pp cross sections at the LHC Forward Physics

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

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

References http: //physics. rockefeller. edu/dino/my. html CDF PRD 50, 5518 (1994) sel @ 1800 & 546 Ge. V CDF PRD 50, 5535 (1994) s. D @ 1800 & 546 Ge. V CDF PRD 50, 5550 (1994) s. T @ 1800 & 546 Ge. V 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 FP@LHC, UK 6 -8 Dec 2008 pp cross sections at the LHC K. Goulianos 3

Strategy (s in Ge. V 2) q Froissart bound q For m 2 = mp 2 p/m 2 ~ 104 mb – large! q If m 2 = so = (mass)2 of a large SUPERglue. BALL, the bound can be reached at a much lower s-value, s. F, q Determine s. F and s 0 from s. TSD q Show that √s. F < 1. 8 Te. V q Show that at √s = 1. 8 Te. V Reggeon contributions are negligible q Get cross section at the LHC as FP@LHC, UK 6 -8 Dec 2008 pp cross sections at the LHC K. Goulianos 4

Renormalization Pomeron flux Pomeron-proton x-section q q Two free parameters: s 0 and g. PPP Obtain product g. PPP • s 0 e / 2 from s. SD Renormalized Pomeron flux determines s 0 Get unique solution for g. PPP FP@LHC, UK 6 -8 Dec 2008 pp cross sections at the LHC K. Goulianos 5

Single Diffraction KG-95 Pomeron flux Renormalization q q Flux integral depends on s and s 0 q “knee” √s-position determines s value where flux becomes unity get so q dso/so = -2 ds/s = -4 (d√s)/√s q get error in so from error in √s-knee FP@LHC, UK 6 -8 Dec 2008 pp cross sections at the LHC K. Goulianos 6

The value of so - a bird’s-eye view KG-95 x Cool [KG] n Albrow o Armitage FNAL ISR √s (Ge. V) 14 20 23. 3 26. 9 23. 3 27. 4 error in knee position: ± 1 Ge. V “knee” @ 22 ± 1 Ge. V s 0 = 1 ± 0. 2 Ge. V FP@LHC, UK 6 -8 Dec 2008 pp cross sections at the LHC K. Goulianos 7

The value of so- limited edition shape of Regge s 2 e shape of renormalized s. SD CDF Ø use CDF points to fix the level of renormalized curve E 396 Ø use E 396 points to fix the level of the Regge curve Ø both curves are somewhat high in this plot adjusting height leads to the same “knee” position FP@LHC, UK 6 -8 Dec 2008 pp cross sections at the LHC K. Goulianos 8

The SUPERBALL cross-section q Froissart bound q Valid above “knee” at √s = 22 Ge. V and therefore at √s = 1. 8 Te. V q Use superball mass m 2 = s 0 = (1± 0. 2) Ge. V 2 q At √s 1. 8 Te. V Reggeon contributions are negligible (see global fit) compatible with CGM-96 global fit result of 114 ± 5 mb (see next slides) FP@LHC, UK 6 -8 Dec 2008 pp cross sections at the LHC K. Goulianos 9

± ± ± Globalfit fitto topp p, p, pp , , KK ppx-sections CMG-96 Use standard Regge theory q INPUT q RESULTS negligible FP@LHC, UK 6 -8 Dec 2008 pp cross sections at the LHC K. Goulianos 10

T s at LHC from global fit Born Eikonal v s @ LHC √s=14 Te. V: 122 ± 5 mb Born, 114 ± 5 mb eikonal error estimated from the error in e given in CMG-96 Compare with SUPERBALL s(14 Te. V) = 113 ± 6 mb caveat: so=1 Ge. V 2 was used in global fit! FP@LHC, UK 6 -8 Dec 2008 pp cross sections at the LHC K. Goulianos 11

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

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

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

BACKUP - Standard Regge theory (KG-95) Parameters: q s 0, s 0' and g(t) q set s 0‘ = s 0 (universal IP) q g(t) g(0) ≡ g. PPP see KG-PR q determine s 0 and g. PPP – how? FP@LHC, UK 6 -8 Dec 2008 pp cross sections at the LHC K. Goulianos 15