pp Cross Sections at the LHC. Konstantin Goulianos The Rockefeller University. Contents. References Single diffraction  Renormalization  triple-Pomeron coupling  ratio of a ' /e Total cross section  the SUPERBALL cross section

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Diffractive, Elastic, and Total pp Cross Sections at the LHC

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

  2. Contents • References • Single diffraction  Renormalization  triple-Pomeron coupling  ratio of a'/e • Total cross section  the SUPERBALL cross section  cross section from a global fit • The elastic cross section • Discussion DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF IIK. GOULIANOS

  3. References http://physics.rockefeller.edu/dino/my.html CDF PRD 50, 5518 (1994) sel @ 1800 & 546 GeV CDF PRD 50, 5535 (1994) sD @ 1800 & 546 GeV CDF PRD 50, 5550 (1994) sT @ 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, p±, K±p DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF IIK. GOULIANOS

  4. Pomeron flux p1 p2 Pomeron-proton x-section • Two free parameters: so and gPPP • Obtain product gPPP•soe / 2 from sSD • Renormalized Pomeron flux determines so • Get unique solution for gPPP Single diffraction KG-95 P DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF IIK. GOULIANOS

  5. Standard Regge theory KG-95 • Parameters: • so, so' and g(t) • set so‘ = so (universal) P • g(t)  g(0) ≡ gPPPsee KG-PR • determine so and gPPP– how? DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF IIK. GOULIANOS

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

  7. sTsd renormalized KG-95 Pomeron flux p1 P p2 • Renormalization • Flux integral depends on s and s0 • “knee” √s-position determines the ssb value where flux becomes unity  get so • dso/so = -2 ds/s = -4 (d√s)/√s • get error in so from error in √s-knee ssb=22 GeV DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF IIK. GOULIANOS

  8. grows slower than se  The Pumplin bound is obeyed at all impact parameters Renormalization and Pumplin bound DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF IIK. GOULIANOS

  9. sTsd (s∞) and ratio of a'/e arXiv:0812.4464v1[hep-ph] submitted to PLB • Constant set to sopp  DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF IIK. GOULIANOS

  10. The value of so - a bird’s-eye view KG-95 √s (GeV) • Cool [KG] FNAL 14 20 • Albrow ISR 23.3 26.9 • Armitage ISR 23.3 27.4 •  error in knee position: ± 1 GeV “knee” @ 22 ± 1 GeV  so = 1 ± 0.2 GeV DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF IIK. GOULIANOS

  11. The value of so- limited edition shape of Regge s2e shape of renormalized sSD CDF • 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 E396 DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF IIK. GOULIANOS

  12. The total cross section • Froissart-Martin bound: (s in GeV2) • For m2 = mp2 p / m2 ~ 104 mb – very large! • But if m2 = so = (mass)2 of a large SUPERglueBALL, a ln2s behavior ala Froissart-Martin an be reached at a much lower s-value, ssb,  • Determine ssb and so from sTSD • Show that √ssb < 1.8 TeV • Show that at √s = 1.8 TeV Reggeon contributions are negligible • Get cross section at the LHC from DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF IIK. GOULIANOS

  13. The SUPERBALLsT • Froissart-Martin bound • Valid above “knee” at √s = 22 GeV and therefore at √s = 1.8 TeV • Use superball mass  m2 = so = (1±0.2) GeV2 • 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) DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF IIK. GOULIANOS

  14. Global fit to p±p, p±, K±p x-sections CMG-96  Use standard Regge theory • INPUT • RESULTS negligible DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF IIK. GOULIANOS

  15. Born Eikonal sT at LHC from global fit • s @ LHC √s=14 TeV: 122 ± 5 mb Born, 114 ± 5 mb eikonal  error estimated from the error in e given in CMG-96 Compare with SUPERBALLs(14 TeV) = 113± 6 mb caveat: so=1 GeV2 was used in global fit! DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF IIK. GOULIANOS

  16. The elastic cross section • Optical theorem: obtain imaginary part of the amplitude from sT • Dispersion relations: obtain real part of the amplitude from sT • Add Coulomb amplitude • Get differential elastic cross section and r-value sT optical theorem Im fel(t=0) dispersion relations Re fel(t=0) DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF IIK. GOULIANOS

  17. DISCUSSION QUESTIONS? DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF IIK. GOULIANOS

  18. thank you thank you DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF IIK. GOULIANOS

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