Small-x, diffraction and QCD results from HERA Small-x...

Small-x, diffraction and QCD results from HERA

Henri Kowalski, DESY (KITP QCD-Strings Conference 11/16/04) 1

Small-x, Diffraction and QCDResults from HERA

Henr i KowalskiDESY

QCD and Str ing Theory Santa Barbara

16 of November 2004



p

e

e

γ*

ZEUS H1

Q2 - vir tuality of the incoming photonW - CMS energy of the incoming photon-proton system

x - Fraction of the proton momentum carr ied by the struck quark x ~ Q2/W2

Liquid Argon Calor imeter Uranium-Scintillator Calor imeter

e27 GeV

p920GeV

Small-x and Diffraction Q2 ~ 2 –100 GeV2 and 0.05-0.6 GeV2

2

2L

223

224

2em

2

eP2

y)(11Y

)]Q(x,Fy)Q(x,xFY )Q(x,F[Y xQ

�� 2dxdQ

�d

−±=

−−⋅=

±

−−y – inelasticityQ2 = sxy

0

0.5

1

1.5

2

10-6

10-5

10-4

10-3

10-2

10-1

1

Infinite momentum frame

Proton looks like a cloud of non-interacting quarks and gluons

p

e

e

γ*

F2 measures par ton density in the proton at a scale Q2



0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

10-6

10-5

10-4

10-3

10-2

10-1

1x

2

0.65

0.1

1.3

2.7

12

4.5

150

Q = 35

F2H1 9697

H1 SVTX95

H1 ISR (prel.)

ZEUS BPT97

ZEUS SVTX95

ZEUS 96/97

BCDMS

E665

SLAC

NMC

H1 QCD

ZEUS Regge97

CSST (GVD/CDP)

LO Gluon splittingfunction at low x

H1

Col

labo

ratio

n

Gluon density

Gluon density dominates F2 for x < 0.01

3

2

2

)( 2

=

≈

A

Asgg

Cz

CQP

πα

Non-Abelian structure of QCD

),(),(ln

),( 221

2

2

Qz

xgQzP

z

dz

Qd

Qxdg

x

gg�=

Dominant par t of evolution eq.



Asymptotic Freedom Nobel Pr ize forPhysics 2004D. GrossD. PolitzerF. Wilczek

Exper imental Discovery of the GluonDESY 1979

TASSO Exper iment

European Physical Society Pr ize 1995P. Soeding, B. Wiik, G. Wolf, S.L. Wu



Diffractive Scatter ing

Non-Diffractive Event ZEUS detector

Diffractive Event

MX - invar iant mass of all par ticles seen in the central detectort - momentum transfer to the diffractively scattered proton

t - conjugate var iable to the impact parameter

p γ*

Y

Detector

ln W2

p γ*

Y

Detector

ln MX2

Non-Diffraction Diffraction

- Rapidity

uniform, uncor related par ticle emission along therapidity axis => probability to see a gap ∆∆∆∆Y is ~ exp(-∆∆∆∆Y) - average multiplicity per unit of rapidity

Diffractive Signature*

1

10

10 2

10 3

0 5 10

Even

ts

W = 55 GeV

1

10

102

103

0 5 10

W = 100 GeV

1

10

102

103

0 5 10ln(MX

2)

W = 221 GeV

Q2 =

14.

0 G

eV2

dN/ dM 2X ~ 1/ M 2X =>

dN/dlog M 2X ~ constnote : ∆∆∆∆Y ~ log(W2 / M 2X)

Non-diff

diff



fm 10001011

qq −≈≈∆≈

xmE pτ

Slow Proton Frame

p

γ γ

z, t

q qk1

k2

kn-1

kn Transverse size of the quark-antiquark cloud

is determined by r ~ 1/Q ~ 2 10-14cm/ Q (GeV)

Diffraction is similar to the elastic scatter ing:replace the outgoing photon by the diffractive final state

ρρρρ , J/ΨΨΨΨ or X = two quarks

incoming vir tual photon fluctuates into a quark-antiquark pair which in turn emits a cascade-like cloud of gluons

0)t,(WImAW

1� 2el2

� ptot == )Q(x, F Q

� �4 )Q(W,� 22 2

em 2

2P�

tot

*

⋅=

Rise of σσσσγγγγptot with W is a measure of radiation intensity

Dipole description of DIS

),,(),(),,(ˆ 22*21

0

2* rzQrxrzQdzrd qqp

tot

�� ΨΨ= �� σσγ

γ* γ*

z

1-z

r

p p

2222*1

0

20 |),,(),(),,(|16

1|

*

rzQrxrzQdzrddt

dqqVMt

pVM �� ΨΨ= ��= σπ

σ γ

)section cross (dipolproton on pair qq

of scatteringfor section cross ),(

function waveQCD qq ),(2rx

rz

qqσγ →Ψ �

),,(),(),,(16

1| 2222*

1

0

20

*

rzQrxrzQdzrddt

dqqt

pdiff �� ΨΨ= ��= σπ

σ γ



22220

22222

22

20

221

22222

22

22,

1

00

22,

)1( )}()1(4{2

3),,(

)}()(])1({ [2

3),,(

),(),,(),(*

qqemf

L

qqemf

T

qqf

fLT

PLT

mQzzrKzzQeQzr

rKmrKzzeQzr

rxQzrdzrdQx

+−=−=Ψ

+−+=Ψ

Ψ= ��∞

εεπα

εεεπα

σσ γ

�

�

��

Q2~1/r2

1for /1)(1 −= rrxrK εεπε

exp(-mq r)

)]4

exp(1[ ),(20

2

0 R

rrxqq −−= σσ

GBW ModelK. Golec-Biernat, M . Wuesthoff

λ

��

��

�=

02

20

1)(

x

x

GeVxR

Parameters fitted to DIS F2 data:σσσσ0 = 23 mb λ λ λ λ = 0.29 x0 = 0.0003

Scaling in

20

2 / Rr

Geometr ical ScalingA. Stasto & Golec-BiernatJ. Kwiecinski



ZEUS 1997 (Preliminary) ZEUS 1997 (Preliminary)

Parameters fitted to HERA DIS data: χ2 /N ~ 1 σ0 = 23 mb λ = 0.29 x0 = 0.0003

σdif

f /σto

t

ZEUS 1994Q2 = 8 GeV2

Q2 = 14 GeV2Q2 = 27 GeV2

Q2 = 60 GeV2

MX < 3 GeV

3 < MX < 7.5 GeV

W(GeV)

7.5 < MX < 15 GeV

0

0.02

0.04

0.06

40 60 80 100 120 140 160 180 200 220

0

0.02

0.04

0.06

40 60 80 100 120 140 160 180 200 220

0

0.02

0.04

0.06

40 60 80 100 120 140 160 180 200 220

Saturation Model Predictions for Diffraction



)(202 xRQ=τ

Geometr ical ScalingA. Stasto & Golec-BiernatJ. Kwiecinski

λ

��

��

�=

02

20

1)(

x

x

GeVxR

GBW model, in spite of its compelling success has some obvious shor tcomings:

The treatment of QCD evolution is only rudimentaryremedy => incorporate DGLAP into dipole cross-section

J. Bar tels, K. Golec-Biernat, H. Kowalski

The dipole cross section is integrated over the transverse coordinatealthough the gluon density is expected to be a strongly varying functionof the impact parameter .

)))/,(3

exp(1(),(

1 ));exp(1(),(

20

222

0

2

0

02

202

0

2

0

µµασπσσ

σσλ

+=−−≈

��

��

�=−−≈

rCxxgrrx

x

x

GeVR

R

rrx

sqq

qq

GBW

Recently: BFKL motivated Ansatz proposed byIancu, I tacura, Munier



γ* γ*

z

1-z

r

p p

Proton

b – impact parameter

Impact Parameter Dipole Saturation Model

T(b) - proton shape 1)( 2

0

=�∞

bdbT

well motivated:

GlauberMueller LevinCapellaKaidalov

��

��

⋅−−⋅= ))(),()(

32exp(12

),( 2222

2bTxxgr

bd

rxds

qq µµαπσ

H. Kowalski D. Teaneyhep-ph/0304189

b (GeV-1)

T(b

)

TGY(b)TG(b)

0

0.01

0.02

0.03

0.04

0.05

0 2 4 6 8 10

d)-(2 parameter impact - d)-(2 momentum transv.- 2 bt��

∆∆−=

t-dependence of the diffractive cross sectionsdetermines the b distribution

22222

2*1

0

22 |),,())(),(32

exp(1),,(|16

1*

rzQbTxxgrrzQdzebdrddt

dsVM

bip

VM ��

Ψ

��

��

⋅−−Ψ= ��

∆− µαππ

σ γ

)2/exp(~)(

)exp(~

2 BbbT

tBdt

d diff

�−

⋅σ

)/()2/)(exp()(

GeV 25.4 )2/exp()(

022

-22

EGGY

GGG

wbKwbbbdbT

wwbbT

′′−−′∝

=−∝

��

�



Q2 > 0.25 GeV2

mu = 0.05 GeVmc = 1.30 GeV

Fit parametersλλλλg = -0.12 C= 4.0 Q02 = 0.8 GeV2

χχχχ2/N = 0.8

x < 10-2

6.520

202

2

)1(1

),( xx

Axxg

r

C

g

g −��

��

�=

+=

λ

µ

µµ

),,())(),(32

exp(1),,( 2222

2*1

0

22* rzQbTxxgrrzQdzbdrd ff

sfp �� Ψ

��

��

⋅−−Ψ=� �� µα

πσ γ

)]4

exp(1[ ),(20

2

0 R

rrxqq −−= σσ

GBW Model

��

��

+⋅

−−⋅= ))()/,(32

exp(12 ),( 2

022

2

2 bTQrCxxgrbd

rxds

qq απσ

IP Saturation Model



xλ e

ff

r=0.5 GeV-1

r=1 GeV-1

r=2 GeV-1

r=3 GeV-1

r=5 GeV-1

IP Sat

IP Non-Sat

0

0.2

0.4

0.6

0.8

1

10-5

10-4

10-3

10-2

))((22

)/1(~),( reffxxxg µλµ

Smaller dipoles �� steeper r iseLarge spread of λλλλeff character istic forImpact Parameter Dipole Models

)()(2 22* )/1(~)(~ QQp tottot xW λλγσ

----- universal rate of r ise of allhadronic cross-sections

Saturation region-------------------------------------------------------------------------------------------------------

��

��

⋅−−⋅= ))(),(

32exp(12

),( 222

2bTxxgr

bd

rxds

qq µαπσ



All quarks Charmed quark

GeV 3.1 MeV 100

),(),,(2

,,

22,

1

0

==

Ψ��

csdu

qqf

fLT

mm

rxQzrdzr σπ �

GeV 3.1

),,(),(2 22,1

0

=

Ψ�

c

cLTqq

m

Qzrrxdzr�σπ

F2

c

IP Sat-Mod, mc= 1.3 GeV ZEUS

x

x

0

0.2

0.4

10 -4 10 -3 10 -2

0

0.2

0.4

10 -4 10 -3 10 -2

0

0.2

0.4

10 -4 10 -3 10 -2

0

0.2

0.4

10 -4 10 -3 10 -2

0

0.2

0.4

10 -4 10 -3 10 -2

0

0.2

0.4

10-4

10-3

10-2

0

0.2

0.4

10-4

10-3

10-2

0

0.2

0.4

10-4

10-3

10-2

Gluon density Charm structure function



Absolute values of cross sections are strongly dependent on mc



Absorptive correction to F2

....4/))2/exp(1(2 22

+Ω−Ω=Ω−−=bd

dσ

Example in Dipole Model

γ* γ*

p p

γ* γ*

p p

F2 ~ -

Single inclusivepure DGLAP

Diffraction

Fit to diffractive data using MRST Structure Functions A. Martin M. Ryskin G. Watt



A. Martin M. Ryskin G. Watt

AGK Rules

)(

)!(!

!2)1( mm

km

kmk Fkmk

m

−−=�

∞

=

−σ

The cross-section for k-cut pomerons:Abramovski, Gr ibov, KancheliSov. ,J., Nucl. Phys. 18, p308 (1974)

γ* γ*

p p

γ* γ*

p p

γ* γ*

p p

1-cut

1-cut

2-cut

QCD Pomeron

F (m) – amplitude for the exchange ofm Pomerons



γ* γ*

p p

γ* γ*

p p

γ* γ*

p p

2-Pomeron exchange in QCD Final States(naïve picture)

0-cut

1-cut

2-cut

pγγγγ*p-CMS

γγγγ∗∗∗∗∆∆∆∆Y

detector

pγγγγ*p-CMS

γγγγ∗∗∗∗

pγγγγ*p-CMS

γγγγ∗∗∗∗

detector

Diffraction

0-cut

1-cut

2-cut

3-cut

Feynman diagrams QCD amplitudes J. Bar telsA. Sabio-VeraH. K.



x

F2

10-3

10-2

10-1

1

10-5

10-4

10-3

10-2

),,()exp(!

),,(

),,()2

exp(12),,(

22*1

0

22

22*1

0

22

*

*

rzQk

rzQdzbdrd

rzQrzQdzbdrd

ff

k

fp

k

ff

fp

��

��

ΨΩ−ΩΨ=

Ψ

��

�� Ω−−Ψ=

� ��

� ��

γ

γ

σ

σ

Probability of k-cut in HERA data

DipoleModel

Problem of DGLAP QCD fits to F2

CTEQ, MRST, …., IP-Dipole Model

0 ,~),( 20 >λµλxxxg at small x

valence like gluon structure function ?

Remedy: Absorptive corrections? MRW

Different evolution? BFKL, CCSS, ABFT



),(),(ln

),( 221

2

2

µµµµ

z

xgzP

z

dz

d

xdg

x

gg�=

πα Cs N

gg xxP

2ln41

~ ��

��

�BFKL ------

from Gavin Salam - Par is2004

As

gg CxP 22

)(~

2

πµαLO DGLAP ---

at low x

Next to leading logs NLLx -----

from Gavin Salam - Par is 2004

Ciafalloni, Colferai, Salam, Stasto

Similar resultsby

Altarelli, BallFor te, Thorn



x

S2

0

0.2

0.4

0.6

0.8

1

1.2

10-6

10-5

10-4

10-3

)())(,())((3

2 222

bTrxxgrD s µµαπ=Density profile

��

�

�

��

�

�⋅−=

2exp

22 rDS

grows with diminishing x and r

approaches a constant value Saturated State - Color Glass Condensate

multiple scatter ing

S – Matr ix => interaction probabilitySaturated state = high interaction probability

S2 => 0

rS - dipole size for which proton consistsof one int. length

12 −= eS

IP SatIP Non-SatGBW

1/x

QS

2 (G

eV2 )

10-1

1

102

103

104

105

106

Saturation scale = Density profile at the saturation radius rS 22 2

SS r

Q =− 2SQ

λλλλS = 0.15

λλλλS = 0.25



Saturated stateis par tially per turbative

cross-sectiomexhibits the universal rate of growth

1/x

QS

2 (G

eV2 )

1

10

102

103

104

105

106

qSqSF

CgS QQC

NQ )(

4

9)()( 222 ==

1

fm 7 1000

1

1

4

2

22

22

≈

≈≈

−=

S

C

CsS

Q

Rdy

dN

dy

dN

RN

NQ

παπ

RHIC

HERASRHICS QQ )()(22 ≅



Conclusions

We are developing a very good understanding of inclusive and diffractive γγγγ*p interactions:

F2 , F2D(3) , F2c , Vector Mesons (J/Psi)….

Observation of diffraction indicates multi-gluon interaction effectsat HERA

Open problems: valence-like gluon density?absorptive cor rectionslow-x QCD-evolution

HERA measurements suggests presence of Saturation phenomenaSaturation scale determined at HERA agrees with the RHIC one

HERA+NMC data => Saturation effects are considerably increased in nuclei

Small-x, diffraction and QCD results from HERA Small-x...

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