deeply virtual compton scattering on the neutron in. dr. malek mazouz ph.d. defense, grenoble 8...

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

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

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

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)

( ) ( )

( )

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

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

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 HWire chamber M

Wire chamber B

Prototype

Scintillator S2

Calorimeter in the black box

(132 PbF2 blocks)

Proton Array

(100 blocks)

Proton Tagger

(57 paddles)

4.1037 cm-2.s-1

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”


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


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)

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+Mπ)2 Mx

2 cut = (MN+Mπ)2


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 analysisR

esol

utio

n of

π0 in

v. m

ass

(MeV

)

Calorimeter block number

Hydrogen

Deuterium

Nb

of

coun

ts

Invariant mass (GeV)

?






- Add nucleon Fermi momentum in deuteron to Hydrogen events







3) Remove the contamination of π0 electroproduction under the missing mass cut.

π0 to subtract

π0 contamination subtraction

Mx2 cut =(Mp+Mπ)2

Hydrogen data







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


Hydrogen data

Deuterium data

Deuterium- Hydrogen

simulation

Nb

of C

ount

s

MX2 (GeV2)

Mx2 cut

n-DVCS ?

d-DVCS ?


N+ - N-

φ (rad)


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 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.

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 =

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+ +≈


One can predict for each (e,γ) event the Proton Array block where the missing nucleon is supposed to be (assuming DVCS event).


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

Time spectrum in the tagger (no Proton Array cuts)

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.

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

DVCS polarized cross-sections


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.

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

deeply virtual compton scattering on the neutron in. dr. malek mazouz ph.d. defense, grenoble 8...

Documents

calibration hydrogen

deuterium data

resolution slide

calorimeter calibration

luminosity slide

dvcs amplitude slide

h slide

hydrogen events