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

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

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

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

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

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 6 October 2006 SPIN2006 Kyoto

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

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

SDME Results for Total Set 6 October 2006 SPIN2006 Kyoto

Comparison to Zeus and H1 SDMEs 6 October 2006 SPIN2006 Kyoto

Longitudinal to Transverse Cross Section Ratio 6 October 2006 SPIN2006 Kyoto

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: 0.2-0.3 (DIS) 6 October 2006 SPIN2006 Kyoto

Extracting GPDs from Exclusive 0 Electroproduction I Q2 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

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

Transverse Target Spin Asymmetry 6 October 2006 SPIN2006 Kyoto

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

TTSA Results from HERMES II Not L/T separated yet Ellinghaus, Nowak, Vinnikov, Ye hep-ph/0506264 6 October 2006 SPIN2006 Kyoto

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

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

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

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

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

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

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

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

SDME Fit Examples 6 October 2006 SPIN2006 Kyoto

Q2 Dependences of SDMEs 6 October 2006 SPIN2006 Kyoto

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