1. Hard exclusive production at HERMES
Cynthia Hadjidakis
2nd workshop on the QCD structure of the Nucleon
Rome, June, 2006
Generalized Parton Distributions
Compton scattering (DVCS)
Exclusive mesons production
Summary and perspectives

2. Hard exclusive production of photons and mesons
p0, r0L, g Q2
Q2>>, t<<
4 Generalized Parton Distributions (GPDs)
H H conserve nucleon helicity
E E flip nucleon helicity ~
-2 x ~
x+x
x-x
Vector mesons
(r, w, f)
Pseudoscalar
mesons (p, h)
DVCS (g) depends on 4 GPDs t t
Add gluon exchange diagram: ZEUS
for each quark flavour Hq, for gluon Hg 1 2 q L J D + S =
Ji’s sum rule:
(DIS)
quark flavour decomposition possible
from meson production
GPDs depend on 3 variables: x, x, t
30%(DIS) 1
( H(x,x,t=0) + E(x,x,t=0) ) x dx = Jquark
=1/2 DS + D Lz -1 ρ0
2u+d, 9g/4 ω
2u-d, 3g/4 f
s, g ρ+
u-d

3. HERMES kinematics coverage
GPDs formalism:
Q2>>, t<<
HERMES:
<Q2>=2.4 (1-10) GeV2, -t < 0.5 GeV2
collider experiments
H1, ZEUS
10-4<xB<0.021 : gluons in the proton
fixed target experiments
COMPASS, HERMES
 0.006/0.02<xB<0.3 : gluons/valence and sea quarks
CLAS
 0.15<xB<0.6 : valence quarks

4. HERMES spectrometer e +/ e - 27.5 GeV PB= 55%→
Tracking system: dP/P = 2 %, dq < 1 mrad
(charged) Particle Identification: RICH, TRD, preshower, calorimeter
Photon: calorimeter: dP/P = 5 % for high energy photon
no recoil detection
e+ p → e+ g (p) only e+ and g detected
Exclusive reaction signed via the missing mass technique
MX = ( e + p – e’ – g )
Exclusive reaction selected with a cut on MX
Background contamination estimated with non-exclusive MC
1H→ <|Pt|> ~ 85 %
2H→ <|Pt|> ~ 85 %
1H↑ <|Pt|> ~ 75 %
Target: polarized H, D / unpolarized H, D, N, Ne, Kr, Xe

5. Deep Virtual Compton Scattering: e p → e’ p’ g
 H, H, E, E ~
DVCS
Deep Virtual Compton Scattering: e p → e’ p’ g
DVCS
Bethe-Heitler
for HERMES kinematics:
DVCS << Bethe-Heitler
DVCS-BH interference leads to non-zero azimuthal asymmetry

6. DsUT DVCS asymmetries I~Ds ~ DsC ~ cosf Re{ H + x H + k E} ~
 H, H, E, E ~
DVCS
DVCS asymmetries
I~Ds
 Different charge : e+ e- (only at HERA!) :
DsC ~ cosf Re{ H + x H + k E} ~ H
 Different polarisations :
DsLU ~ sinf Im{H + x H + k E} ~
DsUT
beam target H
DsUL ~ sinf Im{H + x(H + …} ~ ~
H, H
DsUT ~ sinf Im{H - E + … }
H, E
Suppressed by kinematical factor
x = xB/(2-xB ),k = -t/4M2

7. Beam spin and charge asymmetry
 H, H, E, E ~
DVCS
Beam spin and charge asymmetry
Beam Spin Asymmetry
Beam Charge Asymmetry
[PRL87,2001]
symmetrization f → |f| (cancel sin f
terms from polarized beam)
[hep-ex/ , subm. to PRL]
L=140 pb-1
e+/- p → e+/- p g (MX<1.7 GeV)
─ P1 + P2 cos f + P3 cos 2f + P4 cos 3f
L=10 pb-1
P1 = -0.01±0.02
P2 = 0.06±0.03
P3 = 0.02±0.03
P4 = 0.03±0.03
<-t> = 0.12 GeV2,<xB> = 0.1, <Q2> = 2.5 GeV2

8. Beam charge asymmetry: t-dependence
DVCS ~ ~
 H, H, E, E
Beam charge asymmetry: t-dependence
e+/- p → e+/- p g (MX<1.7 GeV)
(in HERMES acceptance)
Regge, D-term
Regge, no D-term
fac., D-term
fac., no D-term
GPD calculation:
different parameterization for H
[Vanderhaegen et.al. (1999)]
H = double distribution ~ q(x) with skewing effect
D-term or not
t dependence:
Regge-inspired t-dependence
factorized t-dependence (ebt)
BCA: no sensitivty to profile parameter :bsea, bval
→ AC sensitive to GPD-models
tiny e-p sample (L=10 pb-1) HERA: e- beam (x10)
P1 = -0.01±0.02
P2 = 0.06±0.03
P3 = 0.02±0.03
P4 = 0.03±0.03
<-t> = 0.12 GeV2,<xB> = 0.1, <Q2> = 2.5 GeV2
symmetrization f → |f| (cancel sin f
terms from polarized beam)

9. Longitudinal target spin asymmetry
DVCS ~ ~
 H, H, E, E
Longitudinal target spin asymmetry
Lp = 50 pb-1
Ld = 170 pb-1
sin f in agreement with GPD models
unexpected large sin 2f (NLO contributions): from qGq correlations twist-3 GPDs?

10. Transverse target spin asymmetry
DVCS ~ ~
 H, H, E, E
Transverse target spin asymmetry ~
AUT ~ sin(f-fS) cos(f) Im{H - E + … }+ cos(f-fS) sin(f) Im{H + … }
+ 2005: 2 times more statistics
GPD calculation:
[Goeke et.al. (2001)] , [Ellinghaus et.al. (2005)]
H = double distribution Regge-inspired t-dep.
D-term
E = double distribution ~ sensitive to Jq: Ju (Jd=0)
factorized t-dep. (dipole form factor)
L = 64 pb-1
→ First (model dependent) constraints on Ju and Jd !
talk by Zhenyu Ye

11. DVCS on nuclear target  H, H, E, E~ ~
 H, H, E, E
DVCS on nuclear target
GPDs modification in nuclear matter: spatial distribution of energy, angular momentum and shear forces inside the nuclei
coherent nuclear DVCS (-t<0.05 GeV2) different from proton DVCS
incoherent nuclear DVCS similar to proton DVCS (small BH cross section on neutron at small t)
proton and deuteron data consistent
highest t-bin may be affected by associated production (30%)
2H (720 pb-1), 4He (30 pb-1), 14N (50 pb-1), Ne (86 pb-1), Kr (135 pb-1), Xe (80 pb-1)
study of properties of quarks and gluons inside nuclei

12. Beam spin asymmetry on nuclear target
DVCS ~ ~
 H, H, E, E
Beam spin asymmetry on nuclear target
L=30 pb-1
L=86 pb-1
→ clear sin f amplitude in the exclusive region for Ne and Kr
→ soon: Anucleus/Aproton (He, N, Ne, Kr, Xe )
t-dependence (separation of coherent and incoherent part)
A-dependence for coherent production
[Guzey et al. (2003)], [Liuti et al. (2005)]

13. Factorization theorem for meson productionQ2
Q2>>, t<<
Meson production: wave function: additional information/uncertainty
hard scale t
Meson production: factorization for longitudinal photons only
sT suppressed by 1/Q2 → at large Q2, sL dominates
for fixed xB and t
asymptotically
« scaling law »

14. 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

15. e p → e r0 (p): exclusive r0 selection
VECTOR MESONS
e p → e r0 (p): exclusive r0 selection
r0 →p+ p- : h+h- detected
Missing energy DE = (M2X-M2p)/2Mp (MX = e + p – e’ – h+ – h- )
0.6 < M2h< 1.0 GeV
DE < 0.6 GeV
-t’=-t+tmin<0.4 GeV2
DE < 0.6 GeV
-t’< 0.4 GeV2
Fit with skewed Breit-Wigner
0.6 < M2p< 1.0 GeV
-t’< 0.4 GeV2
data
non exclusive MC
Monte Carlo simulation of non-exclusive (DIS) background

16. extraction of sL: r0 → p+p- angular distributions
VECTOR MESONS
extraction of sL: r0 → p+p- angular distributions
g*-p CMS
23 SDMEs (15 unpolarised, 8 polarised)
extracted in 3-D: F, f, cos q
r° rest
frame p’ f e’ p g* e r°
L=250 pb-1 p+ F q p-
if SCHC holds
(VM retains g* helicity):
→ violation of SCHC
→ at Q2 = 2 GeV2, sL=sT

17. r0 longitudinal cross sections
VECTOR MESONS
 H, E
r0 longitudinal cross sections
[EPJC17,2000]
L = 106 pb-1
[Vanderhaegen et.al. (1999)]
corrections to LO: quark transverse momenta
quark exchange dominates
--- 2-gluon exchange quark exchange
GPD model calculations for sL: H
indication of a larger gluon contribution
[Diehl et.al. (2005)]
[Vinnikov et.al. (2005)]
[Frankfurt et.al. (1996)]
more data to come: r, f, w, r+

18. r0 transverse target spin asymmetry
VECTOR MESONS
 H, E
r0 transverse target spin asymmetry
interference between E and H
[Vinnikov et.al. (2005)]
- Goeke, Polyakov & Vanderhaeghen (2001) -
E related to Jq  TSA sensitive to Jq
sS: |ST| sin (f-fS) E H
L=64 pb-1 xB x
GPD model calculations (quarks+gluons GPDs)
E related to Jq  TSA sensitive to Jq
2 times more data with 2005: sL/sT separation
→ talk by Armine Rostomyan

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

20. Legendre Moment: Mpp dependence
PION PAIRS
 H, E
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
L=250 pb-1
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)]

21. 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 )

22. p+ cross section measurement
PS MESONS
 H, E
~ ~
p+ cross section measurement
L/T separation not possible
sT suppressed by 1/Q2
L=250 pb-1
→ 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

23. Transverse target spin asymmetry for exclusive p+
PS MESONS
 H, E
~ ~
Transverse target spin asymmetry for exclusive p+
interference between E and H ~ ~
g*L p → p+ n
[Frankfurt et al. (1999)]
sS: |ST| sin (f-fS) E H ~ ~
[Belitsky et al. (2001)]
L = 145 pb-1

24. Future analysis: recoil detector
Jan Jun. 07
Detection of the
recoiling proton
associated prod. ~11%
semi-incl. ~5%
associated prod. ~1%
semi-incl. <<1%
clean reaction identification
improve statistical precision (Lp = 750 pb-1, Ld = 200 pb-1)
→ talk by Ralf Kaiser

25. CONCLUSION Polarisation provides observable sensitive~ ~
 H E ~
 H, H, E, E
 H E
 H E
CONCLUSION
GPDs probed by hard exclusive photon and meson production H
DVCS: BSA, BCA
excl. r0: sL
excl. pions pairs H
DVCS: LTSA ~
E: TTSA
DVCS, excl. r0 ~ E
excl. p+ : s
Corrections to leading order are needed to describe the cross sections
Leading order calculations describe asymmetries
Jan. 06: polarized target removed, recoil detector installed and under commissioning
→ HERMES dedicated to exclusive processes! ~
Asymmetries: powerful tool to constrain GPD models
H H
E E ~ ~ ~
Reaction Observable GPDs ~
ep→epg BCA, BSA, L(T)TSA H (2u+d)
ep→epρ σL H (2u+d)
TTSA H.E
ep→epf σL H (s)
ep→epω σL H (2u-d)
ep→epp+p Legendre Moment H
ep→epp σtot E (u-d)
TTSA H.E
ep→epp σtot H (2u+d) ~ ~ ~
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

27. HERMES at DESY e-beam: e+/e-, Ee=27.5 GeV, PB= 55%
spin HERMES for longitudinal beam polarization

28. Longitudinal target spin asymmetry:sin 2f~ ~
 H, H, E, E
Longitudinal target spin asymmetry:sin 2f
unexpected large sin 2f: from qGq correlations twist-3 GPDs?
upper limits for qGq correlations twist-3 GPDs [D. Mueller]

29. Model dependent constraint on Ju and Jd~ ~
 H, H, E, E
Model dependent constraint on Ju and Jd

30. Exclusive p+ production: e p → e p+(n)
Missing Mass2 = (p-g*-p+)2
e p → e p-n : use of p- yield to subtract the non exclusive background
e p → e p+ X
e p → e p+ n
-t (GeV2) 1
Monte Carlo (arbitrary norm.)
data
#events
p+ enhancement
Exclusive peak clearly centered at the nucleon mass
Mean and width in agreement with exclusive MC
Good description of data by MonteCarlo (acceptance determination)
- Vanderhaeghen, Guichon & Guidal (1999) -