Semi-Inclusive Deep Inelastic Scattering

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

3. vector charge axial charge tensor charge HERMES 1996-2000 HERMES >2002 Distribution Functions Leading Twist • 3 distribution functions survive the integration over transverse quark momentum unpolarized DF Helicity DF Transversity DF Transversity basis

4. Virtual Photon Asymmetry - Path to Dq • Virtual photon can only couple to quarks of opposite helicity • Select quark helicity by changing target polarization direction • Different targets give sensitivity to different quark flavors

5. Linear System in Quark Polarizations Correlation between detected hadron and the struck quark allows flavor separation Inclusive DIS →DS Semi-inclusive→

6. The HERMES Experiment • 27.5 GeV polarized positron beam (<P>~53%) • Longitudinally polarized H • (<P>~85%) • Transversely polarized H (<P>~78%)

7. is an all sea object and The Measured Hadron Asymmetries PROTON DEUTERIUM

8. 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. Properties of the Transversity DFs • For non-relativistic quarks dq(x)=Dq(x) • dq(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. Forbidden • Need chiral odd fragmentation function Measuring Transversity • 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 • Need a chiral odd fragmentation function: ‘Collins FF’

11. 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. How to Measure Transversity Collins azimuthal moment Sivers azimuthal moment Assuming gaussian distributions for initial an final quark momentum

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

14. 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. 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. Purities - - -