1. New Results on 0 Production at HERMES
Edward R. Kinney
University of Colorado, Boulder, USA
on behalf of the HERMES Collaboration
Spin Density Matrix Elements (SDMEs)
Transverse Target Spin Asymmetries
6 October 2006
SPIN2006 Kyoto

2. Exclusive 0 Electroproduction: Vector Meson Dominance
At high energy, strong fluctuation of photon into 0 followed by gluonic interaction (Pomeron)
Intermediate energies appear to have dominant quark exchange mechanism (Reggeon)
Polarization of 0 correlated with polarization of * (SDMEs)
Reaction Dynamics
Q2 = -q2 = (k - k’)2
W2 = (q+p)2
t = (q-v)2
6 October 2006
SPIN2006 Kyoto

3. Spin Density Matrix Elements I
Without data at different beam energies we cannot separate transverse and longitudinal components
Measured matrix elements r combine L and T parts
6 October 2006
SPIN2006 Kyoto

4. Spin Density Matrix Elements III
SDME’s are the coefficients which describe the angular distribution of the +- decay relative to the electron scattering plane and the 0 momentum
6 October 2006
SPIN2006 Kyoto

5. Simplifying Assumptions
If the helicity of photon is equal to the vector meson helicity,
T01 = T10 = T-10 = T0-1 = T-11 = T1-1 = 0
leaving only T00, T11 and T-1-1 to be determined. This is known as S-channel helicity conservation (SCHC).
If the reaction is dominated by exchange of particles with natural parity (NPE) (J = 0+, 1-, 2+ …) then we a simple symmetry between the helicity amplitudes:
T11 = T-1-1, T01 = -T0-1, T10 = T-10, and T1-1 = T-11
along with T00, this leaves 5 independent helicity amplitudes.
6 October 2006
SPIN2006 Kyoto

6. HERMES Data Set for SDME Analysis
Ee = 27.5 GeV, Pe = ± 0.53
Unpolarized H2, D2 and Long. Polarized H, D ( )
Events with 3 tracks only: (e’, h+,h- )
y = /E <0.85 and Q2 > 0.7 GeV2
Invariant 2 mass: 0.6 GeV< M2< 1.0 GeV
Invariant 2K mass: M2K > 1.06 GeV
-t’ = t - tmin < 0.4 GeV2
Exclusivity Constraint: -1 GeV < E < 0.6 GeV, where
 9600 events from H, events from D
6 October 2006
SPIN2006 Kyoto

7. HERMES Exclusivity
SIDIS background determined from PYTHIA simulation (blue), normalized at large E
6 October 2006
SPIN2006 Kyoto

8. Data binned in 8x8x8 bins in cos, , and 
Extraction of SDMEs
Data binned in 8x8x8 bins in cos, , and 
Angular distributions corrected for SIDIS background shape, predicted by PYTHIA.
Maximum likelihood method used to fit isotropic angular distributions to data; SDME’s are fit parameters.
6 October 2006
SPIN2006 Kyoto

9. SDME Results for Total Set
6 October 2006
SPIN2006 Kyoto

10. Comparison to Zeus and H1 SDMEs
6 October 2006
SPIN2006 Kyoto

11. Longitudinal to Transverse Cross Section Ratio
6 October 2006
SPIN2006 Kyoto

12. Generalized Parton Distributions
Exclusive 0 Electroproduction: Generalized Parton Distributions
p0, r0L, g
4 Generalized Parton Distributions (GPDs)
H H conserve nucleon helicity
E E flip nucleon helicity ~ ~
Vector mesons
(r, w, f)
Pseudoscalar mesons (p, h)
for each quark flavor Hq, Eq ; for gluon Hg, Eg 1 2 q L J D + S =
Ji’s sum rule:
(DIS)
6 October 2006
SPIN2006 Kyoto

13. Extracting GPDs from Exclusive 0 Electroproduction IQ2
Meson production vs DVCS
Meson wave function has additional information/uncertainty
Hard scale: Q2 large
GPD dependence: t small
Factorization for longitudinal photons only!
sT suppressed by 1/Q2 → at large Q2, sL dominates
6 October 2006
SPIN2006 Kyoto

14. Extracting GPDs from Exclusive 0 Electroproduction II
Cross section:
Kinematic suppression
Transverse Target Spin (Azimuthal) Asymmetry:
E is unknown! Related to distortion of quark distributions in b (see M. Burkhardt’s talk)
6 October 2006
SPIN2006 Kyoto

15. Transverse Target Spin Asymmetry
6 October 2006
SPIN2006 Kyoto

16. TTSA Results from HERMES I
Still includes Transverse and
Longitudinal 0s
6 October 2006
SPIN2006 Kyoto

17. TTSA Results from HERMES II
Not L/T separated yet
Ellinghaus, Nowak, Vinnikov, Ye hep-ph/
6 October 2006
SPIN2006 Kyoto

18. L/T Separation of TTSA
cos of +
6 October 2006
SPIN2006 Kyoto

19. TTSA L/T Separation Underway + 2x statistics on tape
Summary and Outlook
TTSA L/T Separation Underway + 2x statistics on tape
Constraint of E and Ju
New SDME results, including new beam polarization dependent elements, available for H and D targets
Kinematic dependence studied
Little difference between H and D
Evidence of violation of SCHC and NPE
6 October 2006
SPIN2006 Kyoto

20. HERA at DESY HERA Polarized Electron(positron) Beam I = 40 -> 10 mA
P = 55% (average for longitidinal)
6 October 2006
SPIN2006 Kyoto

21. The HERMES Internal Target
Polarized H, D: t = 0.8 x 1014 atom/cm2, P=85%
Unpolarized H,D: t ≥ 1 x1015 atom/cm2
Breit-Rabi Polarimeter + Moeller/Bhabha Luminosity Monitor
6 October 2006
SPIN2006 Kyoto

22. The HERMES Spectrometer
In 1998 Cherenkov replaced with dual radiator RICH
6 October 2006
SPIN2006 Kyoto

23. Spin Density Matrix Elements II
Without data at different beam energies we cannot separate transverse and longitudinal components
Measured matrix elements r combine L and T parts
 23 r’s, including 8 which depend on beam helicity
6 October 2006
SPIN2006 Kyoto

24. S-Channel Helicity Conservation
If the helicity of photon is equal to the vector meson helicity,
T01 = T10 = T-10 = T0-1 = T-11 = T1-1 = 0
leaving only T00, T11 and T-1-1 to be determined.
In terms of “r” SDMEs, only
are non-zero, and we have the relations
6 October 2006
SPIN2006 Kyoto

25. Natural Parity Exchange
If the reaction is dominated by exchange of particles with natural parity (J = 0+, 1-, 2+ …) then we a simple symmetry between the helicity amplitudes:
T11 = T-1-1, T01 = -T0-1, T10 = T-10, and T1-1 = T-11
along with T00, this leaves 5 independent helicity amplitudes,
and the relation
Natural Parity Exchange: Pomeron, , , A2, f2,…
Un-natural Parity Exchange: , A1, f1,…
6 October 2006
SPIN2006 Kyoto

26. SDME Fit Examples
6 October 2006
SPIN2006 Kyoto

27. Q2 Dependences of SDMEs
6 October 2006
SPIN2006 Kyoto

28. corrections to LO: quark transverse momenta quark exchange dominates
[Vanderhaegen et.al. (1999)]
corrections to LO: quark transverse momenta
quark exchange dominates
--- 2-gluon exchange quark exchange
GPD model calculations for sL: H
6 October 2006
SPIN2006 Kyoto