New Results on  0 Production at HERMES

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 SPIN2006 Kyoto

2. Exclusive 0 Electroproduction: Vector Meson Dominance 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 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 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 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. SPIN2006 Kyoto

6. HERMES Data Set for SDME Analysis • Ee = 27.5 GeV, Pe = ± 0.53 • Unpolarized H2, D2 and Long. Polarized H, D (1996-2000) • 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, 16000 events from D SPIN2006 Kyoto

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

8. 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. SPIN2006 Kyoto

9. SDME Results for Total Set SPIN2006 Kyoto

10. Comparison to Zeus and H1 SDMEs SPIN2006 Kyoto

11. Longitudinal to Transverse Cross Section Ratio SPIN2006 Kyoto

12. Generalized Parton Distributions p0, r0L, g for each quark flavor Hq, Eq ; for gluon Hg, Eg 0.2-0.3 (DIS) Ji’s sum rule: 1 = D S + J L q q 2 Exclusive 0 Electroproduction: Generalized Parton Distributions 4 Generalized Parton Distributions (GPDs) HH conserve nucleon helicity EEflip nucleon helicity ~ ~ Pseudoscalar mesons (p, h) Vector mesons (r, w, f) SPIN2006 Kyoto

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

15. Transverse Target Spin Asymmetry SPIN2006 Kyoto

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

17. TTSA Results from HERMES II Not L/T separated yet Ellinghaus, Nowak, Vinnikov, Ye hep-ph/0506264 SPIN2006 Kyoto

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

19. 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 SPIN2006 Kyoto

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

22. The HERMES Spectrometer In 1998 Cherenkov replaced with dual radiator RICH 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 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 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,… SPIN2006 Kyoto

26. SDME Fit Examples SPIN2006 Kyoto

27. Q2 Dependences of SDMEs SPIN2006 Kyoto

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