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-
Deeply Virtual Compton Scattering
on the neutron in .
Dr. Malek MAZOUZ
Ph.D. Defense, Grenoble
8 December 2006GPDs
+x x
t
Physics case
n-DVCS experimental setup
Analysis method
Results and conclusions
C. Hyde-Wright,
Hall A
Collaboration
Meeting
-
How to access GPDs: DVCS
222
2222
)'(
)'(
Qppt
MkkqQ
==
kk’
q’
GPDsp p’
Deeply Virtual Compton Scattering
is the simplest hard exclusive
process involving GPDs
pQCD factorization
theorem
Perturbative description
(High Q virtual photon)
Non perturbative description by
Generalized Parton Distributions
Bjorken
regime
2 2
2 2
2
x
B
B
B
Q Qx
pq M
x
x
= =
=
± = fraction of longitudinal
momentum
Handbag diagram
-
)0,,(xH
x
Deeply Virtual Compton Scattering
1
1
( , , )( , , ) ...P i
GPD x tGd PDx x
xt
+
± = +±
±=
The GPDs enter the DVCS amplitude as an integral over x :
Real part
Imaginary partDVCS amplitude
-
Expression of the cross-section difference
{ }25 5
232 12 2
1 2
1 2
( , , )1( , , )
2sin( ) sin(2 ) sin( )
( ) ( )
DVCSB I I
B
B e B e
x Q td dx Q t s
dQ dx dtd d dQ dx dtd ds s
P P= + +
r s
{ })()2(81
FII CyKys m=
{ } { }2 ( , , ) ( , )m ,qqq
qH te H t=H
2 25 5 2 m( .BH DVCS DVCS DVCSd ó d ó T T ) T T+
r sr s
GPDs
If handbag
dominance
CI (H , ˜ H ,E) = F1(t)H( ,t)+ GM (t) ˜ H ( ,t)+t
4M 2F1(t)E( ,t)
-
( ) ( )
( )
1 1 2 22( ) ( ) ( ) ( )
2 4
m 0.03 0.01 0. 3
m
1
B
B
I
I x tF t F t F t F t
M
C
Cx
= + +
= +
%HH E
-0.07-0.17-0.04-0.910.3
Neutron Target
2 ( )n
F t 1 ( )n
F t ( )1 2( ) ( ) /(2 )n n B BF t F t x x+ 2 2( / 4 ) ( )n
t M F tt
1.73-0.070.81neutron
Target H %H E(Goeke, Polyakov
and Vanderhaeghen)
Model:2 2
2
2 GeV
0.3
0.3 GeV
B
Q
x
t
=
=
=
CI (H , ˜ H ,E) = F1(t)H( ,t)+ GM (t) ˜ H ( ,t)+t
4M 2F1(t)E( ,t)
H
-
n-DVCS experiment
19.32
19.32
e
(deg)
2.95
2.95
Pe(Gev/c)
18.25
18.25
- *(deg)
240001.914.22
43651.914.22
Q
(GeV )
s
(GeV )
An exploratory experiment was performed at JLab Hall A on hydrogen target
and deuterium target with high luminosity (4.1037 cm-2 s-1) and exclusivity.
Goal : Measure the n-DVCS polarized cross-section difference
which is mostly sensitive to GPD E (less constrained!)
E03-106 (n-DVCS) followed directly the p-DVCS experiment and was
finished in December 2004 (started in November).
Ldt (fb-1)xBj=0.364
Hydrogen
Deuterium
Requires good experimental resolutionSmall cross-sections
-
Two scintillator layers:
-1st layer: 28 scintillators, 9 different
shapes
-2nd layer: 29 scintillators, 10 different
shapes
Proton array
Proton tagger : neutron-proton discrimination
Tagger
-
Proton tagger
Scintillator S1
Wire chamber H
Wire chamber M
Wire chamber B
Prototype
Scintillator S2
-
Calorimeter in theblack box
(132 PbF2 blocks)
Proton
Array
(100 blocks)
Proton
Tagger
(57 paddles)
4.1037
cm-2.s-1
-
Calorimeter energy calibration
bloc number0 20 40 60 80 100 120
gai
n v
aria
tio
n (
%)
0
10
20
30
40
50
60
70
80
90
2 elastic runs H(e,e’p) to calibrate the calorimeter
Achieved resolution :( )
2.4% at 4.2 GeV ; 2 mmE
xE
= =
Variation of calibration coefficients
during the experiment due to
radiation damage.
Ca
libra
tio
n v
ari
atio
n (
%)
Calorimeter block number
Solution : extrapolation of elastic
coefficients assuming a linearity
between the received radiation
dose and the gain variation
H(e,e’ )p and D(e,e’ )X data measured “before” and “after”
-
Calorimeter energy calibration
We have 2 independent methods to check and correct the calorimeter calibration
1st method : missing mass of D(e,e’ -)X reaction
Mp2
By selecting n(e,e’ -)p events,
one can predict the energy
deposit in the calorimeter using
only the cluster position.
a minimisation between the
measured and the predicted
energy gives a better
calibration.
2
-
Calorimeter energy calibration
2nd method : Invariant mass of 2 detected photons in the calorimeter ( 0)
0 invariant mass position
check the quality of the
previous calibration for
each calorimeter region.
Corrections of the previous
calibration are possible.
Differences between the results of the 2 methods introduce a
systematic error of 1% on the calorimeter calibration.
invariant mass (GeV)0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24
Nb
of C
ount
s
0
2000
4000
6000
8000
10000
12000
14000
16000
= 8.5 MeVσ
mass0π
Nb
of
co
un
ts
Invariant mass (GeV)
-
Triple coincidence analysis
Identification of n-DVCS events with the recoil detectors is impossible because
of the high background rate.
Many Proton Array blocks contain signals on time for each event .
Proton Array and Tagger (hardware) work properly during the experiment, but :
Accidental subtraction is made for p-DVCS events and gives stable beam
spin asymmetry results. The same subtraction method gives incoherent
results for neutrons.
Other major difficulties of this analysis:
proton-neutron conversion in the tagger shielding.
Not enough statistics to subtract this contamination correctly
The triple coincidence statistics of n-DVCS is at least a factor 20 lower
than the available statistics in the double coincidence analysis.
-
Double coincidence analysis
eD e X eH e X
accidentals accidentals
( , ' ) ( , ' ) ( , ' ) ( , ' )D e e X p e e p n e e n d e e d= + + +K
p-DVCS
events
n-DVCS
events
d-DVCS
events
Mesons
production
Mx2 cut = (MN+M )
2 Mx2 cut = (MN+M )
2
-
Double coincidence analysis
1) Normalize Hydrogen and Deuterium data to the same luminosity
-
Double coincidence analysis
1) Normalize Hydrogen and Deuterium data to the same luminosity
2) The missing mass cut must be applied identically in both cases
- Hydrogen data and Deuterium data must have the same calibration
- Hydrogen data and Deuterium data must have the same resolution
-
Double coincidence analysis
block number20 40 60 80 100 120
inva
riant
mas
s re
solu
tion
(MeV
)
6
7
8
9
10
11
12
13
cinematique 2
cinematique 4
Re
so
lutio
n o
f 0 in
v.
ma
ss (
Me
V)
Calorimeter block number
Hydrogen
Deuterium
invariant mass (GeV)0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24
Nb
of
Co
un
ts
0
2000
4000
6000
8000
10000
12000
14000
16000
= 8.5 MeVσ
mass0π
Nb
of
co
un
ts
Invariant mass (GeV)
?
-
Double coincidence analysis
1) Normalize Hydrogen and Deuterium data to the same luminosity
2) The missing mass cut must be applied identically in both cases
- Hydrogen data and Deuterium data must have the same calibration
- Hydrogen data and Deuterium data must have the same resolution
- Add nucleon Fermi momentum in deuteron to Hydrogen events
-
Double coincidence analysis
1) Normalize Hydrogen and Deuterium data to the same luminosity
2) The missing mass cut must be applied identically in both cases
- Hydrogen data and Deuterium data must have the same calibration
- Hydrogen data and Deuterium data must have the same resolution
- Add nucleon Fermi momentum in deuteron to Hydrogen events
3) Remove the contamination of 0 electroproduction under the missing
mass cut.
-
0 to subtract
0 contamination subtraction
Mx2 cut =(Mp+M )
2
Hydrogen data
-
Double coincidence analysis
1) Normalize Hydrogen and Deuterium data to the same luminosity
2) The missing mass cut must be applied identically in both cases
- Hydrogen data and Deuterium data must have the same calibration
- Hydrogen data and Deuterium data must have the same resolution
- Add nucleon Fermi momentum in deuteron to Hydrogen events
3) Remove the contamination of 0 electroproduction under the missing
mass cut.
Unfortunately, the high trigger threshold during Deuterium runs did
not allow to record enough 0 events.
But :0
0
( )0.95 0.06
( )
e e Xsys
e e X
d
p= ± ±
In our kinematics 0 come essentially
from proton in the deuterium
No 0 subtraction needed for neutron and coherent deuteron
-
Double coincidence analysis
)2 (GeV2xM0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Nb
of
cou
nts
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
cinematique 2cinematique 4
cin.4 - cin.2simulation
Hydrogen data
Deuterium data
Deuterium- Hydrogen
simulation
Nb o
f C
ounts
MX2 (GeV2)
Mx2 cut
-
n-DVCS ?
d-DVCS ?
Double coincidence analysis
(rad)φ0 1 2 3 4 5 6
- - N+ N
-1000
-500
0
500
1000N+ - N-
(rad)
-
Double coincidence analysis
MC Simulation
MC Simulation
-
Extraction results
Exploration of small –t regions in future experiments might be interesting
Large error bars (statistics + systematics)
d-DVCS extraction results
-
Extraction results
n-DVCS extraction results
Neutron contribution is small and close to zero
Results can constrain GPD models (and therefore GPD E)
-
Systematic errors
of models are not
shown
n-DVCS experiment results
-
Summary
- n-DVCS is mostly sensitive to GPD E : the least constrained
GPD and which is important to access quarks orbital momentum
via Ji’s sum rule.
Our experiment is exploratory and is dedicated to n-DVCS.
To minimize systematic errors, we must have the same calorimeter
properties (calibration, resolution) between Hydrogen and Deuterium data.
n-DVCS and d-DVCS contributions are obtained after a subtraction of
Hydrogen data from Deuterium data.
The experimental separation between n-DVCS and d-DVCS is plausible due to the
different kinematics. The missing mass method is used for this purpose.
-
Outlook
Future experiments in Hall A (6 GeV) to study p-DVCS and n-DVCS
For n-DVCS : Alternate Hydrogen and Deuterium data taking to
minimize systematic errors.
Modify the acquisition system (trigger) to record enough 0s
for accurate subtraction of the contamination.
Future experiments in CLAS (6 GeV) and JLab (12 GeV) to study
DVCS and mesons production and many reactions involving GPDs.
-
VGG parametrisation of GPDs
( ) ( )11
1 1
( ,( , ), , ) qq qF tx
d d x x DH x t+
= +
D-term
Non-factorized t dependenceVanderhaeghen, Guichon, Guidal,
Goeke, Polyakov, Radyushkin, Weiss …
( ) ( )
( )( )( )
( )
( )
2 2
2 12
'
1 2
1
12 2
2 1 1
( , , ) ,
,
b
q
t
bb
F
hb
qh
b
t
++
=
+=
+
Double distribution :
Profile function :
Parton distribution
( )for , the spin-flip parton densities is used :G PD qE e
Modelled using Ju and Jd as free parameters
-2' 0.8 GeV for quarks=
-
0 electroproduction on the neutron
Pierre Guichon, private communication (2006)
( ) 0 3( , ) ,3 NT N T T i T+= + +
Amplitude of pion electroproduction :
is the pion isospin
nucleon isospin matrix
0 electroproduction amplitude ( =3) is given by :
( )
( )
0
0
2 1,3
3 3
1 2,3
3 3
T T T
T
p
T Tn
u d
u d
+
+
= + +
= +
Polarized parton distributions in the proton
( ) ( )( )
,3 ,3 3 31.15
,3
/
/2
dpT
d
nT u
T up +
+ +
-
Triple coincidence analysis
One can predict for each (e, ) event the Proton Array block where the
missing nucleon is supposed to be (assuming DVCS event).
-
Triple coincidence analysis
PA energy cut (MeV)0 10 20 30 40 50 60
rela
tive
asy
mm
etry
(%
)-60
-50
-40
-30
-20
-10
0
10
20 1 predicted block
9 predicted blocks
25 predicted blocks
PA energy cut (MeV)0 10 20 30 40 50 60
rela
tive
asy
mm
etry
(%
)
-5
0
5
10
15
20 1 predicted block
9 predicted blocks
25 predicted blocks
Re
lative
asym
me
try (
%)
Re
lative
asym
me
try (
%)
PA energy cut (MeV)
PA energy cut (MeV)
After accidentals subtraction
neutrons selection
protons selection
-proton-neutron conversion in
the tagger shielding
- accidentals subtraction
problem for neutrons
p-DVCS events (from LD2
target) asymmetry is stable
-
hEntries 41118Mean -1.57RMS 6.12
time (ns)-30 -25 -20 -15 -10 -5 0 5 10 15 200
500
1000
1500
2000
2500
3000
3500
4000
hEntries 41118Mean -1.57RMS 6.12
= 1. nsσ
Time spectrum in the tagger(no Proton Array cuts)
-
0 contamination subtraction
One needs to do a 0 subtraction if the only (e, ) system is used
to select DVCS events.
Symmetric decay: two distinct photons are detected
in the calorimeter No contamination
Asymmetric decay: 1 photon carries most of the 0
energy contamination because DVCS-like event.
-
0.070.130.330.380.7
0.070.170.420.540.5
0.060.240.560.820.3
0.040.380.811.340.1
Proton Target
Proton
2 ( )p
F t 1 ( )p
F t ( )1 2( ) ( ) /(2 )p p B BF t F t x x+ 2 2( / 4 ) ( )p
t M F tt
t=-0.3
0.980.701.13Proton
Target H %H E
Goeke, Polyakov and Vanderhaeghen
Model:
2 22 GeV
0.3
0.3
B
Q
x
t
=
=
=
( )1 1 2 22( ) ( ) ( ) ( )2 4B
B
x tA F t F t F t F t
x M= + + %HHE
( )1 1 2 22( ) ( ) ( ) ( )2 4
0.34 0.17 + 0.06
B
B
x tA F t F t F t F t
x M
A
= + +
= +
%HHE
-
DVCS polarized cross-sections
-
Calorimeter energy calibration
We have 2 independent methods to check and correct
the calorimeter calibration
1st method : missing mass of D(e,e’ -)X reaction
By selecting n(e,e’ -)p events, one can
predict the energy deposit in the
calorimeter using only the cluster position.
a minimisation between the
measured and the predicted
energy gives a better calibration.
2
2nd method : Invariant mass of 2 detected photons in the calorimeter ( 0)
0 invariant mass position check the
quality of the previous calibration for
each calorimeter region.
Corrections of the previous
calibration are possible.
Differences between the results of the 2 methods introduce a
systematic error of 1% on the calorimeter calibration.
-
eD e X
p-DVCS and
n-DVCS
MN2
MN2 +t/2
d-DVCS
Analysis method
0e X XeD e
Contamination by
Mx2 cut = (MN+M )
2
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