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Experimental observables linked to GPDs 3. Experimentally, DVCS is undistinguishable with Bethe-Heitler However, we know FF at low t and BH is fully calculable Using a polarized beam on an unpolarized target, 2 observables can be measured: At JLab energies, |T DVCS | 2 should be small Kroll, Guichon, Diehl, Pire, …
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Deeply Virtual Compton Scattering @ JLabFranck SabatiéSaclay
SPIN’06 - KyotoOctober 6th 2006
From GPDs to DVCS, to GPDs backOnto the DVCS harmonic structureE00-110 experiment in Hall AScaling tests & GPD measurementE1-DVCS experiment at CLAS in Hall BSummary
Collins, Freund
GPDs from Theory to Experiment
Theory
x+ x-
t
GPDs
Handbag Diagram
Physical process
Experiment
Factorization theorem states:In the suitable asymptotic limit, the handbag diagram is the leading contribution to DVCS.
Q2 and largeat xB and t fixed
but it’s not so simple…
1. Needs to be checked !!!1
1
1
1
( , , ) +
( , , - i + ( , ) , )
DVCS
GPD x t
GPD x tT dxx
GPD x tdx
i
P x
2. The GPDs enter the DVCS amplitude as an integral over x:- GPDs appear in the real part through a PP integral over x- GPDs appear in the imaginary part but at the line x=
Experimental observables linked to GPDs
3. Experimentally, DVCS is undistinguishable with Bethe-Heitler
However, we know FF at low t and BH is fully calculable
Using a polarized beam on an unpolarized target, 2 observables can be measured:
4 2
2
4 4
2
2
m2 I
ReBH BH D
DVC
B
BH
C
S
V S
B
d T Tdx dQ dtd
d d Tdx dQ d
T
tdT
At JLab energies,|TDVCS|2 should be small
4 2 2
2
4 4 2 2
2
2
Im2
Re DVCBH BH DVCS
B
BH DVCS DVCSDVCS
B
Sd T T Tdx dQ dtd
d d T T Tdx dQ
T
tT
d d
Kroll, Guichon, Diehl, Pire, …
The cross-section difference accesses the imaginary part of DVCS and therefore GPDs at x =
1
1
1
1
( , , ) +
( , , - i + ( , ) , )
DVCS
GPD x t
GPD x tT dxx
GPD x tdx
i
P x
The total cross-section accessesthe real part of DVCS and therefore an integral of GPDs over x
Observables and their relationship to GPDs
e-’
pe-*
hadronic plane
leptonic plane
0 1
42
1
2 3
1
10 1 22
2
2
1 22
4
21 2
24
2
1 ( , , ) cos cos 2
1 (
( ) ( )
( ) (, , ) cos cos 2 cos3
( , , ) sin sin 2
)
( ) ( )
BH BH BHB
B
B
B
B
I I I I
I I
c c c c
d x Q t c c cdx dQ dtd
x Q t
x Q td ddx
sdQ d
sdt
Into the harmonic structure of DVCS|TBH|2
Interference term
1 2( ) (1
)
BH propagators dependenceBelitsky, Mueller, Kirchner
1
42
1 0 1 22
22
24 4
2
1 2
1 2
0 1 2 3
1 22
1 ( , , ) cos cos 2
1 ( , , ) cos cos 2 cos3
( ) ( )
( ) (
( , , ) sin sin 2
)
( ) (
)
BH BH BHB
B
BI I I I
I IB
B
d x Q t c c cdx dQ dtd
x Q t
x Q td ddx dQ dtd
c c c c
s s
Tests of scaling
1. Twist-2 terms should dominate and All coefficients have Q2 dependence which can be tested!
Analysis – Extraction of observables
Re-stating the problem (difference of cross-section):
24 4
2 1 21 2
sin sin 2( ) ( )
( , , ) IB I
B
x Q td ddx dQ d d
st
s
1 8 I ( )) m(2 IIs y y CK F
1 1 2 22()2 4
( )B
I BC x tF F Fx
F FM
2 ( , , ) ( , )I ,m q qq
q
e H t H t
GPD !!!
What we measure
Special case of the asymmetry
4 42
4 4 0 1
1 2
0 1
sin sin 2( , , )( ) cos ...
A B BH BH
I I
I I
d d x Q tc cd
s scd c
The asymmetry can be written as:
Pros: easier experimentally, smaller RC
Cons: - extraction of GPDs model-dependent (denominator complicated and not well known) - Large effects of the BH propagators in the denominator
Asymmetries are largely used in CLAS and HERMES measurements, where acceptance and systematics are more difficult to estimate.
E00-110 experimental setup and performances
• 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• 11x12 block PbF2 electromagnetic calorimeter
• 15cm LH2 target• Left Hall A HRS with electron package
• 75% polarized 2.5uA electron beam
Pbeam=75.32% ± 0.07% (stat)Vertex resolution 1.2mm
• 5x20 block plastic scintillator array
at
2.7%
4.2
E
EGeV
2.5x y mm t (ns) for 9-blockaround predicted« DVCS » block
E00-110 kinematics
The calorimeter is centeredon the virtual photon direction
50 days of beam time in the fall 2004, at 2.5A intensity113294 fbLu dt
Analysis – Looking for DVCS events
HRS: Cerenkov, vertex, flat-acceptance cut with R-functions
Calo: 1 cluster in coincidence in the calorimeter above 1 GeV
With both: subtract accidentals, build missing mass of (e,) system
Analysis – o subtraction effect on missing mass spectrum
Using 0→2 events in the calorimeter,the 0 contribution is subtracted bin by bin
After0 subtraction
Analysis – Exclusivity check using Proton Array and MC
Normalized (e,p,)triple coincidence events
Using Proton-Array, we compare the missing mass spectrum of the triple and double-coincidence events.
Monte-Carlo(e,)X – (e,p,)
2 cutXM
The missing mass spectrum using the Monte-Carlo gives the same position and width. Using the cut shown on the Fig.,the contamination from inelastic channels is estimated to be under 3%.
Analysis – Extraction of observables
Difference of cross-sections
2 22.3 GeV
0.36B
Q
x
Corrected for real+virtual RCCorrected for efficiencyCorrected for acceptanceCorrected for resolution effects
Twist-2Twist-3
Extracted Twist-3contribution small !
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
Twist 4+ contributions are smaller than 10%
Total cross-section2 22.3 GeV
0.36B
Q
x
Corrected for real+virtual RCCorrected for efficiencyCorrected for acceptanceCorrected for resolution effects
Extracted Twist-3contribution small !
E1-DVCS @ CLAS : a dedicated DVCS experiment
~50 cm
Inner Calorimeter+ Moller shielding solenoid
Beam Polarization: 75-85%Integ. Luminosity: 45 fb-1
M(GeV2)
E1-DVCS kinematical coverage and binning
W2 > 4 GeV2
Q2 > 1 GeV2
E1-DVCS exclusive DVCS selection
Remaining 0 contamination up to 20%, subtracted bin by binusing 0 events and MC estimation of 0(1) to 0(2) acceptance ratio
3-particle final state
E1-DVCS raw asymmetries
Very Preliminary
Integrated over t
ALU
<-t> = 0.18 GeV2 <-t> = 0.30 GeV2 <-t> = 0.49 GeV2 <-t> = 0.76 GeV2
ALU(90°)
Hall A dataOld CLAS data
E1-DVCS corrected ALU(90°)
Very Preliminary
SummaryCross-section difference (Hall A): High statistics test of scaling: Strong support for twist-2 dominance
First model-independent extraction of GPD linear combination from DVCS data in the twist-3 approximation
Upper limit set on twist-4+ effects in the cross-section difference:twist>3 contribution is smaller than 10%
Total cross-section (Hall A):
Bethe-Heitler is not dominant everywhere
|DVCS|2 terms might be sizeable but almost impossible to extract using only total cross-section: e+/e- or +/- beams seem necessary
Despite this, we performed a measurement of 2 different GPD integrals
BSA (CLAS):
Preliminary data in large kinematic range and good statistics !
Outlook
2 experiments to run in Hall B in ~2008
1 experiment to run in Hall A in ~2009
Extension of all the current experiments already proposed and approved for12 GeV running
Many theoretical progress expected in the meantime:
- Radiative corrections (P. Guichon)- Global analysis with adequate model (D. Mueller and others)- …
Backup
Comparison with models
Q2, x t,
Designing a DVCS experiment
Measuring cross-sections differential in 4 variables requires:
The high precision measurement of all 4 kinematical variables
Q2, x
Scattered electrondetected in the Hall A HRS:High precision determination
of the * 4-vector
Emitted photondetected in a high resolution
Electromagnetic Calorimeter:High precision determinationof the real photon directionq
q
t,
Designing a DVCS experiment
Measuring cross-sections differential in 4 variables requires:
Designing a DVCS experiment
Measuring cross-sections differential in 4 variables requires:
A good knowledge of the acceptance
Scattered electronThe HRS acceptance
is well known
Emitted photonThe calorimeter has a simple
rectangular acceptance
e p → e (p)
Perfect acceptancematching by design !Virtual photon « acceptance »placed at center of calorimeter
R-functioncut
*
Simply:t: radius: phase
Measuring cross-sections differential in 4 variables requires:
Good identification of the experimental process, i.e. exclusivity
Designing a DVCS experiment
ep epWithout experimental resolution
oep e
p
p
ep e
Designing a DVCS experiment
Good identification of the experimental process, i.e. exclusivity
Measuring cross-sections differential in 4 variables requires:
Without experimental resolution
o
ep
ep ep
e
ep ep
N
resonant or not
Designing a DVCS experiment
Good identification of the experimental process, i.e. exclusivity
Measuring cross-sections differential in 4 variables requires:
Without experimental resolution
If the Missing Mass resolution is good enough, with a tight cut, one get rids of the associated pion channels, but o electroproduction needs to be subtracted no matter what.
The baby steps towards the full nucleon wave function
After understanding the basic properties of the nucleon,physicists tried to understand its structure:
-By Elastic Scattering, we discovered the proton is not a point-like particle and we infered its charge and current distributions by measuring theForm Factors F1 and F2.
-By Deep Inelastic Scattering, we discovered quarks inside the nucleon and after 30 years of research, have a rather complete mapping of theQuark Momentum and Spin Distributions q(x), q(x).
Since the late 90’s, a new tool was developed, linking these representations of current/charge and momentum/spin distributions inside the nucleon, offering correlation information between different states of the nucleon in terms of partons. The study of Generalized Parton Distributions through Deep Exclusive Scattering will allow for a more complete description of the nucleon than ever before.
Mueller, Radyushkin, Ji
E00-110 custom electronics and DAQ scheme1. 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
ARS system in a high-rate environment
- 5-20% of events require a 2-pulse fit - Energy resolution improved by a factor from 1.5 to 2.5 !- Optimal timing resolution
t (ns)
HRS-Calocoincidence
t=0.6 ns
Analysis – Calorimeter acceptance
The t-acceptance of the calorimeter is complicated at high-t:
5 bins in t:
-0.40 -0.35 -0.37
-0.35 -0.30 -0.33
-0.30 -0.26 -0.28
-0.26 -0.21 -0.23
-0.21 -0.12 -0.17
Min Max Avg
Xcalo (cm)
Ycalo (cm)
Calorimeter
Large-t dependence
Analysis – o contamination
Symmetric decay: minimum angle in lab of 4.4° at max o energy
Asymmetric decay: sometimes one high energy cluster… mimicks DVCS!
Analysis – o subtraction using data
1. Select o events in the calorimeter using 2 clusters in the calorimeter
2. For each o event, randomize the decay in 2-photons and select events for which only one cluster is detected (by MC)
3. Using appropriate normalization, subtract this number to the total number of 1-cluster (e,) events
Note: this not only suppressed o from electroproduction but also part of the o from associated processes
Invariant Massof 2-cluster events
135.5 MeV
9 MeVM
M
Summary plot
1
1
- ( i, ( , , ) , ) + DVCS GP GPD x tD xPT t dxx
Total cross-section and GPDs
4 2
0 1 2 32
22
32
2
0
2
2
1
1
1 ( , , ) cos cos 2 cos3
(2 )8 Re (1 )(2 )(2 )( ) ( ) (Re1
8 (2 ) R
)
e ( )
( ) ( )I I I I
I I
BHB
B
I
I I
I
BC
d T x Q tdx dQ dtd
y tK y y xy
F C F C F
C
c c c
K
c
c
c
Q
Fy
with
1 1 2 22
1 2
(( )2 4
( ) ( )
)
(2 2
)
B
B
B B
B
I
I
B
C F
C F
x tF F F Fx M
x xF Fx x
Interesting !Only depends on H and
E
CLAS: Phys.Rev.Lett.87:182002, 2001 HERMES: Phys.Rev.Lett.87:182001, 2001
DVCS Results : CLAS 4.2 and 4.8 GeV and HERMES
2 2
2
1.25 GeV0.19
0.19 GeVB
Qx
t
Preliminary CLAS analysiswith 4.8GeV data (G. Gavalian)
Preliminary
1-cluster eventscoming from all o
1-cluster eventscoming from o
electroproduction
MM2 cut
MeX (GeV2)
Analysis – missing mass of « subtracted » o
This method gives the number of o for all experimental bins
<-t>=-0.28 GeV2, 100°< <120°
CLAS 6 GeV
DVCSProton
ep→epπo/η
Hall A 6 GeV
DVCSprotonneutron
ep→epπo
CLAS 5.75 GeV
DVCS
DDVCS
ΔDVCS
D2VCS
PolarizedDVCS
ep→epρL
ep→epωL
ep→epπ0/η
ep→enπ+
ep→epΦ
HERMES 27 GeV
DVCS – BSA + BCA
+ nucleid-BSAd-BCA
ep→epρσL + DSA
ep→enπ+
+ ….
HERA27.5-900 GeV
DVCS
CLAS 4-5 GeV
DVCSBSA
HERMES
DVCS
BSA+BCA
With recoil detector
COMPASS
DVCS
+BCA
With recoil detector
Published ….. Preliminary results 2004 2005 ……… ….. 2009 ? … 2010
JLab@
12GeV
Deep Exclusive experimentsEV
ERY
THIN
G, w
ith more statistics than ever before
Deeply Exclusive Scattering program in the near future
2006-2007 HERMES2010-… COMPASS2010-… JLab@12GeV
Q2 and t dependence with 4.8 GeV data
Preliminary Preliminary
No clear dependence seen. Comparison with models necessary.And more accurate data clearly needed!
0.15 < xB< 0.41.50 < Q2 < 4.5 GeV2
-t < 0.5 GeV2
DVCS Beam Spin Asymmetry
PRELIMINARYH. Avakian & L. Elouadrhiri
GPD based predictions
0 are « suppressed » due to analysis cuts (only low t),but no subtraction or correction were done
PRELIMINARY
Once again, exclusivity and high statistics & precision data is the key !
The next generation DES experiments: a challenge
We need: •Resolution and exclusivity (3-particle final state)•High luminosity and/or acceptance (low cross-sections)• High transfers (factorization)
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
πoγB
eam energy
MX2 [MeV2]
MX2 [MeV2]
Dependence of asymmetryand total cross-section asa function of xB, t, Q2 , bins
Projected results (sample)
Fast Digital Trigger
PbF2 block
Plastic ScintillatorProton Array
ARS system
Fast-digitizing electronics and smart calorimeter trigger
Addition of a charged particle vetoin front of the plastic scintillator array
The veto counter consists in 2 layers of2cm-thick scintillator paddles
Use of a deuterium targetProton DVCS is veto-ed by new detector
Neutron DVCS in Hall A at 6 GeV – E03-106 (Nov. 2004)P. Bertin, C.E. Hyde-Wright,F. Sabatié and E. Voutier
1 1 2 22
sin
( ) ( ) ( )4
( )2
B
B
xF t H F t F
A
tA F t EM
t Hx
Main contributionto the neutron
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