Deeply Virtual Meson Production
with CLAS and CLAS12
Valery Kubarovsky
Jefferson Lab
Outline
• Physics motivation
• CLAS data on pseudoscalar meson
electroproduction
• f electroproduction with CLAS12
• Conclusion
Description of hadron structure in
terms of GPDs
Nucleon form factors
transverse charge &
current densities
Nobel prize 1961- R. Hofstadter
Structure functions
quark longitudinal
momentum (polarized and
unpolarized) distributions
Nobel prize 1990 –J.Friedman,
H. Kendall, R. Taylor
GPDs
correlated quark momentum
distributions (polarized and
unpolarized) in transverse
space
Generalized Parton
Distributions
• GPDs are the functions of three kinematic
variables: x, x and t
~
• There are 4 chiral even GPDs where partons
~
do not transfer helicity H, H,
E, E~
• 4 chiral odd GPDs flip the parton helicity
HT, H~ T, ET, E~T
• The chiral-odd GPDs are difficult to access
since subprocesses with quark helicity-flip are
suppressed
Basic properties of chiral-even GPDs
• Forward limit
• Form factors
• Angular Momentum
Chiral-odd GPDs
• Very little known about the chiral-odd GPDs
• Anomalous tensor magnetic moment
• (Compare with anomalous magnetic moment)
• Transversity distribution
The transversity describes the distribution of transversely polarized
quarks in a transversely polarized nucleon
 * p  p 0
Structure functions and GPDs
Leading twist sL
Suppressed by a factor coming from:
The brackets <F> denote the convolution
of the elementary process with the GPD F
(generalized formfactors)
Kroll & Goloskokov
Transversity in electroproduction of
pseudoscalar mesons
Leading twist pion wave function
suppressed
Twist-3 pion wave function
suppressed by
, however
(enhanced by chiral condensate)
 * p  p 0
Structure functions and GPDs
sT
sL
t-dependence at t=tmin is
determined by the
interplay between
Transverse Densities for u and d
Quarks in the Nucleon
Strong distortions
for unpolarized
quarks in transversely
polarized nucleon
Strong distortions
for transversely
polarized quarks
in an unpolarized
nucleon
Described by E
_
~ +E
Described by ET=2H
T T
Gockeler et al, hep/lat/0612032
CEBAF Large Acceptance
Spectrometer CLAS
CLAS Lead Tungstate Electromagnetic Calorimeter
424 crystals, 18 RL,
Pointing geometry,
APD readout
CLAS DVMP program
ep ® enp
+
ep ® enr + , r + ® p +p 0
ep ® epp 0 , p 0 ® gg
ep ® epr 0 , r 0 ® p +p -
ep ® eph, h ® gg
ep ® epw , w ® p +p -p 0
ep ® epf , f ® K + K -
CLAS6: lots of data, cross sections, beam-spin asymmetries
CLAS12: Exp. # E12-06-108
 p  p
*
4 Dimensional Grid






Rectangular bins are used.
Q2- 7 bins(1.-4.5GeV2)
xB- 7 bins(0.1-0.58)
t - 8 bins(0.09-2.0GeV)
φ- 20 bins(0-360°)
0 data ~2000 points
h data ~1000 points
Q2
xB
0
Monte Carlo
• Empirical model for the structure cross sections was
used for the MC simulation and radiative corrections
• This model is based on CLAS data
• MC simulation included the radiative effects and
used empirical model for the Born term.
• 100 M events were simulated with GSIM program.
Radiative Corrections
• Radiative Corrections were
calculated using Exclurad
package with structure cross
sections described by our
empirical cross section.
Q2 = 1.15 GeV2
xB = 0.13
-t = 0.1 GeV2
2010/05/14 10.49
0
1.1
1.05
s Rad
RadCor =
s Born
1
0.95
0.9
h
0.85
0.8
0
50
100
150
200
250
300
f
350
Structure Functions
sU=sT+esL sTT sLT
 p  p
*
0
ds
1 ds T
ds L
ds TT
ds LT
2
(Q , x, t , f ) 
(
e
e
cos 2f  2e (e  1)
cos f )
dtdf
2 dt
dt
dt
dt
f distribution
GM Laget Regge model
-t
sU=sT+esL W dependence
sU~1/W1.5-2
1.7847
s, mb
s~1/W
2
4
2
1
1
2
2.5
4
3
3.5
W, GeV
2
Q =2.25 GeV
3
s~1/W
2
2.63324
0
1
1
2.5
4
3
2
3.5
W, GeV
Q =3.25 GeV
3
s~1/W
1.5682
2
0
1
1
4
2
2.5
3
3.5
W, GeV
0
3.5
W, GeV
2
2
2.5
3
2
s~1/W
2
2.5
2
2.23329
3.5
W, GeV
Q =3.75 GeV
3
2
3
Q =2.75 GeV
s~1/W
2
2.09986
2.5
4
2
0
2
3
2
2
s~1/W
4
2
0
2
Q =1.75 GeV
3
2
s, mb
s, mb
2
Q =1.25 GeV
3
0
s, mb
• sU decreases with W at
Jlab kinematics
• This behavior is typical for
Regge model
• Difficult to get such
dependence with
conventional GPD
models
4
s, mb
s, mb
sT+esL
2
1.03482
3
3.5
W, GeV
2
ds *
(g p ® epp 0 ) µ ebt
dt
Q
dsU/dt
4.6
P1
P2
2.021 / 2
5.712
-0.7572
P1
P2
3.177 / 2
5.947
-0.9289
P1
P2
1.674 / 2
6.509
-1.171
10 2
0.09
4.0
P1
P2
3.409 / 4
5.677
-0.9643
10 2
10
0.09
3.5
P1
P2
10
11.76 / 4
5.655
-1.148
3.0
-t
10
GeV2
P1
P2
10
2.196 / 4
6.083
-1.876
10 2
10
0.09
1.5
10
25.19 / 4
5.908
-1.803
2
P1
P2
2
10
2
P1
P2
9.259 / 4
6.211
-1.915
0.09
3
10
2
2
0.09
2
0.09
2
P1
P2
0.8199 / 4
6.276
-1.392
P1
P2
28.45 / 4
6.564
-1.615
0.09
10
2
3
10 2
2
P1
P2
2
P1
P2
P1
P2
16.44 / 4
6.621
-1.245
0.09
10.64 / 4
5.822
-1.349
2
5.005 / 4
6.065
-1.676
0.09
10
9.972 / 4
6.137
-1.024
2
2
13.95 / 4
6.208
-1.922
2
10
2
P1
P2
10
0.09
P1
P2
P1
P2
10
P1
P2
0.09
10 3
10 2
2.232 / 4
5.850
-1.682
2
2
P1
P2
2
0.09
2.5
2.0
22.15 / 4
5.586
-1.352
P1
P2
2
10 2
2
0.09
P1
P2
2
10.53 / 4
5.910
-1.160
2
6.859 / 4
6.455
-1.793
0.09
10 3
2
0.09
2
2
0.09
2
0.09
2
0.2420E-02/ 3
16.23
-39.21
2
1
0.09
1.0
0.1
2
0.09
0.15
2
0.2
0.09
2
0.25
0.3
0.38
0.48
0.58
xB
B
t-slope parameter: xB dependence
ds
bt
µe
dt
2.5
2
Q
2.25
2
2
1.75
1.25GeV
2
1.75GeV
2
2.25GeV
2
2.75GeV
2
3.25GeV
2
3.75GeV
2
4.3GeV
1.5
1.25
1
0.75
0.5
0.25
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
xB
The slope parameter is decreasing with increasing xB. Looking to this picture we can
say that the perp width of the partons with x1 goes to zero.
CLAS data and GPD theory predictions
S. Goloskokov and P. Kroll, S. Liuti and G. Goldstein
•
Include transversity GPDs HT and
. Dominate
kinematics.
ET = 2HTin
+ CLAS
ET
• The model was optimized for low
xB and high Q2. The corrections t/Q2
were omitted
• The model successfully described
CLAS data even at low Q2
• Pseudoscalar meson production
provides unique possibility to
access the transversity GPDs.
h/0
s (ep ® eph )
s (ep ® epp 0 )
Ratio
• The dependence on the xB and
Q2 is very week.
• The ratio in the photoproduction
is near 0.2-0.3 (very close to what
we have at our smallest Q2).
• Conventional GPD models predict this
ratio to be around 1 (at low –t).
• KG model predicts this ratio to be
~1/3 at CLAS values of t
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
0.9
0.8
0.7
-t=0.30 GeV2
0.6
0.5
0.4
0.3
0.2
0.1
0
0.1
0.2
0.3
-t=0.14 GeV2
0.1
0.2
0.3
0.4
xB
-t=0.50 GeV2
0.1
0.2
0.3
0.4
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.4
xB
-t=0.50 GeV2
0.1
0.2
0.3
xB
ET = 2HT + ET
2
Q2=1.3
Q2=1.8
Q2=2.2
Q2=2.7
Q =3.2
0.4
xB
Data: CLAS preliminary
_
Indication of large contributions from the GPD ET
with the same sign for u and d-quark parts
1035
Luminosity
cm
Forward Detector
2
s-1
- TORUS magnet
- Forward SVT tracker
- HT Cherenkov Counter
- Drift chamber system
- LT Cherenkov Counter
- Forward ToF System
- Preshower calorimeter
- E.M. calorimeter
Central Detector
- SOLENOID magnet
- Barrel Silicon Tracker
- Central Time-of-Flight
-Polarized target (NSF)
Proposed upgrades
- Micromegas (CD)
- Neutron detector (CD)
- RICH detector (FD)
- Forward Tagger (FD)
CLAS12
Exclusive f electroproduction
• Verify the approach to the small-size regime
• Q2 and W -dependence of the cross section
• Q2-dependence of the t-slope
• L/T ratio
• Gluonic radius of the nucleon in the valence region
• relative t-dependence as a function of xB
• GPD model to disentangle the gluon momentum
integral
• Intrinsic strangeness
• alternative mechanism near the threshold
b
x
glu
on s
changes with x
Kinematical Coverage
14
14
12
12
10
10
8
8
6
6
4
4
2
2
0
2
3
4
2
0
5
0
0.2
2
Q vs W
0.4
0.6
0.8
9
10
Q vs xB
14
12
10
8
6
4
2
0
0
1
2
3
4
2
5
Q vs -t
6
7
8
sL / sT separation
S-channel helicity conservation (SCHC)
Q2=2.5 GeV2
xB=0.15
R=sL/sT
Measurements of the ratio R=sL/sT over wide range of Q2=2-8 GeV2
at various fixed xB are one of the major goals of the experiment.
dsL/dt in bins of Q2 and xB
exponential and dipole shapes
Projected results for the differential
cross sections assuming two models
• exponential t-dependence
• dipole t-dependence
Q2=2.5, 4.5 and 6.5 GeV2
DQ2=1.0 GeV2
xB=0.35 +/- 0.05
Dt=0.2 GeV2
• The t-slope measures the transverse
area of the interaction region:
• Effective size of the target +
• Size of the produced meson
• Slope at fixed xB should decrease
and become Q2 independent at high
Q2
Transverse spatial distribution of gluons
• Projected data for the
differential cross section in
xB and Q2 bins. The example compares
a dipole like t-dependence with the
exponential shape.
• Extraction the transverse image
corresponding to the average gluon
GPD <Hg> from the t-dependence of
dsL/dt.
• Good statistical accuracy can be
achieved
Extrapolation to point ds/dt|t=0
• The W-dependence of the cross section is sensitive to the exchange
• Extrapolation to the unphysical point t=0 eliminate the threshold effects (tmin)
Summary
— The discovery of Generalized Parton Distributions
has opened up a new and exciting avenue of hadron
physics that needs exploration in dedicated experiments.
— Clear indication in CLAS data strong contribution from
transition
— Within handbag approach
transitions are related
to transversity GPDs
and
— The JLab 12 GeV Upgrade provides tools the explore the
nucleon at a much deeper level
— Exclusive f electroproduction is a clean tool for the
extraction of the glue average radius in the valence region
The Fin
Structure Functions
s U = s T + es L
Lines – Regge model
Data: CLAS preliminary
s TT
s LT
Eve
Kinematic coverage
10 3
2
10
CLAS-6
0
p
10
2
Examples of the 010MC
simulation
0
A(1+Bcos2
f + fCc
p Asym Asin
/(1
10
W=2.75 +/- 0.75 GeV
10
1
0
2t-distribution
4
6
8
10
5
10 4
10 3
2
0.7
4
6
Simulated cross section
Anticipated systematic errors
2.5 %
0.2 %
1.0 %
Radiative
Corrections
1.O %
sU=sT+esL
4.0 %
sL , sT
0.4
0.6
10-30 %
500
400
300
200
100
0.5
A = 4.47e+05 ± 6.63e+02
A=4.5E5+/-6.6E2
BB=0.047/-0.002
= 4.73e-02 ± 2.08e-03
CC=0.200+/-0.002
= 1.94e-01 ± 2.08e-03
0
0.4
f
4
10 3
10
6
8
10
Q24-distribution
2
t=-t1 GeV
p
6
10 5
10 4
10 4
10 3
10
3
10 2
10
2
10 2
8
10
0
2
02
10
24
4 6
-t Q
GeV
GeV 2
2
6 8
8 10 10
0
GeV2
GeV
Simulated beam-spin asymmetry
a = Asin
j / (1+ Bcos2j +C cosj10) 2
10 3
0.3
100
0.2
800.1
Q2=2 GeV2,t=1 GeV2
Xb ®
Xb ®
0.5
Particle ID
s = A(1+ Bcos2j + C cosj )
Error
10
Events/1 GeV
2
-t
Beam Charge
2
10
10
0
Acceptance
0
Events/1 GeV
Events/1 GeV
0.7
Source
10
Q2= 5-t GeV2 GeV
10
0.6
3
Q2=2 GeV2,t=1 GeV2
10 2
10
0
60
10
-0.1A A
9.94e-02
2.04e-03
= =8.10e+04
±4 ±9.49e+02
0
2
6
8
10
A=0.100+/-0.002
2
40
-0.2
Q
GeV
4.89e-02± ±1.24e-02
2.71e-02
BB
= =5.31e-02
B=0.049+/-0.030
-0.3
20 C C
=1.80e-01
2.12e-01
2.77e-02
± ±1.97e-02
-0.4 =C=0.210+/-0.030
0.3 0
2000
f
2
0
DVCS and DVMP
• Factorization theorem
• Access to fundamental degrees of
freedom
DVCS:
• the clearest way to access the GPDs
• Only T photons participate in DVCS
• Interference with BH process
DVMP:
• Factorization proven only for sL
sL~1/Q6, sT/sL~1/Q2
• Meson distribution amplitude
• Gluon exchange required
• Vector and pseudoscalar meson production
allows to separate flavor and separate the
helicity-dependent and helicity independent
GPDs.
~ ~
H, E
H, E
Transition from “hadronic” to the partonic
degrees of freedom
*
M
*L
M
p
p’
?
R
p
p’
 p  p
*
Regge Model
J.M. Laget 2010
(a) Regge poles (vector and axial vector mesons)
(b) and (c) pion cuts
Vector meson cuts
0
dsU/dt
nb/GeV2
-t
GeV2
JML Regge model s U = s T + es L
s TT
Q2 = 2.25 GeV2
xB = 0.34
sT + esL
sLT
-t
s LT
sTT
DVCS and DVMP
in leading twist
• Factorization theorem
• Access to fundamental degrees of
freedom
DVCS:
• the clearest way to access GPDs
• Only T photons participate in DVCS
• Interference with BH process
DVMP:
• Factorization proven only for sL
sL~1/Q6, sT/sL~1/Q2
• Meson distribution amplitude
• Gluon exchange required
• Vector and pseudoscalar meson production allows to separate flavor and
separate the helicity-dependent and helicity independent GPDs.
Transversity in hard exclusive
electroproduction of pseudoscalar
mesons
S. Goloskokov, P. Kroll, 2011, arXiv:1106.4897v1
• The data clearly show that a leading-twist calculation of DVMP
within the handbag is insufficient. They demand higher-twist and/or
power corrections
• There is a large contribution from the helicity amplitude M 0-,.
Such contribution is generated by the the helicity-flip
or transversity GPDs in combination with a twist-3 pion wave
function
• This explanation established an interesting connection to
transversity parton distributions. The forward limit of HT is the
transversity
M 0-,~ HT
H (x, 0, 0) = h (x)
q
q
T HT(x,0,0)=h1(x) 1
Nucleon Tensor Charge from Exclusive 0
Electroproduction
*
 p  p 0
Ahmad, Goldstein, Luiti, Phys. Rev. D 79, 054014 (2009), arXiv:1104.5682v1
• The quantum numbers and Dirac structure of π0 electroproduction restrict the
possible contributions to the 4 chiral odd GPDs, one of which, HT , is related to the
transversity distribution and the tensor charge.
• This differs from DVCS and both vector and charge /- electroproduction, where
the axial charge can enter the amplitudes.
• Contrary the tensor charge enters the 0 process.
partonic degrees of
freedom interpretation;
t-channel exchange
diagram
Structure functions and GPDs
Leading twist sL suppressed :
The brackets <F> denote the convolution
of the elementary process with the GPD F
(generalized formfactors)
Kroll & Goloskokov
Transverse Densities for u and d
Quarks in the Nucleon
Strong distortions
for unpolarized
quarks in transversely
polarized nucleon
Strong distortions
for transversely
polarized quarks
in an unpolarized
nucleon
Controlled by E
_
~ +E
Controlled by ET=2H
T T
Gockeler et al, hep/lat/0612032
 * p  p 0
Structure functions and GPDs
Leading twist sL suppressed :
The dominant contributions to the cross section are coming from
The brackets <F> denote the convolution
of the elementary process with the GPD F
(generalized formfactors)
Kroll & Goloskokov
The transversity describes the distribution of transversely polarized
quarks in a nucleon transversely polarized with respect to
the direction of the hard probe, i.e., the virtual photon γ∗.
It is the most difficult one to measure.
The transversity distribution was first mentioned by Ralston and Soper [39],
but re- mains unmeasured until the
recent HERMES measurement [40].
The reason is that the transversity is a
chiral–odd object, which requires the combination
with another chiral– odd object in helicity
conserving process. Hence, unlike the other two,
it is inaccessible in inclusive measurement of DIS
ep ® epp
ep ® eph
0
E12-06-108
Hard Exclusive Electroproduction of
0 and h with CLAS12
• Cross sections of the reactions ep ➝ ep0, ep ➝eph
• Extract structure functions sT+esL, sTT, sLT sLT’ vs.
Q2, xB, t
– Fourier decomposition of the reduced cross section
sT+esL, sTT, sLT
– Beam-spin asymmetry sLT’
• Handbag - 3D nucleon tomography
– transversity GPDs HT and ET = 2HT + ETdata.
– Backward pion production (high-t, low-u). Transition
distribution amplitudes.
CLAS6 data
CLAS12 Kinematic Coverage
CLAS-6
Statistics
W=2.75 +/- 0.25 GeV
Q2-distribution
Dt= 2 GeV2
t-distribution
DQ2= 2 GeV2
p
5
10 5
10
4
10
4
10 3
10
3
10
Events/1 GeV
10
p
10 2
2
10
10
4
6
-t
10
8
10
0
2
4
8
5
10
4
10 3
10
10
10
2
4
10 4
10 3
10 3
10 2
10
2
0
10
2
4
6
Q
10 3
2
5
-t
GeV
10 4
6
Events/1 GeV
2
10
10
1
0
10 6
2
8
10
0
2
4
6
8
10
6
8
10
2
Q
GeV
10 2
10 3
10 2
10
10
10
0
2
4
6
-t
8
10
GeV
0
2
4
6
-t
8
10
10
0
2
4
6
Q
2
8
10
GeV
0
2
4
2
Q
7
Example of the Simulated Cross
Section and Asymmetry
0.7
6
4
3
Simulated beam-spin asymmetry
s = A(1+ Bcos2j + C cosj )
a = Asin j / (1+ Bcos2j +C cosj )
0.6
500
¬ Xb ®
5
Simulated cross section
400
0.5
A=4.5E5+/-6.6E2
300
A = 4.47e+05 ± 6.63e+02
200
BB=0.047/-0.002
= 4.73e-02 ± 2.08e-03
100 CC=0.200+/-0.002
= 1.94e-01 ± 2.08e-03
12
0.4
10
8
0.3
6 A = 9.99e+06 ± 4.05e+03
4 B = 4.72e-02 ± 5.73e-04
0.3
100
0.2
800.1
0
60
-0.1A A
9.94e-02±±9.49e+02
2.04e-03
= =8.10e+04
40
-0.2 A=0.100+/-0.002
4.89e-02± ±1.24e-02
2.71e-02
BB
= =5.31e-02
-0.3 B=0.049+/-0.030
20 C C
=1.80e-01
2.12e-01
2.77e-02
± ±1.97e-02
-0.4 =C=0.210+/-0.030
0.3
2000
0.2
15000.1
0
-0.1
1000
9.83e-02±±2.36e+03
5.62e-04
AA
= =1.54e+06
-0.2
B = 5.96e-02 ± 7.68e-03
-0.3B = 4.65e-02 ± 2.00e-03
500
0.3
0.2
0.1
0
-0.1 AA==1.03
1.1
8000
-0.2
6000 BB==5.01
-1.5
-0.3
4000
2.8
-0.4 CC==1.58
2000
0.3
180
0.2
160
0.1
140
1200
100
-0.1
A = 9.7
80 A = 1.43
-0.2
60 B = 8.4
-0.3 B = 4.87
40
sU=sT+esL xB dependence
4
P1
P2
3
4.007 / 1
0.2443
-4.410
s, mb
s, mb
sT+esL
2
2
Q =1.25 GeV
0.1
0.2
0.3
0.4
0
0.5
xB
4
P1
P2
3
0.3209 / 2
0.3792
-2.617
2
2
Q =2.25 GeV
2
Q =1.75 GeV
0.1
0.2
2
0.3
0.4
0.5
xB
4
P1
P2
3
0.1
0.2
1
2
0.3
0.4
0
0.5
P1
P2
3
0.3105 / 1
0.2167
-1.240
s, mb
xB
4
2
1.080 / 1
0.3931
-1.956
2
Q =2.75 GeV
0.1
0.2
2
0.3
0.4
0.5
xB
4
P1
P2
3
0.000 / 0
0.1020
-0.7843
2
1
0
1.049 / 2
0.2485
-2.966
2
1
0
3
1
2
s, mb
s, mb
0
P1
P2
2
1
s, mb
• Another way to view the
cross section as a
function of xB
• sU increases with xB
• W=Q2(1/x-1)
4
2
Q =3.25 GeV
0.1
0.2
0.3
1
2
0.4
0
0.5
xB
2
Q =3.75 GeV
0.1
0.2
0.3
2
0.4
0.5
xB
Transversity in 0 electroproduction
S. Goloskokov, P. Kroll, 2011
G. Goldstein, S. Liuti, 2011
sT
sLT
sTT
sL
Theory: Goloskokov&Kroll
Transvers cros section
domunates in this model
s T + es L
Data CLAS