Diffractive, Elastic, and Totalpp Cross Sections at the LHC

Konstantin GoulianosThe Rockefeller University

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

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

LISHEP 2009, Brazil, Jan 19-24 DIFFRACTIVE AND EXCLUSIVE PRODUCTION AT CDF II K. GOULIANOS 4

Single diffraction

Two free parameters: so and gPPP Obtain product gPPP•so

from SD

Renormalized Pomeron flux determines so

Get unique solution for gPPP

KG-95

Pomeron-proton x-section

)(sσξ)(t,fdtdξ

σd1/

SD2

PppP

os

)(s /2o tgPPP

Pomeron flux

p2

p1

P

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Standard Regge theory

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

KG-95

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The triple-Pomeron coupling in QCD

Experimentally: KG&JM, PRD 59 (114017) 1999

02.017.0 Pp

PPPg

yoyt

pgap eetFCNyddt

d

222

)(

),( tyPgap soT

18.03

125.0

8

175.0

121f

1

1f

2

Q

NN cq

cgColor factor:

gluon fraction

quark fraction

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Renormalization

Flux integral depends on s and s0

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

ss= -2 s/s = -4 (√s)/√s

get error in so from error in √s-knee

Tsd renormalized

2~ sSD

1dtdξξ)(t,f 02

ζ

/1ξ

/

0

tmin

ssCs

pP

2~ sSD

KG-95

)(sσξ)(t,fdξdt

σd1 /

SD2

PppP

0s

)(s /20 tgPPP

Pomeron flux

ssb=22 GeV

p1

p2

1dtdξξ)(t,f0.1

ξ

/

0

tmin

pP

P

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yoyt

pgap eetFCNyddt

d

222

)(

s

sCdtydtyPsN s

gaptygap ln),()(

2

,1

tybsy eseCyddt

d )2()ln(2

0ln

The Pumplin bound is obeyed at all impact parameters

grows slower than s

),( tyPgap

Renormalization and Pumplin bound

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Tsd (s∞) and ratio of '/

1'2

exp2

sdob

ppPp

00

)!14.3

'0.08) using(GeV25.0

)2ln(4

4/1' 2

2

m

2

2

2

1

2 m

Rb psdo

arXiv:0812.4464v1[hep-ph] submitted to PLB

Constant set to o

pp

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The value of so - a bird’s-eye view

“knee” @ 22 ± 1 GeV so = 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

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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

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Froissart-Martin bound: (s in GeV2)

For m2 = m2 / 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 T

SD

Show that √ssb < 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

sb

2

osbsb s

sln

s

π)σ(sssσ

s22

lnm

πσ

F

CDF2

F

LHC2CDF

1800LHC

s

sln

s

sln

πσσ

0s

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The SUPERBALL T

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))

s22

lnm

πσ

compatible with CGM-96 global fit result of 114 ± 5 mb (see next 2 slides)

mb611963924.203.80s

sln

s

sln

s

πσσ

F

CDF2

F

LHC2

0

CDF1800

LHC14000

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Global fit to p±p, ±, K±p x-sections

INPUT

RESULTS

CMG-96

Use standard Regge theory

negligible

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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

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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 theoremIm fel(t=0)

dispersion relationsRe fel(t=0)

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DISCUSSION

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thank you