Diffraction from HERA and Tevatron to LHC

$Page 1: Diffraction from HERA and Tevatron to LHC$
Manchester 14-16 Dec 2003 Diffraction from HERA and Tevatron to LHC K. Goulianos 1

Konstantin GoulianosThe Rockefeller University

Workshop on physics with forward proton taggersat the Tevatron and LHC

14-16 December 2003, Manchester, UK

Diffraction from HERA and Tevatron to LHCDiffraction from HERA and Tevatron to LHC

results theory predictions


Soft diffraction Elastic and total cross sections M2-scaling Soft diffraction cross sections Multigap diffraction

Diffractive DIS at HERA Derive F2D3 Explain flat ratio of F2D3 / F2 Explain rise of ( or IP) with Q2

Hard diffraction at the Tevatron Explain ratio of Fjj(SD) / Fjj(ND) – magnitude and shape! Double-gap hard diffraction

Diffraction at the LHC Soft and hard single and multigap diffraction

Topics Topics

Determine: triple-pomeron coupling

pomeron intercept diffractive cross section

using soft parton densities

Predict from hard plus soft

parton densities


Elastic scattering Total cross section Diffraction

PRD PRL PRL PRL50 (1994) 5535 87 (2001)141802 submitted 91(2003)011802

SOFT diffraction

HARD diffraction

Control sample

W 78 (1997) 2698 JJ 74 (1995) 855 JJ 85 (2000) 4217

JJ 79 (1997) 2636 JJ 80 (1998) 1156

b-quark 84 (2000) 232 JJ 81 (1998) 5278

J/ 87 (2001) 241802

JJ 84 (2000) 5043

JJ 88 (2002) 151802

with roman pots

PRL reference

PRD 50 (1994) 5518

PRD 50 (1994) 5550

Diffraction at CDF in Run IDiffraction at CDF in Run I 16 papers


Two (most) important resultsTwo (most) important results

45.0

)(

)()( x

xF

xFxR ND

jj

SDjj

jj

KG&JM, PRD 59 (1999) 114017

122 )(

1

MdM

d

M2SCALING POWER LAW

CDF, PRL 84 (2000) 5043

Soft Diffraction Hard Diffraction


Soft Double Pomeron ExchangeSoft 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


Total Cross SectionTotal Cross Section

t exhibits universal rise with energy

the falling term at low energies has

NOTHING to do with this rise!

POWER LAW behavior: y

os

opIPt ees ln2 )0(

t=0 elastic scattering amplitude

ytel etyf )(),(Im

Parton model: # of wee partons grows exponentially


Single Diffraction VariablesSingle Diffraction Variables SOFT DIFFRACTION HARD DIFFRACTION

=PL/PL fractional momentum loss of scattered hadron

Variables: (, t) or (, t)

Additional variables: (x, Q2)

seExjet

T

jetBj /

x

dN/d

=-ln

t

dN/d


Factorization & (re)normalization

Soft Single Diffraction Phenomenology

y

y

'y

sln2ln XM

ysy ln

XM

)0(

)(

pIP

IPIPIP tg

yo e 22 )( yt

p etFC

COLORFACTOR

Gap probability:Normalize to unity

KG, PLB 358 (1995) 379


The factors and The factors and

18.03

125.0

8

175.0

1

1

1 02

2

Q

cq

cg N

fN

f

Experimentally:

02.017.0pIP

IPIPIPg

Theoretically:

KG&JM, PRD 59 (114017) 1999

xxfx

1)(

g=0.20

q=0.0412.0ww qqgg

R=-0.5


2s

X)pp(p)pp( Total cross sectionKG, PLB 358 (1995) 379

Differential cross sectionKG&JM, PRD 59 (114017) 1999

2~ s

12

2

2 )(M

s

dM

d

REGGE

122 )(

1

MdM

d

RENORM

s-independent Differential shape agrees with Regge Normalization is suppressed by factor Renormalize Pomeron flux factor to unity M2 SCALING

Soft Single Diffraction DataSoft Single Diffraction Data

Regge


Double Diffraction Dissociation

One central gap

Double Pomeron Exchange

Two forward gaps

SDD: Single+Double Diffraction Forward + central gaps

Central and Double GapsCentral and Double Gaps


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~Integral 2~ s

Renormalization removes the s-dependence SCALING

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


Differential shapes agree with Regge predictions

One-gap cross sections require renormalization

DD SDD DPE

Two-gap/one-gap ratios are 17.0

Central and Double-Gap CDF ResultsCentral and Double-Gap CDF Results


Multigap variables Parton model amplitude rapidity gap regions color factor = 0.17 particle cluster regions also: t-across gap centers of floating gap/clusters

Soft Diffraction SummarySoft Diffraction Summary

iy

jy

it ji ,

ytty ef

)(),(

Differential cross section jjii

yo

ytp

ii

eetFCdV

d

n2

gaps-i1

2

var

var

)(

Sub-energy cross sectionNormalized gap probability

form factor for surviving nucleon color factor: one for each gap


F2(x,Q2) = c x-

F2 from Compton analysis (H1)(Q2) versus Q2

[from the talk of E. Tassi @ Small-x and Diffraction 2003, Fermilab]


Diffractive DIS @ HERA Diffractive DIS @ HERA

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

xFxFQ

QQQ

D 1)(1

221

232 2

2

)(

)(1),(

1),,(

constant),(

),,( fixed12

2

232

A

xF

xFR

Q

QD

SDND )(2 2

QDDIS


F2D3(xIP,x,Q2)/F2(x,Q2)F2

D3(xIP,x,Q2)/F2(x,Q2)

At fixed xIP: F2

D3(xIP ,x,Q2) evolves as F2(x,Q2)independent of the value of x


Pomeron Intercept in DDISPomeron Intercept in DDIS

1+()/2

1+


)(DJJF

Test Regge factorizationTest QCD factorization

suppressed at the Tevatron

relative to extrapolationsfrom HERA parton densities

mnDJJ CF ),(Regge factorization holds

exchangePomeron1m

Diffractive Dijets @TevatronDiffractive Dijets @Tevatron

H1-2002


Rjj(x) @TevatronRjj(x) @Tevatron

)(

)()(

xF

xFxR ND

jj

SDjj


Rjj=FjjSD/Fjj

ND

sx

MdA jj

max

21.0

min1

)(/1

Power-law region

max = 0.1 < 0.05

xxfx

1)(

g=0.20

q=0. 04

R=-0.5

g =0.5

q =0.3

CAC

xFxFQ

QQ

NDQ

SD 1

RENORM

)(12

12

2

2

)(

)(1),(

1),,(

x

AR jj

11


RENORM prediction of R(x) vs dataRENORM prediction of R(x) vs data

CDF data

RENORM prediction

exp-syst-errors

Ratio of diffractive to non-diffractivestructure functions is predicted from PDF’sand color factors with no free parameters.

Fjj() correctly predicted

Test: processes sensitive to quarks will have more flat R(x) – diff W?

R(x)


HERA vs TevatronHERA vs Tevatron

C

sx

MF jj

QD

1max

2TEVATRON2 1

)(),,(

(re)normalized gap probability

CF Q

D 1

HERA2 176.0),,(

Pomeron flux

RENORM PREDICTIONS

HERA Tevatron Tev/HERAeffective -- 0.55 --Normalization 0.76 0.042 0.06R(x)=FD(x)/F(x) flat x-(eff ~ x-0.5

_eff = [(Q2)]/2 ~ 0.2 -- --


Another issueQCD evolution

No appreciable ET2 dependence observed within 100 < ET2 < 1600 GeV2

Rjj(xBj) vs Q2


(not detected)

R(SD/ND)

R(DPE/SD)

Test of factorization

equal?

Factorization breaks down,

but see next slide!

The second gap is less suppressed!!!

Dijets in Double Pomeron ExchangeDijets in Double Pomeron Exchange

SDND

DPESD RR 5


DSF: Tevatron double-gaps vs HERADSF: Tevatron double-gaps vs HERA

The diffractive structure function derived from double-gapevents approximately agrees with expectations from HERA


SUMMARYSoft and hard conclusions

Soft Diffraction

Hard Diffraction Pay a color factor for each gap

Use reduced energy cross section

Get gap size from renormalized Pgap

Diffraction is an interaction between low-x partons subject to color constraints


Inclusive Diffractive Higgs at the LHCInclusive Diffractive Higgs at the LHC

D(LHC) ~ 2 * ND (Tevatron)

=> (0.17)2 * 1 pb = 30 fb

p+p p-gap-(H+X)-gap-p

TevatronLHC ss lnln

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Diffraction from HERA and Tevatron to LHC

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