Post on 31-Dec-2015
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 :