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14 Νοε 2013 (πριν από 3 χρόνια και 7 μήνες)

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A few basic definitions/features of GPDs

Extracting the GPDs (CFFs)

Review of the data
(JLab, HERMES)

First extractions of the
H
Re
,
H
Im

and

H
Im

CFFs

~

A few basic definitions/features of GPDs

Extracting the GPDs (CFFs)

Review of the data
(JLab, HERMES)

First extractions of the
H
Re
,
H
Im

and

H
Im

CFFs

~


Interpretation


Structure
function

)
(
),
(
1
1
x
g
x
f
ep
a




Diagramme


Process

(
restricting

myself

to LT
-
LO, chiral
even
, quark
sector
)

y

xp
x

z

)
(
),
(
),
(
),
(
2
1
t
G
t
G
t
F
t
F
P
A
ep
a



y

x

z

b

)
,
,
(
~
),
,
,
(
~
),
,
,
(
),
,
,
(
t
x
E
t
x
H
t
x
E
t
x
H




ep
a


g

xp
x

z

b

g*

p

p’

g,M,...

H,E,H,E

~

~

x

t

Deconvolution needed !

x
: mute variable


~
x
B

H
q
(
x
,

,
t
⤠扵琠潮汹

慮搠
t

慣捥獳楢i攠數灥物浥湴慬汹

d
s


d


d
t

B

~

A


H (
x
,

,
t
)

q

x
-

+
i
e

d
x

+B


E (
x
,

,
t
)

q

x
-

+
i
e

d
x
+….

1

1

-
1

-
1

2


=

x

B

1
-
x

/2

B

t
=(p
-
p

’)

2

x
=
x
B

!

/2



+

+

+



+
+

1
1
1
1
)
,
,
(
)
,
,
(
~
)
,
,
(
~


t
H
i
dx
x
t
x
H
P
dx
i
x
t
x
H
T
DVCS





e


Cross
-
section measurement

and beam charge asymmetry (Re
T
)

integrate GPDs over
x

Beam or target spin asymmetry

contain only Im
T,

therefore GPDs at
x
=

and



(at leading order:)

The VGG model/code

M. Vanderhaeghen, P. Guichon, M.G., PRL80, 5064 (98)

Models
GPDs and calculates
amplitudes/observables

(
s
tot
,
d
s
/
dx
,
BSA, BCA
,…)

for
eN

a

eN
g
,

eN
a
eNM
(
r
0,
m
,

0,
m
,h
,…),
eN
a
e
D
,…

M. Vanderhaeghen, P. Guichon, M.G., PRD 60, 094017 (99)

K. Goeke, M. Polyakov, M. Vanderhaeghen, PPNP 47, 401 (01)

M. G., M. Polyakov, A. Radyushkin, M. Vanderhaeghen, PRD 72, 054013 (05)

Inputs of Radyushkin
(DDs)
, Weiss&Polyakov
(D
-
term)
,

Kivel
(twist
-
3)
, Pentinen&Polyakov (
pion pole contribution

E)
,…

~

(x,

⤠摥灥湤敮捥›⁄潵扬攠䑩獴物扵瑩t湳

Satisfies relations with DIS and polynomiality

(Radyushkin,VGG model)



2
2
b
+1
G(2
b
+1
)(1
-
|
b
|)
2
b
+1

H
q
(x,
,
0)~ d
b

d
a d(
x

b

a)
DD
q
(
a,b
)

With :

and

DD
q
(
a,b
,t)=h
b
(a,b
) q(
b
)

h
b
(
a,b
)=
G(2
b
+2
)[(1
-
|
b
|)
2
-
a
2
]
b

(Radyushkin, Muller, Polyakov,VdH, M.G.)

(x,
,
t

⤠摥F敮摥湣攠e⁒杧敩穥搠䑯a扬攠䑩獴物畴u潮s

DD
q
(
a,b
,t)=q

(
b
) h
b
(a,b
)
b
-
a

(1
-
b
)t

x

b

(GeV
-
1
)

H
u
(x,b )

y

xp

z
d
x

z

b

Satisfies Form Factors sum rule and polynomiality

g

f

leptonic

plane

hadronic

plane

N’

e’

e

(
)
dx
x
x
t
x
H
t
x
H
P
Re
q
q

+






+
+




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




2
q
e


H


)
,
,
(
)
,
,
(
q
t
H
t
H
Im
q
q








2
q
e


H
Im
{
H
n
,
E
n
,
E
n
}

Unpolarized

beam,
longitudinal

target
(
lTSA
)
:

Ds
UL

~
sin
f
Im
{F
1
H
+

(F
1
+F
2
)(
H

+
x
B
/2
E
)


kF
2

E
+…
}
d
f

~

Im
{
H
p
,
H
p
}

~

~

~

Polarized
beam
,
longitudinal

target
(
BlTSA
)
:

Ds
LL

~
(
A+B
cos
f
)
Re
{F
1
H
+

(F
1
+F
2
)(
H

+
x
B
/2
E
)…
}
d
f

~


Re
{
H
p
,
H
p
}

~



Re
{
H
n
,
E
n
,
E
n
}

~

Unpolarized

beam,
transverse

target
(
tTSA
)
:

Ds
UT

~
cos
f
Im
{k(F
2
H



F
1
E
) + …..

}
d
f


Im
{
H
p
,
E
p
}

Im
{
H
n
}


=
x
B
/(
2
-
x
B
) k
=
-
t/4M
2

Ds
LU

~
sin
f

Im
{F
1
H

+

(F
1
+F
2
)
H

-
kF
2
E
}
d
f

~

Polarized
beam
,
unpolarized

target
(BSA)
:


Im
{
H
p
,
H
p
,
E
p
}

~


Im
{
H
n
,
H
n
,
E
n
}

Proton

Neutron

~

Extracting GPDs from DVCS observables

A few basic definitions/features of GPDs

Extracting the GPDs (CFFs)

Review of the data
(JLab, HERMES)

First extractions of the
H
Re
,
H
Im

and

H
Im

CFFs

~


Given the well
-
established
LT
-
LO

DVCS+BH amplitude

DVCS

Bethe
-
Heitler

GPDs


8

unknowns

(the
CFFs
), non
-
linear

problem
,
strong

correlations

Obs=Amp(DVCS+BH)
CFFs


Can one recover the
CFFs

from data ?


Model
-
independent fit, at fixed
x
B
,
t

and
Q
2
,




of DVCS observables with



MINUIT + MINOS

(in practice,
E
Im

set to
0
)


~

DVCS : golden

Channel

Anticipated

Leading Twist

dominance

already at low Q
2

In
general
,
8

GPD
quantities

accessible


(Compton
Form

Factors
)


Given the well
-
established
LT
-
LO

DVCS+BH amplitude

DVCS

Bethe
-
Heitler

GPDs


7

unknowns (the CFFs), non
-
linear problem, strong correlations

M.G. EPJA 37 (2008) 319

M.G. & H. Moutarde, EPJA 42 (2009)
71

M.G. PLB 689 (2010) 156

M.G
. PLB 693 (2010) 17



Only

3

CFFs

come out
from

the fit
with

finite

error

bars:







H
Im

,
H
Im

and
H
Re


~

Obs=Amp(DVCS+BH)
CFFs


Can one recover the
CFFs

from data ?


Model
-
independent fit, at fixed
x
B
,
t

and
Q
2
,




of DVCS observables with



MINUIT + MINOS

Other

approach
:


Assume a
functionnal

shape

and

fit
some

parameters


*D. Mueller

& K.
Kumericki

*H. Moutarde

*VGG by the

HERMES and

n
-
DVCS Hall A
coll.

(
slide

from


K.
Kumericki
,

Photons11)

The experimental actors

p
-
DVCS

BSAs,lTSAs


p
-
DVCS

(
Bpol
.) X
-
sec

Hall B

Hall A

JLab

CERN

COMPASS

p
-
DVCS

X
-
sec,BSA,BCA
,

tTSA,lTSA,BlTSA


p
-
DVCS

X
-
sec,BCA


p
-
DVCS

BSA,BCA,

tTSA,lTSA,BlTSA

H1/ZEUS

HERMES

DESY

(
)
2
2
'
'
q
k
p
k
M
X


+

LH
2

/ LD
2

target

Polarized Electron Beam

g

N

Nucleon

Detector

Left HRS

Charged

Particle

Tagger

Electromagnetic Calorimeter

HALL A

DVCS@JLab

ep ep
g

H(e,e’
g
)X

H(
e,e’
g
p
)

H(e,e’
g
)X
-

H(e,e’
gg
’)X'

H(e,e’
g
)N


DVCS : exclusivity


Good resolution : no need for the proton array


Remaining

contamination 1.7%

HRS+calorimeter

ep
-
> ep
g

ep
-
> ep

0

0
-
>
gg

ep
-
> ep

0
g

ep
-
> ep

0
N




HRS+calorimeter + proton array

Unpolarized


cross sections

JLab Hall A Collaboration, PRL 97:262002,2006


DVCS

Bethe
-
Heitler

GPDs

Difference of
(beam
-
)
polarized


cross sections

Hall A

:
s


Ds
z0

,
x
B
=0.36,Q
2
=2.3,t=.17,.23,.28,.33


c
2
=1.01

c
2
=0.92

c
2
=1.44

c
2
=2.31

Result of the (model independent) fit

M.G. EPJA 37 (2008) 319


Bounds (for ALL CFFs):

{
-
3,3}, {
-
5,5}, {
-
7,7} x VGG


H
Im


H
Re

VGG prediction

Result of the (model independent) fit

M.G. EPJA 37 (2008) 319


H
Im


H
Re

e’

p


ep
a


g

g

420 PbWO
4

crystals

:
~10x10 mm
2
, l=160 mm


Read
-
out :
APDs

+
preamps

JLab/ITEP/

Orsay/Saclay

collaboration


HALL B

DVCS@JLab

Without

the
electromagnetic

calorimeter
:

γ

π
0

ep


epX CLAS 4.2 GeV

Phys.Rev.Lett.87:182002,2001


Selection of the DVCS final state

Exclusivity cuts:



P
X
T

< 90 MeV/c (150 MeV/c) [ep
→ep
g
X]



Cone angle
a
(
g
X

) <1.2
°

(2.7
°
) [ep

epX

]



Coplanarity angle between (
g
p) et (
g
*
p)<
±
1.5
°

(
±
3
°
)



E
X

< 300 MeV (500 MeV)

ep

0
→ep
g
(
g
⤠F慣歧~潵d

捡c捵污瑥搠w楴栠䵯湴M䍡牬C

獩浵污瑩潮s慮~數灥e業i湴慬n



0
→ep
gg

data:
5%

on average

CLAS DVCS BSAs

CLAS DVCS
l
TSAs


縰⸱~,
-
瑾〮㌱ⱑ
2
~1.82

Can
we

extract

(in a model
-
independent

way
)
some

CFFs

from

fitting

(
simultaneously
)


the CLAS DVCS
BSAs

and
TSAs

?

(
at

approximatively

the
same

kinematics
)

CLAS DVCS BSAs

CLAS DVCS
l
TSAs


縰⸱~,
-
瑾〮㌱ⱑ
2
~1.82 (average)

Can
we

extract

(in a model
-
independent

way
)
some

CFFs

from

fitting

(
simultaneously
)


the CLAS DVCS
BSAs

and
TSAs

?

(
at

approximatively

the
same

kinematics
)

CLAS DVCS BSAs

CLAS DVCS
l
TSAs


縰⸱~,
-
瑾〮㌱ⱑ
2
~1.82 (average)

Can we extract (in a model
-
independent way)
some
CFFs

from fitting
(simultaneously)


the CLAS DVCS
BSAs

and
TSAs

?

(at approximately the same kinematics)

CLAS DVCS BSAs

CLAS DVCS
l
TSAs


縰⸱~,
-
瑾〮㌱ⱑ
2
~1.82 (average)

Can we extract (in a model
-
independent way)
some
CFFs

from fitting
(simultaneously)


the CLAS DVCS
BSAs

and
TSAs

?

(at approximately the same kinematics)

VGG

prediction

Fit with
7 CFFs

(boundaries
5xVGG CFFs
)

Fit with
7 CFFs

(boundaries
3xVGG CFFs
)

Fit with
ONLY

H

and
H

~

t
-
dependence at fixed

x
B


of

H
Im

&

H
Im

~

Axial

charge more concentrated than


electromagnetic

charge ?

M.G. PLB 689 (2010) 156

p
-
DVCS

BSA
,
BCA,
lTSA
,
tTSA
,
BlTSA


A.
Airapetian

et al.,
JHEP 0806, 066 (2008)

A.
Airapetian

et al.,
JHEP 0911, 083 (2009)

A.
Airapetian

et al.,
JHEP 1006, 019 (2010)

p
-
DVCS

BSA
,
BCA,
lTSA
,
tTSA
,
BlTSA


A.
Airapetian

et al.,
JHEP 0806, 066 (2008)

A.
Airapetian

et al.,
JHEP 0911, 083 (2009)

A.
Airapetian

et al.,
JHEP 1006, 019 (2010)

(
slide

from

M. Murray, Baryons10)

Analysis

of data
with

recoil


detector in
progress

VGG prediction

Result of fit

17

out of
23


F
moments



Bounds
:


{
-
3,3} x VGG


{
-
5,5} x VGG


{
-
7,7} x VGG


{
-
10,10} x VGG

Average

kinematics

x
B
=0.09,Q
2
=2.5

M.G
. & H.
Moutarde


EPJA 37 (2008)
319

M.G.
PLB 693 (2010) 17

VGG

prediction


{
-
5,5} x VGG

Bounds
:


{
-
3,3} x VGG

* «

Shrinkage

»


of
H
Im

*
H
Im
>
H
Re

As energy

increases:

JLab

(Hall A)

x
B
=0.36,Q
2
=2.3

*Different


t
-
behavior for


H
Im
&
H
Re

(model
dependent


Fit of

D. Muller, K.
Kumericki

Hep
-
ph 0904.0458

HERMES


H
Im



H
Re


H
Im



H
Re

x
B
=0.09,Q
2
=2.5

Fitting

the
Hall A
s
,
Ds


䡅e䵅M

䉓䅳
&
䉃Bs
:

x

b

(GeV
-
1
)

H
u
(x,b )

y

xp

z
d
x

z

b

x
B

dependence at fixed t

x
B

dependence at fixed t

x
B

dependence at fixed t

x
B

dependence at fixed t

x
B

dependence at fixed t

x
B

dependence

at

fixed

t

(
slide

from

K.
Kumericki
, Photons11)

First CFFs model independent fits
(leading
-
twist/leading order
approximation);
“Minimal theoretical input”

Procedure tested by
Monte
-
Carlo

Relatively large uncertainties on extracted CFFs

(due to lack of observables
-
and precision on data
-
)

Introducing more theoretical input will reduce

uncertainties
(but model dependency)

Large flow of new observables and data expected soon;

will bring much more experimental constraints to extract

CFFs with
minimum theoretical input

Procedure is working on
real data
;

extraction of
H
im
,
H
Re

and
H
Im

at
JLab

(cross sections)

and HERMES
(asymmetries)

energies

~