Inclusive diffractive DIS

$Page 1: Inclusive diffractive DIS$
Marta Ruspa, "Inclusive diffraction", DIS 2004 1

Inclusive diffractive DIS

Diffractive cross section and diffractive structure function

Comparison with colour dipole models

NLO QCD fit

Marta Ruspa Univ. of Eastern Piedmont-Novara and INFN-Torino (Italy)

XII International Workshop on Deep Inelastic Scattering

Strbske Pleso, High Tatras, Slovakia April 14-18, 2004

on behalf of


IP

Q2

W MX

e’

p’

*e

p

Q2 = virtuality of photon = = (4-momentum exchanged at e vertex)2

t = (4-momentum exchanged at p vertex)2

typically: |t|<1 GeV2

W = invariant mass of photon-proton system

MX = invariant mass of photon-Pomeron system

xIP = fraction of proton’s momentum taken by Pomeron

ß = Bjorken’s variable for the Pomeron = fraction of Pomeron’s momentum carried by struck quark = x/xIP

xIP

t

Inclusive diffraction γ*p Xp

Exchange of an object with the vacuum q. n.

Proton almost intact after the collision


(Breit frame)

Diffractive DIS in the Breit frame

Diffractive Deep Inelastic Scattering probes the diffractive PDFs of the proton relevant when the vacuum quantum numbers are exchanged

)ˆ 2iγIP

2pi

* Q(z,σt),x,Q(z,f~Xp)pσ(γ *

fi/pD(z,Q2,xIP,t): probability to find in a proton, with a probe of

resolution Q2, parton i with momentum fraction z, under the condition that the proton remains intact and emerges with small energy loss, xIP, and momentum transfer,t

HARD SCATTERING FACTORISATION

DIS of a pointlike virtual photon off the exchanged object

PDFs


Diffractive DIS in the colour dipole picture

We can learn more about the structure of the proton by studying DDIS in a frame in which the virtual photon is faster than the proton

(γ* much faster than p)

• Lifetime of dipoles very long due to large γ boost (E γ ~ W2 ~ 1/x 50TeV ! ) it is the dipole that interacts with the proton !

• Transverse size of dipoles proportional to can be so small

that the strong interaction with proton can be treated perturbatively !

)M(Q1/_qq

22

2 gluon exchange: LO QCD realisation of vacuum q.n.


Diffractive DIS in the colour dipole picture

BEKW model : at medium β; at small β

saturation model : : as Q2 0,

growth tamed by requiring saturation

22

qq1/Qrσ _ _

qqσ

β)β(1~FTqq

γT

gqqβ)(1~F _





e pExchange ofcolor singletproducing a

GAPin the

particle flow


No activity in the forward direction

Proton suffers only a small energy loss

MX method


Diffr. Non-diffr.

c, b from fit n.d. events subtracted

contamination from reaction epeXN

Selection of events γ*p Xp with Mx method

Properties of Mx

distribution:

- exponentially falling for decreasing Mx for non-diffractive events

- flat vs ln Mx2 for

diffractive events

Forward Plug Calorimeter (FPC):

CAL acceptance extended by 1 unit in pseudorapidity from η=4 to η=5

higher Mx and lower W

if MN > 2.3 GeV deposits EFPC > 1 GeV recognized and rejected!

Diffr. Non-diffr.


e pExchange ofcolor singletproducing a

GAPin the

particle flow



Proton suffers only a small energy loss

LPS method

MX method


Free of p-diss background

Low acceptance

low statistics

z

zIP p

p'x1

Selection of events γ*p Xp with LPS

Diffractive peak

IPx1


97 LPS sample

0.03 < Q2 < 100 GeV2

25 < W < 280 GeV

1.5 < Mx < 70 GeV

xIP < 0.1

Higher xIP region

99-00 FPC sample(Mx method)

22 < Q2 < 80 GeV2

37 < W < 245 GeV

Mx < 35 GeV

MN < 2.3 GeV

Higher β region

Data samples


diffractive γ*p cross section

dWdMdQ

σd

)y)(α(

WπQ

dM

dσ

X

De'Xp'ep

X

Dpγ*

2

3

2

2

11

diffractive structure function

(assumes ) 0)3( DLF

IP

XpeepD

IPD

dxdQd

d

yy

QxQF

2

''

22

42)3(

2)2/1(4

),,(

Cross section and structure function


xIP dep. of F2

D(3) equivalent to W dep. of dσ/dMx (1/xIP ~ W2)

F2D(3) xIP

dependence

Data agree with Regge factorisation assumption in the region of the fit

)(02.0)(02.016.1)0( sysstatIP

(LPS)

Regge fit (xIP<0.01):

),()( 22

)3(2 QFxfF IP

IPIPD

dtx

exf

tIP

t

IP

tb

IPIP

1)(2)( with

tt IPIPIP ')0()(


p-dissociation events with MN<2.3 GeV included

MX< 2 GeV: weak W dep.

MX> 2 GeV: d/dMX rises with W

Cross section W dependence (Mx method)

power-like fit


fit to total cross section data:

fit to diffractive cross section data:

Evidence of a rise of IPdiff with

Q2 mild Regge factorisation violation .

αIP from diffractive and total γ*p scattering

IPdiff higher than soft Pomeron

Similar W dep. of diffractive and total cross section

(Mx method)

(0)αtotIP

(0)αdiffIP


low MX : strong decrease of

diff/tot with increasing Q2

high MX : no Q2 dependence !

Regge expectation:

19.01)0(2

222

*

*

)(

)(/W

W

WdMdIP

IP

totp

XD

p

σdiff/ σtot W and Q2 dependence(Mx method)

[hep-ph 0203258]

Explained by saturation model

BUT ratio ~ flat in W


Main features of the data described by BEKW parametrization (xIP<0.01)

Cross section Q2 dependence

Transition to a constant cross section as Q20(similar to total cross section )

qqg fluctuations dominant at low Q2

(Bartels, Ellis, Kowalski and Wüsthoff)

medium β

small β

)1(~ Tqq

F

)1(~ Tqgq

F

tot

p*

(LPS)


F2D(3) Q2 dependence(LPS)

Data well described by BGK saturation model (xIP<0.01)

Positive scaling violation at all values of β QCD fit

(prel.)


QCD fit describes data

fractional gluon momentum

is

at initial scale

NLO QCD fit on LPS+charm data

))%(9)(882( sysstat

)36/9.37/( 2 ndf

[F2D(3)cc from DESY-03-094, see N. Vlasov

talk]

• xIP <0.01

• QCDNUM

• Regge factorisation assumption possible for this small data set

• DL flux

• initial scale Q2=2 GeV2

• zf(z)=(a1+a2z+a3z2)(1-x)a4

• other PDFs parametrisation tried

• Thorne-Robert variable-flavour- number-scheme

(LPS)


LPS QCD fit compared to Mx data

Main discrepancies at high β, where no LPS data available

NB: fits scaled by 0.69to account for p-dissbackground in Mx data

Mx method data described by the fit in the region of overlap LPS-Mx method

ZEUS (MX method)


xIP.F2D(3)/F2

Q2 and xBJ dependences(LPS) (LPS)

Compare the proton structure function for events with a leading proton and without

Nearly the same Q2 dep. (except high β and low xIP)

Different behaviour vs x at low xIP


Recent data from ZEUS with improved precision and extended kinematic range

Data described by colour dipole models (BEKW, saturation)

Data described by a NLO QCD fit lots of gluons

Possible indication that αIP increases with Q2 in diffraction

W dep. of diffractive and total cross section similar at high Q2

Summary


RESERVE


Diffractive DIS in the proton rest frame



• Lifetime of dipoles very long due to large γ boost (E γ ~ W2 ~ 1/x 50TeV ! ) it is the dipole that interacts with the proton !

• Transverse size of dipoles proportional to can be so small

that the strong interaction with proton can be treated perturbatively !

)M(Q1/_qq

22


saturation model : (colour transparency)

as Q2 0, growth tamed by saturating

22

qq1/Qrσ _

_qq

σ _qq

σ

β)β(1~FTqq

γT

gqqβ)(1~F _ BEKW model : at medium β; at small β


IP

Q2

W MX

e’

p’

*e

p





MX = invariant mass of photon-Pomeron system

xIP = fraction of proton’s momentum taken by Pomeron

ß = Bjorken’s variable for the Pomeron = fraction of Pomeron’s momentum carried by struck quark = x/xIP

xIP

t


Exchange of an object with the vacuum q. n.



(Breit frame)

Diffractive DIS in the Breit frame

Diffractive Deep Inelastic Scattering probes the diffractive PDFs of the proton relevant when the vacuum quantum numbers are exchanged

)ˆ 2iγIP

2pi

* Q(z,σt),x,Q(z,f~Xp)pσ(γ *

fi/pD(z,Q2,xIP,t): probability to find in a proton, with a probe of resolution

Q2 parton i with momentum fraction z, under the condition that proton remains intact and emerges with small energy loss, xIP, and momentum transfer, t diffractive PDFs are a feature of the proton

HARD SCATTERING FACTORISATION


e p

Exchange ofcolor singletproducing a

GAPin the

particle flow



dWdMdQ

d

y

WQ

dM

d

X

DXpeep

X

D

p

2

''3

2

2

))1(1(

*


(assumes ) 0)3( DLF

IP

XpeepD

IPD

dxdQd

d

yy

QtxQF

2

''

22

42)3(

2 )2/1(4),,,(





dWdMdQ

σd

)y)(α(

WπQ

dM

dσ

X

De'Xp'ep

X

Dpγ*

2

3

2

2

11


(assumes ) 0)3( DLF

IP

XpeepD

IPD

dxdQd

d

yy

QxQF

2

''

22

42)3(

2)2/1(4

),,(

Cross section and structure function

xIP dependence of F2D(3)

and

W dependence of dσ/dMX

- extraction of αIP

- Regge factorisation

Q2 dependence of F2D(3)

and dσ/dMX

-sensitivity to diffractive

PDFs

comparison to BEKW model

and to saturation model


F2D(3) β dependence

Different β dep. at

low and high xIP

Data well described by

BGK saturation model (xIP<0.01)

(LPS)


For high β F2D(2) decrease with

rising Q2

F2D(3) at fixed xIP

As β 0 F2D(2) rises. The rise

becomes stronger as Q2 increases

Maximum near β=0.5 consistent with a β(1- β) behaviour suggesting main contribution from a quark-antiquark state

(Mx method)

Evidence for pQCD evolution


MICHELE


• pQCD: qq r 1/Q2

(colour transparency)

• As Q2 0, qq violation of unitarity

• Growth tamed by qq saturating at qq (p)

Part III: saturation (how dense is the proton at low x ???)

• Saturation occurs at “saturation scale” Qs

2(x) xg(x)] xx) with x010-4, 0.3 (proton denser at small x)

qq

r

Saturation

npQCD

pQC

D

*r

cf talks by S. Munier, D. Kharzeev, C. Marquet

• Connection to high-density QCD, saturation of parton densities, Colour Glass Condensate, geometric scaling, physics of RHIC

~1/Qs

large x small x


Saturation vs data

Q2

x IPF

2D

( 3)

F2

Inclusive diffraction:

Inclusive DIS:

Golec-Biernat,Wuesthoff,Bartels, Golec-Biernat, Kowalski

Diffraction more sensitive to saturationthan inclusive: mainly probe intermediate dipole sizes, close to saturation

Also good description of VM, DVCS...


Standard Deep Inelastic ScatteringFor Q2<< MZ

2:

),()],(1[2

14 2

22

2

4

2

2

2

QxFQxR

yy

xQdxdQ

d

In a frame in which the proton is very fast(Breit frame):

x = Bjorken’s variable= = fraction of proton’s momentum carried by struck quark Q2/W2

W = photon-proton centre of mass energy

y = W2/s

F2=i[ei2 x fi(x,Q2)]

R=LT

DIS probes the partonic structure of the proton

Q2

W

proton PDF


Diffractive Deep Inelastic Scattering

xIP = fraction of proton’s momentum

taken by Pomeron

= inFermilab jargon

= Bjorken’s variable for the Pomeron = fraction of Pomeron’s momentum carried by struck quark = x/xIP

Flux of Pomerons

),,,()1(2

14 2)4(

2)4(

2

4

2

2

4

txQFR

yy

QdtdxdQd

dIP

DD

IP

“Pomeron structure function”

Naively, if IP were particle:

[Ingelman, Schlein]

xIP IP

Q2

t

*

e

e’

p p’

F2D(4) fIP (xIP,t) F2

IP (,Q2)


IP

Q2

W MX

e’

p’

*e

p





MX= invariant mass of photon-Pomeron system

xIP = fraction of proton’s momentum taken by Pomeron = in Fermilab jargon = Bjorken’s variable for the Pomeron = fraction of Pomeron’s momentum carried by struck quark = x/xIP

xIP

Previous talk: Diffractive Deep Inelastic Scatteringprobes the diffractive PDFs of the proton, relevant when the vacuum quantum numbers are exchanged

Diffractive DIS

t

N.B. will drop e, e’ from the diagrams in the rest of the talk


(Diffractive) hard scattering factorisation

universal partonic cross section

fi/pD(z,Q2,xIP,t): probability to find, with probe of resolution Q2, in a

proton, parton i with momentum fraction z, under the condition that proton remains intact, and emerges with small energy loss, xIP, and momentum transfer t – diffractive PDFs are a feature of the proton

A new type of PDFs, with same dignity as standard PDFs. Applies

when vacuum quantum numbers are exchanged

Diffractive DIS, like inclusive DIS, is factorisable [Collins (1998);

Trentadue, Veneziano (1994); Berera, Soper (1996)…]:

diffractive parton distribution functions: evolve according to DGLAP

Rather than IP exchange: probe diffractive PDFs of proton


Diffractive DIS in the proton rest frame

2-gluon exchange:LO realisation of vacuum quantum numbers in QCD

Cross section proportional to probability of finding 2 gluonsin the proton

Gluon density in the proton

!2g][x

X

pp

X

p

+p

X

p

*

IP


Part I:The colour dipole approach

•The picture discussed in the previous talk emerges in a frame in which the proton is fast (the Breit frame)

•Can learn more about the structure of the proton by studying diffraction in a frame in which the virtual photon is faster than the proton. Find out that in exclusive processesdiffr [gluon density in proton]2

Example: exclusive vector meson production Calculable in QCD !

•Correlations in the proton: Generalised Parton Distributions (GPDs)


•Lifetime of dipoles very long because of large boost (E 50TeV!)

it is the dipole that interacts with the proton

•Transverse size proportional to 1/ (Q2+ Mqq2)

(for longitudinally polarised photons)

•This is why can do diffraction in ep collisions !

Virtual photon fluctuates to qq, qqg states (colour dipoles)

Transverse size of incoming hadron beam can be reduced at will. Can be so small that strong interaction with proton becomes perturbative (colour transparency) !

The colour dipole picture

*

qqg

22

1

qqMQ

xWE 1~~ 2

qq

*


Factorization

Regge factorization - “resolved IP model” (IP with partonic structure):

1)(2/ ),( tIP

Bt

IPpIP xe

txf

(Breit frame)

QCD Hard Scattering factorization (by Collins; Trentadue, Veneziano; Berera, Soper…:)

),(ˆ),,,()( 22** QxQxtxpXpp

pIPpq

),(ˆ),(),()( 22** QQptxfXpp

ppqIPpIP

Regge motivated pomeron flux

At fixed xIP and t diffractive Parton Densities evolve according to DGLAP

Shape of diffractive pdfs independent of xIP and t

Documents

Inclusive diffractive DIS