CERN 26-27 March 2004HERA and the LHC: Diffractive Gap Probability K. Goulianos1 HERA and the LHC K....

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CERN 26-27 March 2004 HERA and the LHC: Diffractive Gap Probability K. Goulianos 1

HERA and the LHC

K. Goulianos, The Rockefeller UniversityCERN 26-27 March 2004


Diffractive signatures

Leading hadron(s) Rapidity gap(s)


Leading hadrons

X

Diffractiondissociation

025.0dMdt

σ2

2

dt

1

~

dt

dσ

KG, Phys. Rep. 101 (1983) 171

LL/PΔPξ


Rapidity gapsMinimum bias Diffraction

dissociation

Gaps exponentially suppressed

From Poisson statistics:

dy

dnρey)P( Δyρ

2lnlnln Msy

constantdy

dσ

M

1~

dM

dσ22

MX

gap


QCD aspects of diffraction Quark/gluon exchange across a rapidity gap:

POMERON

No particles radiated in the gap:

the exchange is COLOR-SINGLET with vacuum quantum numbers

Rapidity gap formation: NON-PERTURBATIVE

Diffraction probes the large distance aspects of QCD:

POMERON CONFINEMENT

PARTONIC STRUCTURE FACTORIZATION PROPERTIES

?

MX

gap


History of Diffraction

1960 Good and Walker 1960’s BNL: first observation

1970’s Fermilab fixed target, ISR, SPS 1983 KG, Phys. Rep. 101, 169 (1983)

1992 UA8: diffractive dijets hard diff 1993-2003 Golden decade: HERA, Tevatron,

RHIC

40 years of diffraction


SOFT DIFFRACTION

Soft and Hard Diffraction HARD DIFFRACTION

=PL/PL =fractional momentum loss of scattered (anti)proton

Variables: (, t) or (,

t)

Additional variables: (x, Q2)

seExjet

T

jetBj /

22 )(, jetTEQx

dN/d

MX

=-lnt

dN/d

ln MX2


Breakdown of QCD factorization

dN/dgap

e*

HERA TEVATRON

dN/dgap

p

ppIPt

),( 22 xQF

),,,( 22 tQF D ),,,( tEF Jet

TDJJ

),( xEF JetTJJ

CDF

H1

p

ppIP

pIP

XXX


Diffractive vs inclusive structure fn’s

F2D(x,Q2) /F2(x,Q2)

FDJJ(x,Q2) /F(x,Q2)

x),2F(Q

ξ)x,,2(QDFR

~ no Q2 dependence~ flat at HERA~ 1/x0.5 at Tevatron


CDF Run I results


Unitarity problem: With factorization and std pomeron flux SD exceeds T at

Renormalization: normalize the pomeron flux to unity

Soft Diffraction)(Mσξ)(t,f

dtdξ

σd 2XpIPIP/p

SD2

MX

KG, PLB 358 (1995) 379

TeV.2s

1dtdξξ)(t,f0.1

ξ

IP/p

0

tmin

~10

2~ sSD


A Scaling Law in Diffraction

KG&JM, PRD 59 (1999) 114017

Factorization breaksdown in favor of

M2-scaling

12

2

2 )(M

s

dM

d

renormalization

1


Double Diffraction Dissociation

One central gap

Double Pomeron Exchange

Two forward gaps

SDD: Single+Double Diffraction Forward + central gaps

Central and Double Gaps


Elastic & total

yooT ess )(

2),( ytel ets

y

y

sy ln

sy ln


yy

yt ,2 independent variables:

yoyt

p eetFCyddt

d

2

12

2

)(

Gap probability

ye 2~ 22ln

minsyssy

y

Renormalization removes the s-dependence SCALING

Generalized renormalization (KG, hep-ph/0205141)

colorfactor

17.0)0(

)(

ppIP

IPIPIP tg

t


The factors and

18.03

125.0

8

175.0

1w

1

1w 0

2

2

Q

cq

cg NN

Experimentally:

02.017.0pIP

IPIPIPg

Color factor:

KG&JM, PRD 59 (114017) 1999

12.0ww qqgg

λx

1f(x)x

g=0.20

q=0.04

R=-0.5

Intercept:

wg=gluon fractionwq=quark fraction


colorfactor

1y 2y1y 2y

1y 2y

2t1t 21 yyy 5 independent variables

2122

2-1i1

2

51

5

)( yyo

ytp

ii

eetFCdV

dii

Gap probability Sub-energy cross section(for regions with particles)ye 2~

Two-Gap Diffraction (KG, hep-ph/0205141)

22ln

minsyssy

y

Same suppressionas for single gap!


Differential shapes agree with Regge predictions

One-gap cross sections are suppressed

DD SDD DPE

Two-gap/one-gap ratios are 17.0

Central & Double-Gap Results


Soft Double Pomeron Exchange

ieEs

iTp

particlesall

1

Roman Pot triggered events

0.035 < -pbar < 0.095

|t-pbar| < 1 GeV 2

-proton measured using

Data compared to MC based

on Pomeron exchange with

Pomeron intercept =0.1

Good agreement over 4 orders of magnitude!

2pbar

pbar

GeV1||

095.0035.0

GeV1800

t

s


Soft gap survival probability

0.23GeV)(1800S gapgap/01gapgap/12

0.29GeV)(630S gapgap/01gapgap/12

S =


Hard Diffraction & QCD

• The diffractive structure function measured using SD dijets at the Tevatron is suppressed by about an order of magnitude relative to predictions based on diffractive DIS at HERA

• The discrepancy is generally attributed to additional color exchanges which spoil the diffractive rapidity gap.

~10

Factorization Breakdown

XJetJetppp Diffractive structure function

HERA

Tevatron


Double-Gap Hard Diffraction @TEV vs HERA

R(SD/ND)

R(DPE/SD)

DSF from double-gapsDSF from single-gaps


Diffractive structure functionfrom inclusive pdf’s (KG)

Power-law region

max = 0.1xmax = 0.1 < 0.05

xxfx

1)(

g=0.20

q=0. 04

R=-0.5

g =0.5

q =0.3

CAC

xFxF NORM

Q

QQQ

D 1)(1

21

22

2

)(

)(1),(

1),,(

)(2 constant,:) (noHERA 2fixedRENORM QDDIS

DDISDISR

)(JJ

R:(RENORM)TEVATRON

xND

SD


Pomeron Intercept from H1

RENORM

1+

ttIP 1)(


Pomeron intercept from ZEUS


Gap between jets

jet???gap ΔyΔy Question

gapΔyjetΔy

5%1%/0.2/SR)s(R JGJTEV

JGJLHC

JetGapJetpp


Exclusive Dijets in DPEInterest in diffractive Higgs production Calibrate on exclusive dijets

Dijet mass fraction

X

conejj

jj M

MR

pb10534GeV25

pb27265970GeV10

0.8)(RσE jjjjexcl

DPEjetT

Upper limit for excl DPE-jjconsistent with theory

no peak!


Exclusive c Production in DPE pγ)J/ψ(χppp c

Cross section upper limit comparable to KMR prediction


Summary

M2 – scaling

Non-suppressed double-gap to single-gap ratios

Flavor-independence SD/ND ratio

Get diffractive from non-diffractive pdf’s

SOFT DIFFRACTION

Universality of gap prob. across soft and hard diffraction

HARD DIFFRACTION


HERA &Tevatron->LHCp

p IP

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CERN 26-27 March 2004HERA and the LHC: Diffractive Gap Probability K. Goulianos1 HERA and the LHC K....

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