d eeply v irtual c ompton s cattering on the n eutron in
DESCRIPTION
Physics case n-DVCS experimental setup Analysis method Results and conclusions. GPDs. D eeply V irtual C ompton S cattering on the n eutron in. Hall A. C. Hyde-Wright, Hall A Collaboration Meeting. Dr. Malek MAZOUZ Ph.D. Defense, Grenoble 8 December 2006. k’. k. q’. p. p’. - PowerPoint PPT PresentationTRANSCRIPT
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Deeply Virtual Compton Scattering on the neutron in .
Dr. Malek MAZOUZPh.D. Defense, Grenoble
8 December 2006
GPDs
ξ+x ξ−x
t
Physics case
n-DVCS experimental setup
Analysis method
Results and conclusions
C. Hyde-Wright,Hall A
Collaboration Meeting
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How to access GPDs: DVCS
222
2222
)'(
)'(
Qppt
MkkqQ
<<Δ=−=
>>−−=−=
kk’
q’
GPDsp p’
Deeply Virtual Compton Scattering is the simplest hard exclusive process involving GPDs
pQCD factorization theorem
Perturbative description
(High Q² 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
υ
ξ
ξ
= =
=−
± =fraction of longitudinal momentum
Handbag diagram
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ξ
)0,,( ξxH
x
Deeply Virtual Compton Scattering
1
1
( , , )DVCS GPD x tT dx
x i
ξξ ε
+
−∝ +
±∫ Lm
1
1
( , , )( , , ) ...P i
GPD x tGd PDx x
xtξ
ξξ ξπ
+
−± = +
±±= ∫
The GPDs enter the DVCS amplitude as an integral over x :
Real part
Imaginary partDVCS amplitude
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Expression of the cross-section difference
{ }25 5
232 12 2
1 21 2
( , , )1( , , )
2sin( ) sin(2 ) sin( )
( ) ( )DVCSB I I
BB e B e
x Q td dx Q t s
dQ dx dtd d dQ dx dtd ds s
P Pϕ ϕ ϕ
ϕ ϕ
σ σ
φ ϕ φ ϕ
⎡ ⎤ Γ= + + Γ⎢
⎣− ⎥
⎦
r s
{ })()2(81 FII CyKys mℑ−=
{ } { }2 ( , , ) ( , )m ,qq
q
qH te H tξ ξ ξ ξπℑ − −= ∑H
2 25 5 2 m( .BH DVCS DVCS DVCSd ó d ó T T ) T T⎡ ⎤− ≈ ℑ + −⎢ ⎥⎣ ⎦
r sr s
GPDs
If handbag dominance€
C I (H , ˜ H , E) = F1(t)H(ξ ,t)+ ξGM (t) ˜ H (ξ ,t)+−t
4M 2F1(t)E(ξ ,t)
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( ) ( )
( )
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
= ⋅ + ⋅ + ⋅ − ⋅−
ℑ = − −
ℑ
+
%HH E
0.3 -0.91 -0.04 -0.17 -0.07
Neutron Target
2 ( )nF t 1 ( )nF t ( )1 2( ) ( ) /(2 )n nB BF t F t x x+ ⋅ − 2
2( / 4 ) ( )nt M F t− ⋅t−
Target
neutron 0.81 -0.07 1.73
H %H E(Goeke, Polyakov and Vanderhaeghen)
Model:2 2
2
2 GeV
0.3
0.3 GeV
B
Q
x
t
==
− =
€
C I (H , ˜ H ,E) = F1(t)H(ξ ,t)+ ξGM (t) ˜ H (ξ ,t)+−t
4M 2F1(t)E(ξ ,t)
H
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n-DVCS experiment
s (GeV²)
Q² (GeV²)
Pe (Gev/c)
Θe (deg)
-Θγ* (deg)
4.22 1.91 2.95 19.32 18.25 4365
4.22 1.91 2.95 19.32 18.25 24000
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
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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
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Proton tagger
Scintillator S1
Wire chamber HWire chamber M
Wire chamber B
Prototype
Scintillator S2
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Calorimeter in the black box
(132 PbF2 blocks)
Proton Array
(100 blocks)
Proton Tagger
(57 paddles)
4.1037 cm-2.s-1
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Calorimeter energy calibration
2 elastic runs H(e,e’p) to calibrate the calorimeter
Achieved resolution :( )
2.4% at 4.2 GeV ; 2 mmE
xE
σ δ= =
Variation of calibration coefficients during the experiment due to radiation damage.
Cal
ibra
tion
varia
tion
(%
)
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”
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Calorimeter energy calibration
We have 2 independent methods to check and correct the calorimeter calibration
1st method : missing mass of D(e,e’π-)X reaction
Mp2
By selecting n(e,e’π-)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.
2χ
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Calorimeter energy calibration
2nd method : Invariant mass of 2 detected photons in the calorimeter (π0)
π0 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.
Nb
of
coun
ts
Invariant mass (GeV)
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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.
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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+Mπ)2 Mx
2 cut = (MN+Mπ)2
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Double coincidence analysis
1) Normalize Hydrogen and Deuterium data to the same luminosity
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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
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Double coincidence analysisR
esol
utio
n of
π0 in
v. m
ass
(MeV
)
Calorimeter block number
Hydrogen
Deuterium
Nb
of
coun
ts
Invariant mass (GeV)
?
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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
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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 π0 electroproduction under the missing mass cut.
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π0 to subtract
π0 contamination subtraction
Mx2 cut =(Mp+Mπ)2
Hydrogen data
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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 π0 electroproduction under the missing mass cut.
Unfortunately, the high trigger threshold during Deuterium runs did not allow to record enough π0 events.
But :0
0
( )0.95 0.06
( )
e e Xsys
e e X
d
p
σ πσ π
→= ± ±
→
In our kinematics π0 come essentially from proton in the deuterium
No π0 subtraction needed for neutron and coherent deuteron
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Double coincidence analysis
Hydrogen data
Deuterium data
Deuterium- Hydrogen
simulation
Nb
of C
ount
s
MX2 (GeV2)
Mx2 cut
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n-DVCS ?
d-DVCS ?
Double coincidence analysis
N+ - N-
φ (rad)
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Double coincidence analysis
MC Simulation
MC Simulation
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Extraction results
Exploration of small –t regions in future experiments might be interesting
Large error bars (statistics + systematics)
d-DVCS extraction results
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Extraction results
n-DVCS extraction results
Neutron contribution is small and close to zero
Results can constrain GPD models (and therefore GPD E)
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Systematic errors of models are not shown
n-DVCS experiment results
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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.
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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 π0s 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.
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VGG parametrisation of GPDs
( ) ( )11
1 1
( ,( , ), , ) qq qF tx
d d x x DH x tβ
β
β αβ α δ β αξ ξξ θξ
−
− − +
⎛ ⎞= − − + − ⎜ ⎟
⎝ ⎠∫ ∫
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
qt
bb
F
hb
qh
b
t α ββ
β α
α
β
α
β αβ
β
++
=
⎡ ⎤− −Γ + ⎣ ⎦=Γ + −
Double distribution :
Profile function :
Parton distribution
( )for , the spin-flip parton densities is used :G PD qE e β
Modelled using Ju and Jd as free parameters
-2' 0.8 GeV for quarksα =
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π0 electroproduction on the neutron
Pierre Guichon, private communication (2006)
( ) 03( , ) ,3 NT N T T i Tα βαβα δ α τ ε τ+ −= + +
Amplitude of pion electroproduction :
α is the pion isospin
nucleon isospin matrix
π0 electroproduction amplitude (α=3) is given by :
( )
( )
0
0
2 1,3
3 31 2
,33 3
T T T
T
p
T Tn
u d
u d
+
+
= + ∝ +
= − ∝ +
Δ Δ
Δ Δ
Polarized parton distributions in the proton
( ) ( )( )
,3 ,3 3 31.15
,3
/
/2
dpT
d
nT u
T up
Δ
Δ Δ≈
+
Δ+ +≈
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Triple coincidence analysis
One can predict for each (e,γ) event the Proton Array block where the missing nucleon is supposed to be (assuming DVCS event).
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Triple coincidence analysis
Rel
ativ
e a
sym
me
try
(%)
Rel
ativ
e a
sym
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
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Time spectrum in the tagger (no Proton Array cuts)
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π0 contamination subtraction
One needs to do a π0 subtraction if the only (e,γ) 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 π0 energy contamination because DVCS-like event.
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0.1 1.34 0.81 0.38 0.04
0.3 0.82 0.56 0.24 0.06
0.5 0.54 0.42 0.17 0.07
0.7 0.38 0.33 0.13 0.07
Proton Target
Proton
2 ( )pF t 1 ( )pF t ( )1 2( ) ( ) /(2 )p pB BF t F t x x+ ⋅ − 2
2( / 4 ) ( )pt M F t− ⋅t−
t=-0.3
Target
Proton 1.13 0.70 0.98
H %H E
Goeke, Polyakov and Vanderhaeghen
Model:
2 22 GeV
0.3
0.3B
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
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DVCS polarized cross-sections
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Calorimeter energy calibration
We have 2 independent methods to check and correct the calorimeter calibration
1st method : missing mass of D(e,e’π-)X reaction
By selecting n(e,e’π-)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.
2χ
2nd method : Invariant mass of 2 detected photons in the calorimeter (π0)
π0 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.
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eD e X→
p-DVCS and n-DVCS
MN2
MN2 +t/2
d-DVCS
Analysis method
0e X XeD eπ→ →Contamination by
Mx2 cut = (MN+Mπ)2