Deeply Virtual Compton Scattering on the neutron

Slides by Malek MAZOUZ

June 21st 2007

Physics case

n-DVCS experimental setup

Analysis method

Results and conclusions

For JLab Hall A & DVCS collaborations

Hall A Meeting

Deeply Virtual Compton Scattering

DVCS is the simplest hard exclusive process involving GPDs

kk’

q’

GPDsp p’

Factorization theorem in the Bjorken regime

222

2222

)'(

)'(

Qppt

MkkqQ

Non perturbative description by GPDs

1

1

1 1( , ,0) ( , ,0)

2 2q

qq

qq L xdJ xH Ex x

GPDs give an access to quark angular momentum (Ji’s sum rule)

less constrained GPD No link to DIS

DVCS and Bethe-Heitler

The polarized cross-section difference accesses the Imaginary part of DVCS and therefore GPDs at x=±ξ

2 25 5 m( .2 BH DVCS DVCSDVCST )d σ d σ T T T

����

Purely real and fully calculable Small at JLab energies (twist-3 term)

The total cross-section accesses the real part of DVCS and therefore an integral of GPDs over x

5 5 2( , , , ) sin BId σ d σ x Q t m C

��If handbag dominance

1 1 2 22( ) ( ) ( ) ( ) ( )

4I t

C F F t F t F t F tM

H H E

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

H H E

1 1 2 22( ) ( ) ( ) ( )

2 4m I B

B

x tF t F t F tC F t

x M

H H 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

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 E00-110 (p-DVCS) which shows strong indications of handbag dominance at Q2 about 2 GeV2.

Ldt (fb-1)xBj=0.364

Hydrogen

Deuterium

(C. Muñoz-Camacho et al., PRL 97 (2006) 262002)

Experimental apparatus

LH2 / LD2 targetPolarized Electron Beam

Scattered Electron

N

Recoil nucleon detector

Left HRS

Electromagnetic Calorimeter

The experimental resolution is good enough to identify DVCS events with MX

2

Beam energy = 5.75 GeV

Beam polarization = 75%

Beam current = ~ 4 μA

Luminosity = 4. 1037 cm-2.s-1

charged particletagger

eD e X

p-DVCS and n-DVCS

accidentals

MN2

MN2 +t/2

d-DVCS

Analysis method

0e X XeD e Contamination by

Mx2 cut = (MN+Mπ)2

N + mesons(Resonnant or not)

2

0( ) ( )hS N N d N N d

Helicity signal and exclusivity

After :

-Normalizing H2 and D2 data to the same luminosity

-Adding Fermi momentum to H2 data

2 principle sources of systematic errors :

-The contamination of π0 electroproduction on the neutron (and deuteron).

- The uncertainty on the relative calibration between H2 and D2 data

n-DVCS

d-DVCS

Extraction results

Exploration of small –t regions in future experiments might be interesting

d-DVCS extraction results

Deuteron moments compatible with zero at large -t

F. Cano & B. Pire calculationEur. Phys. J. A19, 423 (2004).

PRELIMINARY

Extraction results

Results can constrain GPD models (and therefore GPD E)

n-DVCS extraction results

Neutron contribution is small and compatible with zero

VGG Code : M. Vanderhaeghen, P. Guichon and M. Guidal

GPD model : LO/Regge/D-term=0 Goeke et al., Prog. Part. Nucl. Phys 47 (2001), 401.

PRELIMINARY

VGG CodeGPD model : LO/Regge/D-term=0 Goeke et al., Prog. Part. Nucl. Phys 47 (2001), 401.

Systematic errors of models are not shown

n-DVCS experiment results

n-DVCS is sensitive to Jd

p-DVCS is sensitive to Ju

Complementarity between neutron and

transversally polarized proton measurements

Summary and conclusion

n-DVCS is mostly sensitive to GPD E : the less 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. n-DVCS and d-DVCS contributions are obtained after a subtraction of Hydrogen data from Deuterium data (no recoil detectors needed).

First measurements of n-DVCS and d-DVCS polarized cross-sections difference.

Neutron results can constrain GPD models (GPD E parametrization)

Neutron experiments are mandatory complements to proton ones.

- PRL draft will circulate in the next few weeks

- New proposal for PAC-33 (6 GeV) in preparation (collaborators welcome…!)

Extraction of observables

2

exp exp

2 2

2 2

2

1

2

sin( , , , ) ( ,m s, , ) inmI In

B

B

e

B d

B

d e

e

e nx x

d d

d

C C

Q dx d d d dQ dx d d d

��

exp exp

( )

( ) .sin .sinm m

e e

e e

I In n

Expe i i

Mdi d

Ce x x i

N i N N

N i L Acc A cC cC

MC sampling MC sampling

MC includes real radiative corrections (external+internal)

2

22

( ) ( )

( )e

Exp MCe e

Expi

e

N i N i

i

Luminosity

exp

exp

m

m

In

Id

C

C

Analysis method

eD e X eH e X

accidentals accidentals

( , ' ) ( , ' ) ( , ' ) ( , ' )D e e X p e e p n e e n d e e d

p-DVCS events

n-DVCS events

d-DVCS events

Mesons production

Mx2 cut = (MN+Mπ)2 Mx

2 cut = (MN+Mπ)2

Double coincidence analysis

Hydrogen data

Deuterium data

Deuterium- Hydrogen

simulation

Nb

of C

ount

s

MX2 (GeV2)

Mx2 cut

Helicity signal and exclusivity

After :

-Normalizing H2 and D2 data to the same luminosity

-Adding Fermi momentum to H2 data

2 principle sources of systematic errors :

-The contamination of π0 electroproduction on the neutron (and deuteron).

- The uncertainty on the relative calibration between H2 and D2 data

n-DVCS

d-DVCS

2

0( ) ( )hS N N d N N d

π0 to subtract

π0 contamination subtraction

Mx2 cut =(Mp+Mπ)2

H2 data

Subtraction of 0 contamination (1 in the calorimeter) is obtained from a phase space simulation which weight is adjusted to the experimental 0 cross section (2 in the calorimeter).

π0 contamination subtraction

Unfortunately, the high trigger threshold during Deuterium runs did not allow to record all exclusive π0 events (MX

2<1.15 GeV2)

But : according to the procedure of π0 contamination subtraction, we must have :

H2 data

0

0

( )0. 0.5

( )

e e n

e p

n

p e

with MX

2<1.15 GeV2

0

0

( )0.95 0.06

( )

e e Xsys

e e X

d

p

Actually, we find :

by comparing two samples of high energy π0 in each case

0 0

00.5 1

h

h

n dS e en e ed

S pe ep

0ep ep0 0 0( ) ( )ed ep n ed en p ed ed

Exclusive π0 asymmetry

Well known from H2 data

D2 data H2 data

sin(φ) and sin(2φ) moments

Results are coherent with the fit of a single sin(φ) contribution

Test of the handbag dominance : E00-110

Twist-2 contribution dominates the total cross-section and the cross-section difference.

No Q2 dependence of twist-2 and twist-3 terms

p-DVCS experiment resultsC. Muňoz-Camacho et al., to appear in PRL (2007)

Strong indications for handbag dominance

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

qt

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

n-DVCS polarized cross-section difference

d-DVCS polarized cross-section difference

Prediction from F. Cano and B. Pire.

Eur. Phys. J. A19, 423 (2004)

Experimental results

+

π0 electroproduction on the neutron

Pierre Guichon, private communication (2006)

03( , ) ,3 NT N T T i T

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

Polarized parton distributions in the proton

,3 ,3 3 31.15

,3

/

/2

dpT

d

nT u

T up

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.

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).

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

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.

2

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)