EDS 2009, June 29-July 3 1Diffractive and Total pp cross sections at LHC

K. Goulianos

Diffractive and Totalpp Cross Sections at LHC

Konstantin GoulianosThe Rockefeller University

13th International Conference on Elastic & Diffractive Scattering (13th "Blois Workshop")

CERN, 29th June - 3rd July 2009

EDS 2009, June 29-July 3 2Diffractive and Total pp cross sections at LHC

K. Goulianos

Contents

References Strategy Unitarity and renormalization Cross sections @ LHC Global fit to p±p, ±p, K±p x-sections The ratio of '/Discussion

EDS 2009, June 29-July 3 3Diffractive and Total pp cross sections at LHC

K. Goulianos

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

Diffractive interactions of hadrons at high energies

KG-95 PLB 358, 379 (1995); Erratum: PLB 363, 268 (1995) Renormalization of hadronic diffraction

CMG-96 PLB 389, 176 (1996) Global fit to p±p, ± and K±p cross sectionsKG-09 arXiv:0812.4464v2 [hep-ph] 26 March 2009 Pomeron intercept and slope: the QCD connection

EDS 2009, June 29-July 3 4Diffractive and Total pp cross sections at LHC

K. Goulianos

Froissart bound (s in GeV2)

For m2 = m2 /m2 ~ 104 mb – large!

If m2 = so = (mass)2 of a large SUPERglueBALL, the bound can be

reached at a much lower s-value, sF, Determine sF and s0 from T

SD

Show that √sF < 1.8 TeV

Show that at √s = 1.8 TeV Reggeon contributions are negligible

Get cross section at the LHC as

Strategy

F

2

oFF s

sln

s

π)σ(sssσ

CDF

LHC2CDF

1800LHC14000 s

sln

πσσ

0s

s22

lnm

πσ

EDS 2009, June 29-July 3 5Diffractive and Total pp cross sections at LHC

K. Goulianos

Standard Regge Theory

Parameters: s0, s0' and g(t) set s0‘ = s0 (universal IP) g(t) g(0) ≡ gPPP see KG-PR determine s0 and gPPP – how?

(KG-95)

EDS 2009, June 29-July 3 6Diffractive and Total pp cross sections at LHC

K. Goulianos

Unitarity and Renormalization

Two free parameters: s0 and gPPP

Obtain product gPPP•s0 from SD

Renormalized Pomeron flux determines s0

Get unique solution for gPPP

Pomeron-proton x-section

)(sσξ)(t,fdtdξ

σdpIPIP/p

SD2

0s

)(s /20 tgPPP

Pomeron flux

EDS 2009, June 29-July 3 7Diffractive and Total pp cross sections at LHC

K. Goulianos

Renormalization

Flux integral depends on s and s0

“knee” √s-position determines s-value where flux becomes unity get so

get error in so from error in √s-knee

ss= -2 s/s = -4 (√s)/√s

Single Diffraction

2~ sSD

1dtdξξ)(t,f 02

ζ

/1ξ

IP/p

0

tmin

ssCs

1dtdξξ)(t,f0.1

ξ

IP/p

0

tmin

KG-95

)(sσξ)(t,fdtdξ

σdpIPIP/p

SD2

0s

)(s /20 tgPPP

Pomeron flux

2~ sSD

EDS 2009, June 29-July 3 8Diffractive and Total pp cross sections at LHC

K. Goulianos

The value of so - a bird’s-eye view

“knee” @ 22 ± 1 GeV s0 = 1 ± 0.2 GeV

KG-95

√s (GeV) Cool [KG] FNAL 14 20 Albrow ISR 23.3 26.9o Armitage ISR 23.3 27.4

error in knee position: ± 1 GeV

11/2 GeV1.1mb0.69(t)g PPP KG-95riple-Pomeron coupling:

EDS 2009, June 29-July 3 9Diffractive and Total pp cross sections at LHC

K. Goulianos

The value of so- 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

EDS 2009, June 29-July 3 10Diffractive and Total pp cross sections at LHC

K. Goulianos

The SUPERBALL cross-section

Froissart bound

Valid above “knee” at √s = 22 GeV and therefore at √s = 1.8 TeV

Use superball mass

m2 = s0 = (1±0.2) GeV2

At √s 1.8 TeV Reggeon contributions are negligible (see global fit)

mb611363324.203.80s

sln

s

πσσ

CDF

LHC2

0

CDF1800

LHC14000

s22

lnm

πσ

compatible with CGM-96 global fit result of 114 ± 5 mb (see next slides)

EDS 2009, June 29-July 3 11Diffractive and Total pp cross sections at LHC

K. Goulianos

Global fit to p±p, ±, K±p x-sectionsGlobal fit to p±p, ±, K±p x-sections

INPUT

RESULTS

CMG-96

Use standard Regge theory

negligible

EDS 2009, June 29-July 3 12Diffractive and Total pp cross sections at LHC

K. Goulianos

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: so=1 GeV2 was used in global fit!

Compare with SUPERBALL (14 TeV) = 113 ± 6 mb

EDS 2009, June 29-July 3 13Diffractive and Total pp cross sections at LHC

K. Goulianos

Extra: the ratio of '/

1'2

exp2

sdob

ppPp00

222

03.025.0'08.0

4.012.3)2ln(4

4/1'

c

GeV

c

GeVm

2

2

2

1

2 m

Rb psdo

The key!

KG-09

EDS 2009, June 29-July 3 14Diffractive and Total pp cross sections at LHC

K. Goulianos

SUMMARY

Froissart bound

Valid above the “knee” at √s = 22 GeV in TSD vs. √s

and therefore valid at √s = 1.8 TeV of the CDF measurement

Use superball mass s0 (saturated dressed proton mass) in the Froissart- Martin formula, where s0 is determined from setting the integral of the Pomeron flux to unity at √s = 22 GeV

m2 = s0 = (1±0.2) GeV2

At √s 1.8 TeV Reggeon contributions are negligible (see global fit)

compatible with CGM-96 global fit result of 114 ± 5 mb

mb611363324.203.80s

sln

s

πσσ

CDF

LHC2

0

CDF1800

LHC14000

s22

lnm

πσ

EDS 2009, June 29-July 3 15Diffractive and Total pp cross sections at LHC

K. Goulianos

thank you

EDS 2009, June 29-July 3 16Diffractive and Total pp cross sections at LHC

K. Goulianos

DISCUSSION