1. Jim Stewart DESY Measurement of Quark Polarizations in Transversely and Longitudinally Polarized Nucleons at HERMES for the Hermes collaboration Introduction Introduction The HERMES Experiment The HERMES Experiment Measurement of the Quark Helicity Distributions Measurement of the Quark Helicity Distributions Transversity Measurements at HERMES Transversity Measurements at HERMES Summary Summary

2. August 2004 J. Stewart Semi-Inclusive Deep Inelastic Scattering The cross section can be expressed as a convolution of a distribution function and a fragmentation function.

3. August 2004 J. Stewart Distribution Functions HERMES 1996-2000 HERMES >2002 Leading Twist Leading Twist  3 distribution functions survive the integration over transverse quark momentum unpolarized DF Helicity DF Transversity DF vector chargeaxial chargetensor chargeTransversitybasis

4. August 2004 J. Stewart Virtual Photon Asymmetry - Path to  q Virtual photon can only couple to quarks of opposite helicity Virtual photon can only couple to quarks of opposite helicity Select quark helicity by changing target polarization direction Select quark helicity by changing target polarization direction Different targets give sensitivity to different quark flavors Different targets give sensitivity to different quark flavors

5. August 2004 J. Stewart Quark Polarizations Correlation between detected hadron and the struck quark allows flavor separation Linear System in Inclusive DIS →  Semi-inclusive →

6. August 2004 J. Stewart The HERMES Experiment 27.5 GeV polarized positron beam ( ~53%) Longitudinally polarized H ( ~85%) Transversely polarized H ( ~78%)

7. August 2004 J. Stewart The Measured Hadron Asymmetries DEUTERIUM PROTON is an all sea object and

8. August 2004 J. Stewart Polarized Quark Densities  Polarized parallel to the proton  Polarized anti-parallel to the proton  Good agreement with LO-QCD fit   No indication for → 0.028 ± 0.033 ± 0.009 Measured range Submitted Phys.Rev.D

9. August 2004 J. Stewart Properties of the Transversity DFs  For non-relativistic quarks  q(x)=  q(x) →  q(x) probes the relativistic nature of the quarks  Due to Angular Momentum Conservation → Different QCD evolution → No gluon component  → Predominately sensitive to valence quarks  Bounds   Soffer Bound:  T-even  Chiral odd → Not measurable in inclusive DIS

10. August 2004 J. Stewart Measuring Transversity  Need a chiral odd fragmentation function: ‘Collins FF’ Forbidden Forbidden Need chiral odd fragmentation function Need chiral odd fragmentation function  Transverse quark polarization affects transverse hadron momentum  Observed asymmetry in azimuthal angle about lepton scattering plane Collins Effect Artru string fragmentation model  String break produces quark- antiquark pair  pair must preserve vacuum quantum numbers  angular momentum conservation gives the produced hadron transverse momentum

11. August 2004 J. Stewart Sivers Function f  1T (x)  Distribution function → Naïve T-ODD → Chiral even  a remnant of the quark transverse momentum can survive the photo-absorption and the fragmentation process  Can be inherited in the transverse momentum component → influence azimuthal distribution  Non-vanishing Sivers function requires quark orbital angular momentum  Cross section depends on the angle between the target spin direction and the hadron production plane

12. August 2004 J. Stewart How to Measure Transversity Collins azimuthal moment Sivers azimuthal moment Assuming gaussian distributions for initial an final quark momentum

13. August 2004 J. Stewart RESULTS Collins Sivers   Unexpected result: - Possible interpretation: Sivers Moment  More theoretical input needed to clarify interpretation  f  1T (x) DIS = - f  1T (x) DY UNIVERSALITY Collins Moment  - Same Size Submitted to Phys.Rev.Lett.

14. August 2004 J. Stewart Summary and Conclusions Longitudinally Polarized Target Data  First direct measurement of the helicity distributions Transversely Polarized Target Data  Collins: Disfavored fragmentation functions appear to be important and have opposite sign to the favored  Sivers: Amplitude is greater than zero

15. August 2004 J. Stewart Polarized Sea  Unpolarized data on sea shows the Gottfried sum rule is broken  QSM expectation: Eur.Phys.J.C14,147(2000)  Meson cloud model: Phys.Rev.D68,074002(2003) Data favor symmertic,but large uncertainties

16. August 2004 J. Stewart Purities - --

17. August 2004 J. Stewart