Hard exclusive processes -

Andrzej Sandacz

Sołtan Institute for Nuclear Studies, Warsaw

DVCS at fixed target experiments and HERA

Transverse target spin asymmetry for ρ0 production

Vector Meson production at HERA

EIC Collaboration Meeting, Stony Brook University, December 8, 2007

experimental results and simulations for EIC

DVCS at EIC

Exclusive π+ and π0 production

GGeneralizedeneralized P Partonarton D Distributionsistributions

GPDs

x+ x-

P1 P2

hard

soft

* Factorisation:Q2 large, -t<1 GeV2

t

4 Generalised Parton Distributions : H, E, H, Efor each quark flavour and for gluons

depending on 3 variables: x, x, , t, t~~

for DVCS gluons contribute only at higher orders in αs

GPDs properties, link to DIS and form factors

)()(2

1tJEHxdx qqq Ji’s sum rule

)0(qJ total angular momentum carried by quark flavour q(helicity and orbital part)

'~

, ssHH qq

'~

, ssEE qq

for P1 = P2 recover usual parton densities

0)()0,0,(~

),()0,0,( xforxqxHxqxH qq

no similar relations; these GPDs decouple for P1 = P2

0)()0,0,(~

),()0,0,( xforxqxHxqxH qq

0~

, qq EE needs orbital angular momentum between partons

)(),,( 1 tFtxHdx qq

)(),,( 2 tFtxEdx qq

)(),,(~

tgtxHdx qA

q

)(),,(~

tgtxEdx qP

q

Dirac axial

pseudoscalar Pauli

GPD= a 3-dimensional picture of the partonic nucleon structure or spatial parton distribution in the transverse plane H(x, =0, t) → H(x,, rx,y ) probability interpretation Burkardt

‘Holy Grails’ or the main goals

Contribution to the nucleon spin puzzle

E related to the angular momentum

2Jq = x (Hq (x,ξ,0) +Eq (x,ξ,0) ) dx

½ = ½ ΔΣ + ΔG + < Lzq > + < Lz

g >

t

p p

q q

x P

x

y

r

z

E

The imaginary part of amplitude T probes GPD at x =

1

1

1

1

( , , ) +

( , ,

- i + ( , )

, )

DVCS

GPD x t

GPD x tT dx

x

GPD x tdx

i

P x

The real part of amplitude T depends on the integral of GPD over x

Observables and their relationship to GPDs

DG

LAP

DGLAP

ERBL

T

UT ~ sin(s)cos∙Im{k(H - E) + … }

C ~ cos∙Re{ H + H +… }~

LU ~ sin∙Im{H + H + kE}~

UL ~ sin∙Im{H + H + …}~

polarization polarization observables:observables:

kinematically suppressedkinematically suppressed

H

H

H, E

~

different charges: edifferent charges: e++ e e-- (only (only @HERA!):@HERA!):

H

DVCS Asymmetries measured up to now

= xB/(2-xB ),k = t/4M2

* 2 2*~ | | | |BH DVCS DVC BS HB DVCSHd

CLAS: DVCS - BSA

Integrated over tIntegrated over t

<-t> = 0.18 GeV2 <-t> = 0.30 GeV2 <-t> = 0.49 GeV2 <-t> = 0.76 GeV2

Accurate data in a Accurate data in a large kinematical large kinematical domaindomain

Difference of polarized cross sectionsDifference of polarized cross sections

Unpolarized cross sectionsUnpolarized cross sections

Q2 = 2.3 GeV2 xB = 0.36

Results from JLAB Hall A E00-100

Twist-2Twist-3

PRL97, 262002 (2006)

extracted twist-3 contribution small

1 1 2 22()

2 4( )

B

I BCx t

F F Fx

F FM

2 ( , , ) ( , )I ,m q qq

q

e H t H t

No Q2 dependence: strong indication for scaling and handbag dominance

GPD !!!

dominant term at small |t|

s1int ~

Towards E and Ju, Jd

2 1Im( )F H F E

sin( )cos( ) ~sUTA

Hermes DVCS-TTSA:Hermes DVCS-TTSA:

Hall A nDVCS-BSA:Hall A nDVCS-BSA:

x=0.36 and Qx=0.36 and Q22=1.9GeV=1.9GeV22

Neutron obtained combining Neutron obtained combining deuterdeuteronon and proton and proton

FF11 small small and and u & d cancel in u & d cancel in H

1 1 2 22~ ( )4LU

tF H x F F H F E

MA

Present status of the MODEL-DEPENDENT Ju-Jd extraction

With VGG Code

Lattice hep-lat 07054295

Unpolarised DVCS cross sections from HERA σDVCS at small xB (< 0.01) mostly sensitive to

Hg, Hsea

Q² and W dependence: NLO predictions

bands reflect experimental error on slope b: 5.26 < b < 6.40 GeV-2

- Wide range of Q2 - sensitivity to QCD evolution of GPDs

- Difference between MRS/CTEQ due to different xG at low xB

- Meaurements of b significantly constrain uncertainty of models

t dependence of DVCS cross section

New H1 results on slopes - DIS07

DIS06

Lessons from DVCS at H1/ZEUS

Skewing parameter R=Im DIS / Im DVCS ~ 0.5

Good agreement with NLO predictions

GPDs ≡ PDFs at low scale; skewing generated by QCD evolution

Sensitivity to Hg ; 15% change of Hg => 10% change of cross section

Real part of DVCS amplitude – small effect, few%

Low sensitivity to b(Q2) vs. b(const.)

Interplay of Rs (sea) and Rg (gluons)

Color dipole phenomenology (no GPDs) also a satisfacory description

Hard exclusive meson production

necessary to extract longitudinal contribution to observables (σL , …)

allows separation and wrt quark flavours

ρ0 2u+d, 9g/4

ω 2u-d, 3g/4

φ s, g

ρ+ u-d

J/ψ g

Flavour sensitivity of DVMP on the proton

factorisation proven only for σL

4 Generalised Parton Distributions (GPDs)for each quark flavour and for gluons

GPDs depend on 3 variables: x, x, , t, t

conserve flip nucleon helicity

H E Vector mesons (ρ, ω, φ)

H E Pseudoscalar mesons (π, η)~~

σT suppressed of by 1/Q2

wave function of meson (DA Φ)

additional information/complication

quarks and gluons enter at the same order of αS

Dipole models for exclusive VM production at small x

at very small x huge NLO corrections, large ln(1/x) terms (BFKL type logs)

pQCD models to describe colour dipole-nucleon cross sections and meson WF

• Martin-Ryskin-Teubner (MRT) Phys.Rev. D62 (2000) 014022

• Farshaw-Sandapen-Shaw (FSS) Phys.Rev. D69 (2004) 094013

• Kowalski-Motyka-Watt (KMW) Phys.Rev. D74 (2006) 074016

• Dosch-Fereira (DF) hep-ph/0610311 (2006)

• Frankfurt-Koepf-Strikman (FKS) Phys.Rev. D57 (1998) 512

sensitivity to different gluon density distibutions

sensitivity to ρ0 wave function

at small x sensitivity mostly to gluons

dipole transv. size W-dep. t-dep.

large weak steep

small strong shallow

Recent ZEUS results on exclusive ρ0 production

W-dependence σ ∞ Wδ

steeper energy dependence with increasing Q2

96-00 data: 120 pb-1 2 < Q2 < 160 GeV2 32 < W < 180 GeV 2∙10-4 < xBj < 10-2

| t | < 1 GeV2

significant increase of precision + extended Q2 range

arXiv:0708.1478[hep-ex]

W-dependence for hard exclusive processes at small x

ϕϕ J/J/ψψ ϒϒ

steep energy dependence for all vector mesons in presence of hard scale

Q2 and/or M2

‘universality’ of energy dependence at small x?

at Q2+M2 ≈ 10 GeV2 still significant difference between ρ and J/ψ

dσ / dt - ρ0

ZEUS

example (1 out of 6)

||tbedt

d

Fit

shallower t-dependence with increasing Q2

t-dependence for hard exclusive processes at small x

b-slopes decrease with increasing scale

approximate ‘universality’ of slopes as a function of (Q2 + M2)

Q2 and/or M2

approaching a limit ≈ 5 GeV-2 at large scales

recent data suggestive of possible ≈ 15% difference between ρ and J/ψ

Selected results on R = σL/σT for ρ0 production

the same W- and t-dependence for σL and σT

i.e. contribution of large qqbar fluctuations of transverse γ* suppressed

the same size of the longitudinal and transverse γ* involved in hard ρ0 production

δL ≈ δT bL ≈ bT

Comparison to ‘dipole models’

extensive comparison of the models to recent ZEUS ρ0 data inbelow just selected examples

considered models describe qualitatively all features of the data reasonably well

recent ZEUS data are a challenge; none of the models gives at the momentsatisfactory quantitative description of all features of the data

arXiv:0708.1478[hep-ex]

Comparison to GPD model

• Goloskokov-Kroll ‘Hand-bag model’; GPDs from DD using CTEQ6 power corrections due to kt of quarks included

both contributions of γ*L and γ*

T calculated

■ H1 □ ZEUS

ZEUS (recent)

W=75 GeV

W=90 GeV

W=90 GeV

σ/10

complete calculation

leading twist only (in collinear approx.)

leading twist prediction above full calculation, even at Q2 = 100 GeV2

≈ 10% sea quark contribution, including interference with gluons, non-negligible

25% at Q2 = 4 GeV2

contribution of σT decreases with Q2, but does not vanish even at Q2 = 100 GeV2

≈ 20%

arXiv:0708,3569[hep-ph]

Transverse target spin asymmetry for exclusive ρ0 production

So far GPD E poorly constrained by data; mostly by Pauli form factors

Give access to GPD E related to the orbital angular momentum of quarks

Ji’s sum ruleqq

The asymmetry defined as

),(),(

),(),(1),(

ss

ss

TsUT dd

dd

SA

to disentangle contributions from γL and γT the

distribution of ρ0 decay polar angle needed in addition Diehl and Sapeta

Eur. Phys. J.C 41, 515 (2005)

The asymmetry defined as

),(),(

),(),(1),(

ss

ss

TsUT dd

dd

SA

to disentangle contributions from γL and γT the

distribution of ρ0 decay polar angle needed in addition Diehl and Sapeta

Method for L/T separation used by HERMES

Angular distribution W(cos θ, φ, φs) and Unbinned Maximum Likelihood fit

)},()(1{cos[),,(cos ,,04

002

SLUTTLUUS ASArW

)}],()(1{)1(sin2

1,,

0400

2STUTTTUU ASAr

Assuming SCHC

)sin()(,

SmTLUTA

Simultaneous fit of 12 parameters of azimuthal distributions

~Im 00)sin(

,L

LUTSA

Im (E*H) / |H|2

a prerequisite for the method: determination of acceptance correction as a function of cos θ, φ and φs

A. Rostomyan and J. Dreschler arXiv:0707.2486

ρ0 transverse target spin asymmetry from HERMES

Transversely polarised proton target, PT ≈ 75% 2002-2005 data, 171.6 pb-1

for the first time ρ0 TTSA extracted separately for γ*L and γ*

T

ρ0 transverse target spin asymmetry from HERMES

in a model dependent analysis data favours positive Ju

in agreement with DVCS results from HERMES

ρ0 transverse target spin asymmetry from COMPASS

Transversely polarised deuteron target (6LiD), PT ≈ 50% 2002-2004 data

2

2

)]sin(1[

)]sin(1[

)()(

)()(

)()(

)()()(

du

du

du

du

aa

aa

NN

NNDRin bins of ϑ = φ – φS:

)]sin(41[ C

obtained using Double Ratio Method

)sin( SUTA

raw asymmetry ε from the fit to DR(η)

TUT Pf

A S )sin(

dilution factor f ≈ 0.38

u (d) are for upstream (downstream) cell of polarised targetarrows indicate transverse polarisation of corresponding cells

ρ0 transverse target spin asymmetry from COMPASS

asymmetry for deuteron target consistent with zero

ongoing work on:

longitudinal/transverse separation separation of incoherent/coherent

in 2007 data taken with transversely polarised proton target (NH3)

new

Exclusive π+ production from HERMES

σL VGG LO σL VGG LO+power corrections σT + ε σL Regge model (Laget)

LO calculations strongly underestimate the data

data support magnitude of the power corrections (kt and soft overlap)

Regge calculations provides good description of the magnitude of σtot

and of t’ and Q2 dependences

at leading twist σL sensitive to GPDs H and E ~ ~

at small |t’| E dominates as it contains t-channel pion-pole~

L/T separation not possible at HERMES, σT expected to be supressed as 1/Q2

e p → e n π+

Beam spin asymmetry in exclusive π0 production from CLAS

a fit α sinφ Regge model (Laget) pole terms (ω, ρ, b1) + box diagrams (cuts)

first measurement of BSA for exclusive π0 production above resonance region

sizeable BSA (0.04 – 0.11) indicate that both T and L amplitudes contribute necessity for L/T separation and measurements at higher Q2

prelim

inary

at leading twist σL sensitive to GPD H

no t-channel pion-pole (in contrast to exclusive π+ production) any non-zero BSA would indicate L-T interference, i.e. contribution not described

in terms of GPD’s

~ e p → e p π0

Cross sections for exclusive π0 production from JLAB HALL A DVCS Collab.

from P. Bertin, Baryon-07

t-slope close to 0, maybe even small negative

E00-110

dt

dh

dt

d

dt

d

dt

d

dt

d

ddt

dTLTLTTLTpp '*

2

sin)1(2cos)1(22cos2

10

h = ±1 is the beam helicity

dashed – prediction for σL from VGG model using GPDs

Vanderhaeghen, Guichon, Guidal

Summary for existing measurements

New precise data on cross sections result in significantly more stringent constraints on the models for GPDs

To describe present data on DVMP, both at large and small x, including power corrections (or higher order pQCD terms) is essential

First experimental efforts to constrain GPD E and quark orbital momentum

Results on DVCS promissing;

good agreement with NLO for HERA data

indication of scaling and handbag dominance in valence region

Precision of DVCS unpolarized cross sections at eRHIC (1)

eRHIC measurements of cross section will provide significant constraints

For one out of 6 W intervals (30 < W < 45 GeV)

Lint = 530 pb-1

(2 weeks)

Q2 [GeV2]

eRHIC HE setup

<W> = 37 GeV

σ(γ*

p →

γ p

) [n

b]

HE setup: e+/- (10 GeV) + p (250 GeV) L = 4.4 · 1032 cm-2s-1 38 pb-1/day

EIC measurements of cross section will provide significant constraints

For one out of 6 Q2 intervals (8 < Q2 < 15 GeV2)

W [GeV]

<Q2> = 10.4 GeV2

σ(γ*

p →

γ p

) [n

b]

also significantly extend the range towards small W

Precision of DVCS unpolarized cross sections at eRHIC (2)

LE setup: e+/- ( 5 GeV) + p ( 50 GeV) L = 1.5 · 1032 cm-2s-1 13 pb-1/day

eRHIC

Lint = 530 pb-1

Lint = 180 pb-1

HE setup: e+/- (10 GeV) + p (250 GeV) L = 4.4 · 1032 cm-2s-1 38 pb-1/day

Towards 3D mapping of parton structure of the nucleon at EIC

|)|exp()(/ * tBppdtd

)/ln('2)()( 0 xxxBxB o α’ = 0.125 GeV-2

(assumed for illustration)

simultaneous data in several (6) Q2 bins

Sufficient luminosity to do triple-differential measurements in x, Q2, t at EIC!

Lint = 4.2 fb-1

Lepton charge asymmetry at eRHIC

BMK use ‘improved’ charge asymmetries ACcosφ and AC

sinφ

model of Belitsky, Mueller, Kirchner (2002) for GPDs at small xB

parameters of sea-quark sector fixed using H1 DVCS data (PL B517 (2001))except magnetic moment κsea (-3 < κsea < 2), which enters Ji’s sum rule for Jq

κsea = 2

κsea = 2

κsea = -3

κsea = -3

measurements of asymmetries at EIC sensitive tool to validate models of GPDs

Q2 [GeV2]

W = 75 GeV , -t = 0.1 GeV2

W [GeV]

Q2 =4.5 GeV2 , -t = 0.1 GeV2

HE setup, Lint = 530 pb-1 divided equally between e+ and e-

Summary for DVCS at eRHIC

Wide kinematical range, overlap with HERA and COMPASS 1.5 ·10-4 < xB < 0.2 - sensitivity to quarks and gluons

1 < Q2 < 50 GeV2 - sensitivity to QCD evolution

DVCS cross sections - significant improvement of precision wrt HERA

Intereference with BH - pioneering measurements for a collider

powerfull tool to study DVCS amplitudes full exploratory potential, if e+ and e- available as well as longitudinaly and transversely polarized protons

Sufficient luminosity to do tripple-differential measurements in xB, Q2, t

Backup slide

A simulation of DVCS at eRHIC

HE setup: e+/- (10 GeV) + p (250 GeV) L = 4.4 · 1032 cm-2s-1 38 pb-1/day

acceptance of Central Detector (improved ZDR) 2° < θlab < 178°

diam. of the pipe - 20 cm, space for Central Detector: ≈ +/- 280 cm from IP

event generator: FFS (1998) parameterization with R=0.5, η = 0.4 and b = 6.2 GeV-2

DVCS + BH + INT cross section

due to acceptance and to ‘reasonably’ balance DVCS vs. BH following kinematical range chosen

acceptance simulated by kinematical cuts

kinematical smearing: parameterization of resolutions of H1 (SPACAL, LArCal) + ZEUS (θγ, φγ) + expected for LHC (θe’ , φe’ )

LE setup: e+/- ( 5 GeV) + p ( 50 GeV) L = 1.5 · 1032 cm-2s-1 13 pb-1/day

Ee’ > Emin GeV Eγ > 0.5 GeV 2° < θe’ < 178° 2° < θγ < 178°

Emin = 2 GeV (HE) or 1 GeV (LE)

2.5 < W < 28 GeV

1 < Q2 < 50 GeV2

0.05 < |t| < 1.0 GeV2

1 < Q2 < 50 GeV2

10 < W < 90 GeV

0.05 < |t| < 1.0 GeV2

HE setup LE setup