Exclusive vs. Diffractive VM production in nuclear DIS

Cyrille Marquet

Institut de Physique Théorique

CEA/Saclay

based onF. Dominguez, C.M. and B. Wu, Nucl. Phys. A823 (2009) 99, arXiv:0812.3878

+ work in progress

Outline

• Saturation, the CGC and the dipole picturethe CGC picture of the nuclear wave function at small xhigh-energy dipole scattering off the CGC and geometric scaling

• Lessons from HERA diffractive datathe success of the dipole picturegeometric scaling and other hints of parton saturation

• The process eA → eVYVM production off the CGC and dealing with the nuclear break-upexplicit calculation in the MV modelresults and work in progress

Parton saturation, the CGCand the dipole picture in DIS

The saturation momentum

gluon kinematics

recombination cross-section

gluon density per unit areait grows with decreasing x

recombinations important when

for a given value of , the saturation regime in a nuclear wave functionextends to a higher value of x compared to a hadronic wave function

McLerran and Venugopalan (1994)

• the CGC: an effective theory to describe the saturation regime

lifetime of the fluctuations

in the wave function ~

high-x partons ≡ static sources

low-x partons ≡ dynamical fields

the idea in the CGC is to take into account saturation via strong classical fields

• gluon recombination in the hadronic wave function

the saturation regime: for with

The Color Glass Condensate

gggggqqqqqqgqqq .........hadron CGC][hadron xD

small x gluons as radiation field

),(,

z zFD cc

valence partonsas static random

color source separation between

the long-lived high-x partons

and the short-lived low-x gluons

CGC wave function

classical Yang-Mills equations

• the CGC wave function

the solution gives 3.03/12 ~),(Q xAAxs

the evolution of with x is a renormalization-group equation2

][x

Jalilian-Marian, Iancu, McLerran,Weigert, Leonidov, Kovner (1997-2002)

from , one can obtainthe unintegrated gluon distribution,

as well as any n-parton distributions

2][x

• the small-x evolution

in the A+=0 gauge

Scattering off the CGC

scattering of a quark:

• this is described by Wilson lines

dependence kept implicit in the following

in the CGC framework, any cross-section is determined by colorless combinations ofWilson lines , averaged over the CGC wave function ][][

2 SDS xx ][S

))()((1 1 ),( xyyx FFc

qq WWTrN

T

x : quark transverse coordinatey : antiquark transverse coordinate

the dipole scattering amplitude:qq

this is the most common Wilson-line average

• the 2-point function or dipole amplitude

or

The dipole factorization

dipole-hadron cross-section

• inclusive DIS

at small x, the dipole cross section is comparable

to that of a pion, even though r ~ 1/Q << 1/QCD

overlap ofsplitting functions

• exclusive diffraction

)M,,()Q,,()M,Q,( 2V

22V

2 zzdz V rrr

the overlap function:

instead of

)Q,,( 2zr)M,,( 2

VzrV

access to impact parameter

2.22

V22

*

),( )M,Q,( 41

xqq

iVpp

Tebdrddt

dbrr bq

r

the dipole is probing small distancesinside the hadron/nucleus: r ~ 1/Q

what does the proton look like in (Q², x) plane:

Geometric scalinggeometric scaling can be easily understood as a consequence of large parton densities

lines parallel to the saturation lineare lines of constant densities

along which scattering is constant

T = 1

T << 1

Hard diffraction and saturation

dipole size r

the dipole scattering amplitude• the total cross sections

in inclusive DIS

in diffractive DIS

contribution of the different rregions in the hard regime

DIS dominated by relatively hard sizes

DDIS dominated by semi-hard sizes Sr Q1~Sr Q1Q1

22 QQ S

1 )/Qln(Q 1 Q 2S

22 DIS

1 1 Q

1 Q

22 DDIS

• diffraction directly sensitive to saturation

Things we learned with HERA

Inclusive diffraction in DIS

k

k’

p

k

k’

p

p’

when the hadronremains intact rapidity gap

some events

are diffractive

22

22

Q

Q

)').('(2

Q

tMkkpp X

momentum fraction of the exchanged object(Pomeron) with respect to the hadron

diffractive mass

MX2 = (p-p’+k-k’)2

• the measured cross-section

momentum transfert = (p-p’)2 < 0

Inclusive Diffraction (DDIS)

(~450 points)

parameter-free predictionswith IIM model

at fixed , the scaling variable is

C.M. and Schoeffel (2006)C.M. (2007)

Important features of DDIS

tot = F2D

contributions of the different final statesto the diffractive structure function:

at small : quark-antiquark-gluon

at intermediate : quark-antiquark (T)

at large : quark-antiquark (L)

• the β dependence

saturation naturally explains theconstant ratio

• the ratio F2D,p / F2

p

Munier, Stasto and Mueller (2001)

HERA is entering the saturation regime

the scattering probability (S=1-T )is extracted from the data

S(1/r 1Gev, b 0, x 5.10-4) 0.6

Exclusive processes: ep → eVp

rho J/Psi

• success of the dipole models

t-CGC

b-CGC appears to work wellalso but no given

DVCS predictions checked by H1

C.M., Peschanski and Soyez (2007)

Kowalski, Motyka and Watt (2006)

• for the total VM cross-section

Geometric scaling

C.M. and Schoeffel (2006)

• scaling at non zero transfer

C.M., Peschanski and Soyez (2005)predicted

checked H1 collaboration (2008)

Diffractive Vector Mesonproduction in nuclear DIS

eA → eVY

Dealing with the target break-up

• from a proton target to a nucleus

in e+p collisions at HERA, both exclusive and diffractive processes can be measuredalready at rather low |t| (~0.5 GeV2), the diffractive process is considered a background

in e+A collisions at a future EIC, at accessible values of |t|, the nucleus is broken upit is crucial to understand and quantify the transition from exclusive to diffractive scattering

this can be calculated in the CGC framework work in progress

• exclusive vs. diffractive process

the target is intact (low |t|)

)M,,()Q,,()M,Q,( 2V

22V

2 zrzrdzr V upper part described with the overlap function:

exclusive process diffractive processthe target has broken-up (high |t|)

interaction at small :

)M,,( 2VzrV

)Q,,( 2zr

description of both within the same framework ? possible at low-xDominguez, C.M. and Wu, (2009)

22

22

Q

Q

W

Mx V

VM production off the CGC• the diffractive cross section

overlap functions

amplitude

xqqqqiq

VYp

TTebdbdrdrddt

d)','(),(')M,Q,'()M,Q,('

4

1 )'.(222V

2*2V

222*

brbrrr bb

target average at the cross-section level:

contains both broken-up and intact events

conjugate amplitude

r : dipole size in the amplituder’ : dipole size in the conjugate amplitude

one needs to compute a 4-point function, possible in the MV model for2

][x

• the exclusive part

xqqxqqxqqqq TTTT )','(),()','(),( brbrbrbr

2.22

V22

*

),( )M,Q,( 4

1xqq

iqVpp

Tebdrddt

dbrr b

obtained by averaging at the level of the amplitude:

one recovers

The MV model

µ2 characterizes the density of color charges along the projectile’s path

with this model for the CGC wavefunction squared, it is possible to compute n-point functions

• a Gaussian distribution of color sources

2][

is the two-dimensional massless propagator

)()( )()'(),'(),( 22 zyzxyx GGzdzzzzz cddc

• applying Wick’s theorem

when expanding in powers of α and averaging,

all the field correlators can be expressed in terms of

)','(),( brbr qqqq TT),'(),( yx zz dc

the difficulty is to deal with the color structure

Fujii, Gelis and Venugopalan (2006)

Analytical results

qqqq TS 1

• the 4-point function

(using transverse positions and not sizes here)

it can also be consistently included, andshould be obtained from (almost) the BK equation

but for now, we are just using models

• the x dependence)(rFx

Results and work in progress

The case of a target proton

• as a function of t

exclusive production:the proton undergoes elastic scatteringdominates at small |t|

diffractive production :the proton undergoes inelastic scatteringdominates at large |t|

exclusive→ exp. fall at -t < 0.7 GeV2

diffractive→ power-law tail at large |t|

• two distinct regimes

Dominguez, C.M. and Wu, (2009)

the transition point is where thedata on exclusive production stop

exclusive production is called coherent diffractionthe nucleus undergoes elastic scattering, dominates at small |t|

intermediate regime (absent with protons)the nucleus breaks up into its constituents nucleons, intermediate |t|

then there is fully incoherent diffractionthe nucleons undergo inelastic scattering, dominates at large |t|

From protons to nuclei• qualitatively, one expects three contributions

coherent diffraction→ steep exp. fall at small |t|breakup into nucleons→ slower exp. fall at 0.05 < -t < 0.7 GeV2

incoherent diffraction→ power-law tail at large |t|

• three regimes as a function of t:

next step: computation for vector mesons

Kowalski, Lappi and Venugopalan (2008)

Including small-x evolution• our calculation can be used as an initial condition

a stage-I EIC can already check this model, and constrain the Adependence of the saturation scale at values of x moderately small

with higher energies, the x evolution (which is the robust prediction) can be tested too

• actual CGC x evolution instead of modeled x evolution

this is what should be done now that running-coupling corrections have been calculated

see for instance the recent analysis of F2 with BK evolutionAlbacete, Armesto, Milhano and Salgado (2009)

the complication in our case is that the BK approximation of JIMWLK cannot be used:it has no target dissociation ( ) and is useful for the exclusive part only

one needs a better approximation of JIMWLK that keeps contributions to all order in Nc this can be done and running-coupling corrections can be implemented too

C.M. and Weigert, in progress

Conclusions• Diffractive vector meson production is an important part of the physics

program at an eA collider

it allows to understand coherent vs. incoherent diffraction

• The CGC provides a framework for QCD calculations in the small-x regime

explicit calculations possible in the MV model for the CGC wave function

consistent implementation of the small-x evolution is also possible

• VM production off the proton understood, preliminary results for the nucleus case

a stage-I EIC will constrain initial conditions at moderate values of x

with higher energies the small-x QCD evolution will be tested

coherent diffraction→ steep exp. fall at small |t|breakup into nucleons→ slower exp. fall at 0.05 < -t < 0.7 GeV2

incoherent diffraction→ power-law tail at large |t|