J. Roche Ohio University and Jefferson Laboratory
Results shown are from the ”DVCS HALL A collaboration” (E00-110 and E03-106)
First steps toward nucleon tomography
usingthe Generalized Parton Distribution
functions
Carlos MUNOZ CEA/SaclayAlexandre CAMSONNE IN2P3/ClermontMalek MAZOUZIN2P3/Grenoble
Pierre BERTIN IN2P3/Clermont Charles HYDE ODU/ClermontRon RANSOMME RutgersFranck SABATIE CEA/SaclayEric VOUTIER IN2P3/Grenoble
Form factorIn 1956, R. Hofstadter confirms that the proton is not a point like objectBut has a spatial extension that can be described in terms of form factors.
Q2=-q2
),( 0 kkkr
)','(' 0 kkkr
),( PMPr
)','(' 0 PPPr
F1(Q2),F2(Q2)
Lowest order
'),( kkqq −=r
ν
In 1972, with the discovery of the weak currents ( Z0, W), the axial () form factor GA(Q2) and the pseudo-scalar form Gp(Q2) are introduced.
00 'kk −=ν
Spin flip
In 1969-1973, the experiments at Stanford (R.Taylor et al.) showed that hadrons are made up of point like parts. These partons wereidentified to quarks and gluons predicted by theorists (M. Gellmann)in 1964. In these experiments an electron scatters inclusively off the nucleonWith a large energy transferred to the target. These experimentsAre know as “Deep Inelastic Scattering”
)','(' 0 kkkr
),( 0 kkkr
00 'kk −=ν
Extensively measured at SLAC, CERN, DESY,JLAB…..Beam: e,νpolarized and non polarizedTarget: P,D,… polarized and non-polarized
⎥⎦
⎤⎢⎣
⎡
−−+−
−= 22
2
12
24
222
)()1(
)(4F
Ms
MxFyFy
Q
Ms
dydx
d απσ
νM
Q
Pq
Qx
2.2
22
==
kPk
Pqy
ν==
.
.q=(k-k’)
k0-k’0=ν Q2=-q2),( 0 kkkr
)','(' 0 kkkr
),( PMPr
DEEP INELASTIC SCATTERING
Note: There are two more structure functions corresponding to the weak exchange (Z0,W)
Structure functions
X
Proton
Particle Data Book
Photon flux before the target - photon flux after the target = all the photons that interacted
€
σX (r k ')
all X
∑ ≡ 4π ℑm[A(kp,kp)]
Optical theorem
X
€
all X
∑p
k
q
The photon couples to a charge
€
≡p p’
k k’
q q
p=p’ k=k’
€
Q2 = −(k − k')2 → ∞
ν = k0 − k0' → ∞
x =Q2
2Mνfixed
In the Bjorken’s limit(no transverse extension)
The scattering happens off a parton (quark or antiquark) carrying a fractionx of the proton momentum
•The structure functions F1,2(x,Q2) ought to be independent of Q2 : there is “scaling” This is wrong but one knows their evolutions through DGLAP
•The structure functions can be de-convoluted in flavor:
Parton distributions
€
q f (x), q f (x)
P P
K K
q q
P P
K K
q q
u
d
g/10
u,d
x
xf(
x)
Polarized structure functions
X
e
P
€
d2 r σ (→,↓)
dx dy−
d2 s σ (←,↑)
dx dy⇒ g1
n,p (x,y),g2n,p (x, y)
⇒ Δu(x),Δd(x),Δu (x),Δd (x),....
= Δq f
Polarized electron
Polarized target: transverse or longitudinal
Neutron, proton….
Proton
Deuteron
Neutron (from 3He)
PDG
If not at the Bjorken’s limit
€
f = u,u ,d,d ....TWISTQTWIST(1/Q4)+….
P P
K K
q q
+ + …=
Sum rules
Nucleon observables
Parton distributions Observables of the partons (charge, spin ….)+
€
dx∫ Q f [q f (x) − q f (x)]f
∑ =1.602 10−19 Coulomb
€
1
2Δq f
f
∑ (x)dx0
1
∫ =0.3± 0.04
2≠
1
2
Charge
Spin
Consider the quarks only:
Add the gluons:
€
1
2Δq f (x) + Δg(x)
⎡ ⎣ ⎢
⎤ ⎦ ⎥
f
∑ dx0
1
∫ ≠1
2
€
[1
2Δq f
f
∑ (x) + Δg0
1
∫ (x)]dx + Lq + Lg =1
2
The quarks orbit !!
But around what ? ?
Orbital momentum
In order to determine Lq, one needs to observe2 partons interacting that is
the correlations between partons.
To describe the waltz, one needs to count the number of dancers, their sexes, their race, their individual spin but none of that tells enough
about the spinning of the whole dance group.
Only a measure of the correlation between all the possible couples gives that information.
DIS only measures the parton distributions anddoesn’t give access to the correlations between the partons therefore
doesn’t give access to the orbital momentum.
The waltz
In 1996, D. Mueller, A. Radyushkin, and X. Ji generalized the partondistributions by breaking the handbag symmetry
),,(~
),,(
),,(~
),,(
5
txEtxEflipspin
txHtxHflipspinno
ff
ff
ξξ
ξξ
4 functions per flavor
Off Forward Parton Distributions
Skewed Parton Distributions
Generalized Parton Distributions
x+ξ x-ξ
t
GPDs
P P’
2)'( PPt −=
GPDs
)()()0,0,(
)()()0,0,(
xqxqxE
xqxqxH
fff
fff
−Δ−=Δ=
−−==
)(),,(~
)(),,(~
)(),,(
)(),,(
1
1
1
1
2
1
1
1
1
1
tGtxEdx
tGtxHdx
tFtxEdx
tFtxHdx
pf
f
Af
f
ff
ff
−=
−=
−=
−=
∑∫
∑∫
∑∫
∑∫
−
−
−
−
ξ
ξ
ξ
ξ
)]0,,()0,,([2
1
2
1 1
1
ξξ xExHxdxLJ ffff
f +=+ΔΣ= ∫−
),,( txGPD ξ€
t = 0
ξ = 0
Limits and sum rules
Ji’s sum rule
There are many GPDs modelsIn all cases, the models predictions are valid if the hand bag dominates Q2, S >>M2 et t << Q2.
The results presented today will be compared to the VGG (M. Vanderaghen, M. Guidal et P.A.M. Guichon ) model.
• x dependency is constrained by the form factors and the structure functions• ξdependency is constrained by mathematical conditions (positivity, polynomiality…)• t dependency is factorized Hq(x)=q(x) F1(t)• inspired by the quark-soliton model
• is a code that you can use to do your plots…
GPDs models
From theory to experiment
Theory
x+ξ x-ξ
t
GPDs
Experiment
But nothing is that simple
Handbag Diagram
Collins, Freund
Physical process
This needs to be tested !!!
Factorisation theorem : If one is close enough from the asymptotic limit then the handbag diagram is the mainContribution to DVCS.(leading twist)
Q2 and ν largewith xB and t fixed
The GPDs enter in the DVCS amplitude as integrals over x
• GPDs appear in the real part through a Principal-value integral over x• GPDs appear in the imaginary part along the line x=+/-ξ
GPDs in the DVCS amplitude
VGG model
€
T DVCS = dxH(x,ξ , t)
x −ξ + iε+L =
−1
+1
∫
= P dxH(x,ξ , t)
x −ξ− i
−1
+1
∫ πH(x = ξ ,ξ , t) + L
x-ξ x+ξ
GPD observables
Experimentaly, DVCS has the same final state than the Bethe-Heitlerprocess. The BH is known if the form factors are known.
With a longitudinaly polarized beam, the GPD observables are:
At JLab energies,|TDVCS|2 is small (?)
( )
( )
42 2
2
4 42 2
2
2
Im2
Re DVCBH BH DVCS
B
BH DVCS DVCSDVCS
B
SdT T T
dx dQ dtd
d dT T T
dx dQ
T
tT
d d
σ
ϕ
σ σ
ϕ
→ ← → ←
≈ + ⋅ +
⎡ ⎤−≈ ⋅ + −⎢ ⎥
⎢ ⎥⎣ ⎦
P.Kroll, P.A.M. Guichon, M. Diehl, B. Pire, …
Parametrization of the cross sections
Terms from the handbag (Twist 2) should dominate σ and ΣTheir dependence in Q2 is predicted by the handbag and can be
tested
Belitsky, Mueller, Kirchner, Nucl. Phys. B629,323(2002)
Decomposed the amplitudes in terms of angular harmonicsand limited Fourier expansions
Twist 2 Twist 3 azimuth between the virtual and real photon
€
d4σ = d4σ BH2
( )
€
+Γ0
ℜ − cosφ( ) ℜe C I( ) + Γ0,Δ
ℜ ℜe C I + ΔC I( ) + cos2φ Γ2
ℜ ℜe CeffI
( )
1+ cosφ + cos2φ+ ΓηCDVCS
|DVCS|2Interference BH-DVCS
€
d4Σ = 12 d4 r
σ − d4 s σ ( ) = sinφ Γ1
ℑ ℑm C I( ) − sin2φ Γ2
ℑ ℑm CeffI
( ) + sinφ η Γ1ℑ ℑm CDVCS
( )
CI’s are linear combinations of the GPDs integrals and discrete values (x=ξ)
The Jlab/Hall A DVCS experiments
The cross section is 4 times differential, so one needs to measure 4 variables:
Q2, x
The Scattered electronIs detected in the Jlab/Hall A HRS:
High precision determination of the quadri-vector of the *
Δp/p~5 10-5 Δrd
t,
The outgoing real photon is detected in an
high precisionelectromagnetic calorimeter:
This allows an excelentdetermination of the directionof the real photon Δ=2. 10-3 rd
The Jlab/Hall A DVCS experiments
Scattered electron The HRS acceptance
Is well known(standard equipmennt)
1~2 %
Emitted photonThe calorimeter is a
simple box
e p → e (p)
The ‘matching’ of the two acceptances is perfect
The virtual photon pointsTo the center of the calorimeter
*
One of the key strength of this experimental program is the excellentKnowledge of the acceptance which allow the extraction of cross sections.
The Jlab/Hall A experimental apparatus
• 75% polarized 2.5uA electron beam• 15cm LH2 target• Left Hall A HRS with electron package• 11x12 block PbF2 electromagnetic calorimeter• 5x20 block plastic scintillator array
at
2.7%
4.2
E
EGeV
σ=
2.5x y mmσ σ; ;
The Jlab/Hall A experimental apparatus
• 75% polarized 2.5uA electron beam• 15cm LH2 target• Left Hall A HRS with electron package• 11x12 block PbF2 electromagnetic calorimeter• 5x20 block plastic scintillator array
Δt (ns) for 9-blockaround predicted« DVCS » block
E00-110 custom electronics and DAQ scheme
1. Electron trigger starts the game
2. Calorimeter trigger (350ns):
- selects clusters- does a fast energy reconstruction- gives a read-out list of the modules which enter clusters over a certain threshold- gives the signal to read-out and record all the experiment electronics channels
3. Each selected electronics channel is digitized on 128ns by ARS boards
t (ns)
4. Offline, a waveform analysis allows to extractreliable information from pile-up events
H(e,e’)X
H(e,e’p)
H(e,e’)X - H(e,e’’)X'
H(e,e’)N
DVCS : exclusivity
•Good resolution : no need for the proton array•Remaining contamination 1.7%
HRS+calorimeterep -> epep -> ep0 0->ep -> ep0ep -> ep0N…
HRS+calorimeter + proton array
E00-110: difference of cross-sections
2 22.3 GeV
0.36B
Q
x
=
=
Corrected for real+virtual RCCorrected for efficiencyCorrected for acceptanceCorrected for resolution effectsChecked elastic cross-section @ ~1%
Twist-2Twist-3
Extracted Twist-3contribution small !
PRL97, 262002 (2006)
E00-110: Q2 dependence and test of scaling
<-t>=0.26 GeV2, <xB>=0.36
No Q2 dependence: strong indication forscaling behavior and handbag dominance
Twist-2Twist-3
0 electro-production cross section:• Dominance of twist 2 (isolation of leading twist)• Sensitive to different linear combinations of GPDs than DVCS
NEW: E12-06-114: Jlab/Hall A 12 GeV experiment
Q2 variation:• 2:1 range at each xBj
• Accurate measurement of the twist-2 dominance
xBj variation (dependence):• Precision data on variation of
t-dependence with xBj
• Study of transverse correlations
t variation:• 5 bins in 0 < t-tmin < 1 GeV2
• Fourier-conjugate to the spatial distributions of quark as a function of their momentum fraction xBj
E00-110: Total cross-sections
Extracted Twist-3contribution small !
PRL97, 262002 (2006)
With these data, it is impossible to disentangle DVCS2 from the interference term: they mix in the azimuthal analysis
22
2
4
)Re(2 DVCSDVCSBHBH TTTT
dtddxdQ
d++≈
σ
large
€
Q2 = 0.23GeV 2 x = 0.36
NEW: E07-007: Complete separation of the observables.
22
2
4
)Re(2 DVCSDVCSBHBH TTTT
dtddxdQ
d++≈
σ
Azimuthal analysis and 2 beam energies,the 2 contributions can be separatedRosenbluth type separation
Goal 1: measure the total cross section d4σ using two beam energiesat fixed xBj=0.36 for three Q2=2.3, 1.9 and 1.5 GeV2.
Ebeam ranging from 3.5 to 6 GeV
• will provide a test of the scaling of the total cross section• will allow to separated the interference BH-DVCS from DVCS2
Goal 2: measure the 5 response functions of ep->ep0 at Q2=2.3, 1.9, 1.5 GeV2
–Separate σLT, σTT , σLT’ from σL+ σT by azimuthal variation
and σL from σT by Rosenbluth method
–First test of factorization in this deep meson production channel –If scaling is observed can extract flavor information on GPDs
Some of the topics I did not talk about
• The same collaboration published results on the neutron (E03-106) got some electro-pion production data
• Other collaborations have published dedicated and non-dedicated DVCS data. DESY (HERMES and HERA) JLab/Hall B: large x and Q2 data but asymmetry data only
• Many DVCS experiments have been approved to run in a near future:COMPASS: using as beamJLab/Hall B
• Information about the structure of the nucleon can be obtained by measuringDeep Meson Production (, , etc..)
The Jlab/Hall A DVCS collaboration• has measured DVCS cross sections with high statistical and systematic precision using a HRS and a calorimeter both off the proton and the neutron
•
€
p(e,e'γ) pσσ sr
−σσ sr
+
•Tests of the dominance of the handbag are positive•The VGG model is too small by 30%•The DVCS2 cannot be neglected
In summary
The GPDs provide a new window on the nucleon structure that allow to study the correlation between its constituents BUT
•One needs to test the regime of applicability of the formalism (handbag dominance)
•The interpretability of the cross-section in term of GPDs is still in its infancy
Many groups have and will continue to perform DVCS/GPD experiments. The Jlab/Hall A DVCS collaboration will study
• E07-007: complete separation of the cross section observables (DVCS2)• E12-06-114: extended Q2 and x ranges• data coming up off proton, neutron (deuterium) on electro production of photon and 0 WANT TO JOIN US?
END
n-DVCS is sensitive to Jd
p-DVCS is sensitive to Ju
Complementarity between neutron and proton measurements
E03-106 results
Model dependent extraction of
Ju and Jd
€
Jq = 12 ΔΣq + Lq
= 12 dx x Hq (x,ξ , t = 0) + Eq (x,ξ , t = 0)[ ]
−1
+1
∫
E00-110 kinematics
The calorimeter is centeredon the virtual photon direction
50 days of beam time in the fall 2004, at 2.5A intensity
113294 fbLu dt −⋅ =∫
Remaining contribution: ~1.7%(all non-o electroproduction)
Analysis – Looking for DVCS events
MM2 cut
MM2 cut
However: One needs to do a thorougho subtraction if the only (e,) system is used to select DVCS events !!!
(e,g,p) events
Testing the handbag dominance
Symmetry around thevirtual photon
Broken by : the photon polarization the beam polarization
If the handbag dominates in the case of a real photon
σλ sin)1(2 '
dt
d TL−+
td
d
dtdxdQ
d
Bj
σσ×Γ=
σσσσσ2coscos)1(2
dt
d
dt
d
dt
d
dt
d
dt
d TTLTLT ++++=
virtual photon polarization longitudinal polarization of the beam
There are 12 independant helicity amplitudes but only 5 observables in the case of a polarized beam and an unpolarized target.
e-’
pe-*
hadronic plane
leptonic plane