New Results on 0 Production at HERMES

6 October 2006 SPIN2006 Kyoto 1

New Results on 0 Production at HERMESEdward R. Kinney

University of Colorado, Boulder, USA

on behalf of the HERMES Collaboration

• Spin Density Matrix Elements (SDMEs)• Transverse Target Spin Asymmetries


Exclusive 0 Electroproduction: Vector Meson Dominance


e +N → e'+N + 0

• 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



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


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


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.


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

E =M x

2 −M targ2

2M targ

9600 events from H, 16000 events from D


HERMES Exclusivity

SIDIS background determined from PYTHIA simulation (blue), normalized at large E


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.


SDME Results for Total Set


Comparison to Zeus and H1 SDMEs


Longitudinal to Transverse Cross Section Ratio


00L,

Generalized Parton Distributions Exclusive 0 Electroproduction: Generalized Parton Distributions

4 Generalized Parton Distributions (GPDs) H H conserve nucleon helicity

E E flip nucleon helicity

~ ~

Vector mesons (

Pseudoscalar mesons (

( )( )1

1 0

1

2q

qq

t

HJ Exdx− →

+= ∫1

2q qLJ

Ji’s sum rule: 0.2-0.3 (DIS)0.2-0.3 (DIS)

for each quark flavor Hq, Eq ; for gluon Hg, Eg


Extracting GPDs from Exclusive 0 Electroproduction I

t

Q2Meson production vs DVCS Meson wave function has additional information/uncertainty

Hard scale: Q2 large

GPD dependence: t small

Factorization for longitudinal photons only!T suppressed by 1/Q2 → at large Q2, L dominates


Extracting GPDs from Exclusive 0 Electroproduction II

Cross section:

Transverse Target Spin (Azimuthal) Asymmetry:

d L

dt: H∫

2+ T

2 E 2

Kinematic suppression

AUT

sin(−s ) :Im{HE}|H ,E |2

E is unknown! Related to distortion of quark distributions in b (see M. Burkhardt’s talk)


Transverse Target Spin Asymmetry

)(N)(N

)(N)(N

P

1)(A

TUT

SS

SSS

−+−−−−

=− −+

−+


TTSA Results from HERMES I

Still includes Transverse and Longitudinal 0s


TTSA Results from HERMES II

Ellinghaus, Nowak, Vinnikov, Ye hep-ph/0506264

Not L/T separated yet


L/T Separation of TTSA

cos of +


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


HERA at DESY

HERA Polarized Electron(positron) BeamI = 40 -> 10 mAP = 55% (average for longitidinal)


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


The HERMES Spectrometer

In 1998 Cherenkov replaced with dual radiator RICH


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


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

r00

04 , Re{r1-1

1 }, Im{r1-1

2 }, Re{r10

5 }, Im{r10

6 }, Im{r10

7 }, Re{r10

8 }

are non-zero, and we have the relationsr1-1

1 = - Im{r1-1

2 }

Re{r10

5 } = - Im{r10

6 }

Im{r10

7 } = Re{r10

8 } .


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

1−r0004 + 2r1−1

04 −2r111 −2r1−1

1 =0

Natural Parity Exchange: Pomeron, , , A2, f2,…

Un-natural Parity Exchange: , A1, f1,…


SDME Fit Examples


Q2 Dependences of SDMEs


[[Vanderhaegen et.al. (1999)]Vanderhaegen et.al. (1999)]

corrections to LO: quark transverse momenta→ quark exchange dominates

--- 2-gluon exchange --- quark exchange

GPD model calculations for L: H

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New Results on 0 Production at HERMES