1. Deeply Virtual Meson Production
Cynthia Hadjidakis
6th research conference on
Electromagnetic Interactions with Nucleon and Nuclei
Milos, September, 2005
Generalized Parton Distributions
Experimental results
Future measurements

2. Hard exclusive meson production
GPDs
Hard exclusive meson production
4 Generalized Parton Distributions (GPDs)
H H conserve nucleon helicity
E E flip nucleon helicity
Vector mesons
(r, w, f)
Pseudoscalar
mesons (p, h) ~
-2 x
x+x
x-x
GPDs depend on 3 variables: x, x, t t
for each quark flavour Hq, for gluon Hg
Add gluon exchange diagram: ZEUS ρ0
2u+d, 9g/4 ω
2u-d, 3g/4 f
s, g ρ+
u-d
quark flavour decomposition possible
from meson production
Ji sum rules 1
30%(DIS)
( H(x,x,t=0) + E(x,x,t=0) ) x dx = Jquark
=1/2 DS + D Lz -1

3. Factorization for hard meson production
GPDs
Factorization for hard meson production Q2
Q2>>, t<<
wave function for meson production: additional information/uncertainty
hard scale t
factorization for longitudinal photons only
sT suppressed by 1/Q2 → at large Q2, sL dominates
for fixed xB and t
asymptotically
« scaling law »

4. Experimental facilities
DESY: H1, ZEUS, HERMES:
27.5 GeV e+
H1, ZEUS collider
 10-4<xB<0.021: gluons in the proton
 distinct signature
H1, ZEUS: p (920 GeV)
Exclusive processes measurement requirements:
high luminosity  s~1/Q4, 1/Q6
high Q2  hard regime
high resolution  exclusivity
HERMES: p , d
fixed target experiments
COMPASS, HERMES
 0.006/0.02<xB<0.3: gluons/valence and sea quarks
CLAS
0.15<xB<0.75: valence quarks
signature of exclusive process
with missing mass/energy technique
CERN SPS: Compass
160 GeV m+
Compass: d
missing energy ep→er0X
Jlab: CLAS
up to 5.7 GeV e-
CLAS: p
kinematics
DE = (M2X-M2p)/2Mp

5. Vector Mesons cross sections transverse target spin asymmetry  H, E
~ | ∫ dx H(x,x,t) + E(x,x,t) |2
E kinematically suppressed at low t
H = double distribution ~ q(x)/G(x) with skewing effect
factorized t-dependence (ebt with slope from data)
transverse target spin asymmetry
AUT~ Im( H .E )
E = double distribution ~ sensitive to Jq
factorized t-dependence (dipole form factor)
higher order corrections cancel: scaling region reached at lower Q2

6. Total cross section vs W at HERA
VECTOR MESONS s
 Hg, Eg
Total cross section vs W at HERA
s ~ Wd(Q2) with d=0.7
no dependence on Q2
 hard scale provided by MJ/Y
J/Y
 general transition to hard behaviour at
high Q2+M2 r
r, f, J/Y

7. GPD based model comparison
VECTOR MESONS s
 Hg, Eg
GPD based model comparison
GPD combined with Modified Perturbative Approach
corrections to LO: quark transverse momenta, Sudakov suppression
NLO calculations for sL
[Ivanov et.al. (2004)]
[Goloskokov et.al. (2005)] r0 r0
M=MRST2001 C=CTEQ6M
different renormalization scale mR
calculations of sL, sT, sTL, sTT

8. r0 → p+p- angular distributions: extraction of sL
VECTOR MESONS s
 H, E
r0 → p+p- angular distributions: extraction of sL
if SCHC holds (VM retains g* helicity):
from polarized lepton beam:
→ weak violation of SCHC
COMPASS 02/03 6 times more statistics expected (sL , f, w)
HERMES times more statistics expected

9. r0 → p+p- angular distributions: extraction of sL
VECTOR MESONS s
 H, E
r0 → p+p- angular distributions: extraction of sL f p’
Definitions :
in g*-p CM frame
if SCHC holds (VM retains g* helicity): m’ p g* m r° p+ F
in r° rest frame q
2002 p-
→ at Q2 = 2 GeV2, sL=sT

10. Cross sections at HERMES
VECTOR MESONS s
 Hq, Eq
Cross sections at HERMES
[EPJC17,2000]
[Vanderhaegen et.al. (1999)]
corrections to LO: quark transverse momenta
quark exchange dominates
--- 2-gluon exchange quark exchange
GPD model calculations for sL:
indication of a larger gluon contribution
[Diehl et.al. (2005)]
[Vinnikov et.al. (2005)]
[Frankfurt et.al. (1996)]
→ talk by Markus Diehl

11. r0 cross sections at CLAS
VECTOR MESONS s
 Hq, Eq
r0 cross sections at CLAS
CLAS (4.2 GeV)
CLAS: analysis of sL for r0 (r+, f) from
5.7 GeV data (higher W, higher Q2)
Analysis in progress
Two-pion invariant mass spectra r+
frozen coupling constant at 0.56 to average out non perturbative effect
[Vanderhaegen et.al. (1999)] n

12. w production at CLAS  Hq, Eq CLAS (5.7 GeV)
VECTOR MESONS s
 Hq, Eq
w production at CLAS
CLAS (5.7 GeV)
Analysis of ω decay angular distributions:
SCHC does not seem to hold
→ not possible to extract σL
Evidence for unnatural parity exchange  0 exchange very probable even at high Q2 (4 GeV2)
[Laget (2005)]
Cross sections described by REGGE model
[Vanderhaegen et.al. (1999)]
handbag diagram estimated to contribute only about 1/5 of measured cross sections

13. r0 transverse target spin asymmetry
VECTOR MESONS asym
 Hq, Eq
r0 transverse target spin asymmetry
sS ~ |ST| sin (f-fS) E∙H
[Goeke et.al. (2001)]
E related to Jq  TSA sensitive to Jq
+ Hg : smaller AUT
[Vinnikov et.al. (2005)] xB
same xB-dependence behaviour as GPD calculations
no sL/sT separation yet
2 times more data for 2005
 r0 TSA can be investigating at COMPASS

14. Pion pairs production: e p (d)→ e’ p (d) p+ p-
 Hq, Eq
Pion pairs production: e p (d)→ e’ p (d) p+ p-
Legendre moment:
<P1> sensitive to the interference between different p+p- isospin states

15. Legendre Moment: Mpp dependence
PION PAIRS
 Hq, Eq
Legendre Moment: Mpp dependence
interference between
S-wave and lower r0 tail
mpp < 0.6 GeV
[PLB599,2004]
minimum interference
between S-P waves
mpp ~ 0.77 GeV
indication of
r0 –f2 interference
mpp ~ 1.3 GeV
GPD model calculations for sL:
■▲ quark exchange
― quark + 2-gluon exchange
[Lehmann-Dronke et.al. (2001)]

16. Pseudoscalar Mesons cross sections target spin asymmetry  H, E ~ ~
PS MESONS
 H, E
~ ~
Pseudoscalar Mesons
cross sections ~ ~
~ | ∫ dx H(x,x,t) + E(x,x,t) |2 ~
E kinematically suppressed at low t
H = double distribution ~ Dq(x) with skewing effect
factorized t-dependence ~
At low t and large x, E dominated by the pion pole
E related to Fp ~
p+ production:
target spin asymmetry ~ ~
AUT~ Im( H .E )

17. p+ cross section at HERMES
PS MESONS s
 Hq, Eq
~ ~
p+ cross section at HERMES
L/T separation not possible
sT suppressed by 1/Q2
→ at large Q2, sL dominates
supported by REGGE model
[Laget (2005)]
GPD model calculations for sL:
[Vanderhaegen et.al. (1999)]
Q2 dependence is in general agreement with the theoretical expectation
Corrections to LO (k┴ and soft overlap) calculations overestimate the data
Leading Order
LO + power corrections
- Huang, Wu & Wu (2004) -
- Vanderhaeghen et al. (1999) -
CEA, Cornell, Jlab
Pion Electromagnetic
Form Factor

18. Cross section ratios xB  Hq, Eq p0 production: no p-pole measure at
PS MESONS s
 Hq, Eq
~ ~
Cross section ratios
p0 production: no p-pole
e p→e p+ n / e p→e p0 p
measure at
 HERMES
 Jlab:
[Mankiewicz et al. (1999)] xB
e p → e p+ X
CLAS (5.7 GeV)
Q2~2.3 GeV2
x~0.3
Missing mass (GeV) xB

19. p+ transverse TSA ~ ~ sS ~ |ST| sin (f-fS) E∙H HERMES COMPASS  Hq, Eq
- Belitsky & Müller (2001) -
- Frankfurt, Pobylitsa, Polyakov & Strikman (1999) -
- Frankfurt, Polyakov, Strikman & Vanderhaeghen (2000) -
PS MESONS asym.
 Hq, Eq
~ ~
p+ transverse TSA ~ ~
g*L p → p+ n
sS ~ |ST| sin (f-fS) E∙H
[Frankfurt et al. (1999)]
[Belitsky et al. (2001)]
TARGET SPIN ASYMMETRY
HERMES
COMPASS

20. HERMES with a recoil detector
PERSPECTIVES
HERMES with a recoil detector
2006/2007
Detection of the
recoiling proton
clean reaction identification
improve statistical precision (unpolarised data with high density target)
improve detector resolution: multi-dimensional binning in xB and t
→ poster by Yves Van Haarlem

21. Jlab upgrade to 12 GeV beam energy
PERSPECTIVES
Jlab upgrade to 12 GeV beam energy
Projections for 11 GeV (sample kinematics)
AUT r0 xB
TARGET SPIN ASYMMETRY sL sT
xB =
-t = GeV2
Other bins measured
concurrently
sTot
COMPASS:
2010 CERN proton luminosity upgrade
proposal for a recoil detector
 up to Q2= 20 GeV2
    up to Q2= 7 GeV2

22. Combining all the measurements will allow to constrain GPD models~
 H E
 H E
CONCLUSION
GPDs can be probed by hard exclusive meson production
Reaction Observable Exploration Experiment
ep→epρ σL H (2u+d) H1, ZEUS, HERMES, CLAS
TSA H.E HERMES
ep→epρ σL H (u-d)
ep→epf σL H (s) H1, ZEUS, HERMES
ep→epω σL H (2u-d) CLAS
ep→epp+p Legendre Moment H HERMES
ep→epp σtot E (u-d) HERMES
TSA H.E
ep→epp σtot H (2u+d) ~ ~ ~ ~
Corrections to leading order are needed to describe the cross sections
Scaling region expected to be reached at lower Q2 for TSA, cross section ratios
Combining all the measurements will allow to constrain GPD models
Measurements of different exclusive processes:
vector mesons, p+p-, pseudoscalar mesons ~ ~ ~
Hpp0: 2/3 Hu/p + 1/3 Hd/p
Hpp+: Hu/p Hd/p
Polarisation provides observable sensitive
to different combinations of GPDS ~ ~ ~
dedicated experiments for exclusive measurements starting soon at HERMES

23. Factorization theorem prediction
for fixed xB and t
asymptotically
fit: 1/Qp
p=1.9±0.5
p=1.7±0.6
p=1.5±1.0

24. SDME from GPD model Good agreement with the data (sL,SDME)
Modified Perturbative Approach
[Goloskokov et.al. (2005)]
Model Ivanov et al..???
Good agreement with the data (sL,SDME)
for Q2>5 GeV2
t-dependence can be different for stot and sL
no separate measurements for the t-slope on the data

25. Sum Rules and Limited cases
Forward limit (t →0, x→0)
Hq(x, x=0,t=0) = Dq(x) ~
Hq(x,x=0,t=0) = q(x)
Hq(x, x=0,t=0) = xDG(x) ~
Hq(x,x=0,t=0) = xG(x)
Sum rules
dx Hq(x,x,t) = Fq1 (t)
dx Eq(x,x,t) = Fq2 (t) ~ ~
dx Hq(x,x,t) = gqA (t)
dx Eq(x,x,t) = hqA (t)
Ji sum rules 1
30%(DIS)
( H(x,x,t=0) + E(x,x,t=0) ) x dx = Jquark
=1/2 DS + D Lz -1