DVCS & DVCS & Generalized Parton Distributions. Compton Scattering “DVCS” (Deep Virtual Compton Scattering) “DVCS” (Deep Virtual Compton Scattering)

DVCS & DVCS & Generalized Parton DistributionsGeneralized Parton Distributions

Compton ScatteringCompton Scattering

“ “DVCS” (Deep Virtual Compton Scattering)DVCS” (Deep Virtual Compton Scattering)

Bjorken Sum Rule :Bjorken Sum Rule : ( ( ) ( ))g x g x dxg

gp

Bn

B BA

V1 1 6

1/4 1/4 spin carried by quarksspin carried by quarks ( ( ) ( ))g x e q xqq

121

2

)()( 2'

1'

1 BB xgBxgAA

d

dQ dxAf Q x Bf Q x

BB B

2

2 12

22

( , ) ( , )

: : spin ½ objectsspin ½ objectsf x fB2 12

( ( ) ( ))f x e q xqq

121

2 1/2 1/2 momentum carried by quarksmomentum carried by quarks

Bjorken scaling (Q >1 GeV ) : pointlike objectsBjorken scaling (Q >1 GeV ) : pointlike objects2 2

DEEP INELASTIC DEEP INELASTIC

Q e e

xQ

p qB

2 2

2

2

( )

( . )

'

} ( , )' 'Ee e

((INCLUSIVEINCLUSIVE))

e q

e’

f ,1 f2

(( ((

((

))))

))

p

Final state constrained : Final state constrained :

New generation of machines :New generation of machines :- high energy- high energy- high duty cycle - high duty cycle

+ spectrometers :+ spectrometers :- large acceptance- large acceptance- high resolution- high resolution

}accessibleaccessible now !now !

e

p

e’

p’

DEEP INELASTIC DEEP INELASTIC ((EXCLUSIVEEXCLUSIVE))

),,(),,((2

2

txbEtxaHdtdxdQ

d

B

2)),,(),,( txdEtxcH ~ ~

e e’

p p’

H,E,H,E~ ~x

t

21 Bx

Bx

p p’(=p+)

H,E(x,,t)H,E(x,,t)~~

x-

t

x+

GPD formalismGPD formalism

{{[[Hq(x,,t)N(p’)N(p’)++N(p)N(p) + + Eq(x,,t)N(p’)iN(p’)i++N(p)]N(p)]

5 5 [[Hq(x,,t)N(p’)N(p’)+ + 5 5 N(p) +N(p) + Eq(x,,t)N(p’)N(p’)N(p)]N(p)]}}22MM_ ~~

22MM

_

_

_

Vector Ms : H,E

Large Q2, small t

PS Ms : H,E~ ~

(Ji, Radyushkin, Collins, Strikman, Frankfurt)

: T lead. twist

Mesons : L

H, H, E, E (x,ξ,t)~ ~

“Ordinary” parton distributions

H(x,0,0) = q(x), H(x,0,0) = Δq(x) ~

x

Elastic form factors

H(x,ξ,t)dx = F(t) ( ξ)

x

Ji’s sum rule

2Jq = x(H+E)(x,ξ,0)dx

gq LGL 21

21

(nucleon spin)

x+ξ x-ξ

tγ, π, ρ, ω…

GPDs are not completely unknownGPDs are not completely unknown

-2ξ

( )b

0 b

y

xz

b

Transverse Transverse localisation of the localisation of the partons partons in the nucleonin the nucleon(independently(independently of their of their longitudinallongitudinal momentum) momentum)

Form FactorsForm Factors

N 'N

'ee

x

)(xf

1

0

y

xpz

xz

LongitudinalLongitudinal momentum distributionmomentum distribution(no (no information information on the on the transversetransverse localisation) localisation)

Parton DistributionParton Distribution

N

'ee

(Belitsky et al.)(Belitsky et al.)

y

xpz

b

x

f x b( , )

1

0

xz

b

The The GPDGPDs contains contain information information on the on the longitudinallongitudinal ANDAND transversetransverse distributions ofdistributions ofthethe partons partons in the nucleonin the nucleon

Generalized Parton DistributionsGeneralized Parton Distributions

N 'N

3-D picture of the nucleon3-D picture of the nucleon (femto-graphy of the nucleon)(femto-graphy of the nucleon)

GPDs probe the nucleon at GPDs probe the nucleon at amplitudeamplitude level level

q(x)~<p|q(x)~<p|(x)(x)(x)|p ’>(x)|p ’> H(x,H(x,)~<p|)~<p|(x-(x-))(x+(x+)|p ’>)|p ’>

pp p’p’

x+x+ x-x-

zz00 1100 11 zz

pp p’p’

x+x+ x-x-x<x<::x>x>::

DIS :DIS : DES :DES :

pp p’p’

xx xx

pp p’p’

x+x+ x-x-

<<x >x >00

<<x >x >-1 -1

t=0t=0

<<x >x >11

DDsDDs

« « D-term »D-term »kk

GPDsGPDs

Pion cloudPion cloudTrans. Mom. of partonsTrans. Mom. of partons

F (t), G (t)F (t), G (t)1,21,2 A,PSA,PS

q(x),q(x),q(x)q(x)

R (t),R R (t),R (t)(t)AA VVJJqq

(z)(z)

e e’

p p’

H,E,H,E~ ~

Access experimentally the GPDs through the measurement of the angular and energy distributions of EXCLUSIVE reactions

q’q

H,E,H,E(x,,t) : GPDs~ ~

H E q spin average

H E q spin diff.~ ~

p spin no flip

p spin flip

p p’

H,E,H,E~ ~

x

t

Deconvolution needed !Deconvolution needed !x : mute variable

x

Hq(x,,t) but only and t accessible experimentally

d

dQ d dt2

B

~ AH (x,,t,Q )2q

x-idx +BE (x,,t,Q )2

q

x-idx +….

1 1

-1 -1

2

= xB1-x /2B t=(p-p ’)2

x = xB !

/2

GPD and DVCSGPD and DVCS

1

1

1

1

),,(),,(

~),,(

~ tHidxx

txHPdx

ix

txHT DVCS

Cross-section measurementand beam charge asymmetry (ReT)

integrate GPDs over x

Beam or target spin asymmetrycontain only ImT,

therefore GPDs at x = and

(at leading order:)(M

. V

and

erh

aeg

he

n)

- “Trivial” kinematical corrections

- Quark transverse momentum effects (modification of quark propagator)

- Other twist-4 ……

DES: finite Q2 corrections(real world ≠ Bjorken limit)

DES: finite Q2 corrections(real world ≠ Bjorken limit)

GPD evolution

O (1/Q)

O (1/Q2)

Dependence on factorization scale μ :

Kernel known to NLO

- Gauge fixing term- Twist-3: contribution from γ*L may be expressed in terms of derivatives of (twist-2) GPDs.

- Other contributions such as small (but measureable effect).

(here for DVCS)

The actorsThe actors

JLab

Hall A Hall B Hall C

p-DVCS

n-DVCS

Vector mesons

p-DVCS

d-DVCS

Pseudoscalar mesons

DESYHERMES ZEUS/H1

Vector & PS mesons

DVCS

CERNCOMPASS

Vector mesons

DVCS

+ theory (almost) everywhere

JLab(Ee=6 GeV):CLAS/Hall B (2001+2005) and Hall A (2004)

HERA (Ee=27 GeV) : HERMES and ZEUS/H1 (up to 2006)

CERN (E=200 GeV) : COMPASS (2007 ?)

« « DES » in the worldDES » in the world

e

p

e’

p’

The epThe ep ep ep process process

DVCSDVCS

e

p

e’

p’

e

p

e’

p’

Bethe-HeitlerBethe-Heitler

GPDs

...

2

1''

5

dt

d

dt

d

dtddkd

d LTV

ee

1

1V

Vete

B ECxQ 1,2

Energy dependenceEnergy dependence

BH

DVCS

Calculation (M.G.&M.Vanderhaeghen)

e

p

e’

p’

The epThe ep ep ep process process

DVCSDVCS

e

p

e’

p’

e

p

e’

p’

Bethe-HeitlerBethe-Heitler

Interference between the 2 processes : if the electronbeam is polarised => beam spin asymmetry

GPDs

First experimental signaturesFirst experimental signatures

Magnitude and Q2 dependence of DVCS X-section (H1/ZEUS)

First observations of DVCS beam asymmetries

CLAS HERMES

DVCS

First observations of DVCS charge asymmetry (HERMES)

All in basic agreement with theoretical predictions

2 2

2

1.25 GeV

0.19

0.19 GeV

B

Q

x

t

Phys.Rev.Lett.87:182002,2001

4.8 GeV data (G. Gavalian)

PRELIMINARY

0.15 < xB< 0.41.50 < Q2 < 4.5 GeV2

-t < 0.5 GeV2

PRELIMINARY

PRELIMINARY

5.75 GeV data (H. Avakian &L. Elhouadrhiri)

CLAS/DVCS at 4.8 and 5.75 GeVCLAS/DVCS at 4.8 and 5.75 GeV

• Resolution• Exclusivity• Luminosity

ep epX MAMI 850

MeV

ep epX Hall A 4 GeV

ep eγX HERMES 28 GeV

N+πN

Missing mass MX2

ep epX CLAS 4.2 GeV

π0γ

D.E.S.: an experimental challengeD.E.S.: an experimental challenge

are the key issues for this physics!

e’

p

A typical DVCSevent in CLAS

N

Only 2-parameter fit: N and N0

ep→epX (CLAS at 4.2 GeV) : X = γ or π0 ?ep→epX (CLAS at 4.2 GeV) : X = γ or π0 ?

e’

p

A typical ep epevent in CLAS

Add EMcalorimeterat forward angles

Add solenoidMoller shieldaround target

Dynamical range : 50 MeV < E < 5 GeV (~5%/sqrt(E))Counting rates ~ 1 MHzMagnetic field environment : B~ 1 T

~400 PbWO4 crystals : ~10x10 mm2, l=160 mm (18 ’s)Read-out : APDs +preamps

JLab/ITEP/Orsay/Saclay/UVAcollaboration

0 mass peak

σ 21 MeV

(with online calibration)

About 380 bins in, xB, t

60 days of beam time in spring’05 Experiment E01-113 : V. Burkert,

L. Edouardrihi, M. Garçon, S. Stepanyan et al. Run March-May 2005

Projected resultsProjected results

•High Resolution Hall A spectrometer for electron detection•100-channel scintillator array for proton detection•132-block PbF2 electromagnetic calorimeter for photon detection Detection of all 3 final-state particles ensures exclusivity

Experiment E00-110 :P. Bertin, C.E. Hyde-Wright,R. Ransome and F. Sabatié.To run mid-september

DVCS in Hall ADVCS in Hall A

to the p-DVCS set-up n-DVCS :n-DVCS :Veto detector added Also HERMES

& COMPASS

γ*Lρ

Handbag diagram calculation (frozen s) can account for CLAS and HERMES data on σL(ep->ep)

Q2(GeV2)

CLAS 4.2 GeV data (C. Hadjidakis, hep-ex/0408005)

W=5.4 GeV

HERMES (27GeV)A. Airapetian et al., EPJC 17

σL(ep->ep)

Regge (Laget)

GPD (MG-MVdh)

Mesons

Ludyvine M

orand’s thesis

Analysis of ω polarization from ep → epπ+π-X configurations (for the first time for this channel above Q2 ~ 1 GeV2)

Evidence for unnatural parity exchange 0 exchange dominating even up to large Q2 (see also J.-M. Laget, hep-ph/0406153)

SCHC does not seem to hold → not possible to extract σL

handbag diagram estimated to contribute only about 1/5 of measured cross sections ω more challenging/difficult channel to access GPD

Q2 from 1.6 to 5.6 GeV2

xB from 0.16 to 0.70

ω peak in MM[epX] for (Q2,xB) bins

Deeply virtual Deeply virtual ωω production at 5.75 GeV production at 5.75 GeV (CLAS)(CLAS)

s

ExtensionsExtensions

RCS : p->p (intermediate t) (Radyushkin, Dihl, Feldman, Jakob, Kroll)

VCS : ep->e (Frankfurt, Polyakov, Strikman, Vanderhaeghen)

tDDVCS : ep->ep* (e+e-) (M.G., Vanderhaeghen, Belitsky, Muller,...)

IDVCS : pp->(Freund, Radyushkin,Shaeffer,Weiss)

tDVCS : p->p* (e+e-) (Berger, Pire, Diehl,...)

N-DVCS : eA->eA(Scopetta, Pire, Cano, Polyakov, Muller, Kirschner, Berger....)

Hybrids, pentaquarks,... (Pire, Anikin,Teryaev,...)

sDDVCS : ep->ep (Vanderhaeghen, Gorschtein,...)

_

The most complete information on the structureof the nucleon : GPDs

SummarySummary

(f (x), g (x), F (t), G (t), (z), pion cloud,…)11 1111 AA

Q2 evolution worked out to NLO, twist-3 contributions to DVCS estimated, first lattice calculations have been recently published,...

THEORY :

Further higher twists –mesons–, deconvolution issues,....

First experimental signatures very encouragingUp to 2005: definitely sign the validity of the approach (factorization, scaling,...)Beyond : systematically measure and extractthe GPDs (JLab@11 GeV)

EXPERIMENT :