1. Single-spin asymmetries in two hadron production of polarized deep inelastic scattering at HERMES Tomohiro Kobayashi Tokyo Institute of Technology for the HERMES collaboration Second Joint Meeting of the Nuclear Physics Divisions of APS and JPS, Hawaii (Sep. 22 nd, 2005 Session JE-9) Contents The HERMES experiment Quark distribution functions Single-spin asymmetry in 2-hadron semi-inclusive DIS Conclusion and outlook

2. HERMES experiment at DESY positron (electron) beam 27.6 [GeV] current ~ 30[mA] Transversely polarized hydrogen target (2002~2005) polarization ~ 75[%] HERA Target magnet

3. ＨＥＲＭＥＳ Spectrometer acceptance : 40 mrad ≦  ≦ 220 mrad Tracking resolution ：  P/P = (0.7-1.3)% 、  = 0.6 mrad PID ： Hodoscope 、 Calorimeter 、 TRD and RICH Lepton ID efficiency > 97%, Hadron contamination < 1% Hadron ID(  K, P) at 2 ‐ 15 GeV/c e + beam 27.6GeV 8m Internal gas target H(pol) 、 D （ pol ）、 He 、 Ne 、 Kr 、 Xe

4. unknown chiral odd Quark distribution functions Quark momentum distribution: Quark Helicity: Quark Transversity: At leading twist quark’s relativistic nature positivity bound : Soffer bound ： quark spin proton spin

5. Access to transversity chiral odd Need another chiral odd objects. Transversity couples to … Collins fragmentation function (FF) 2-hadron interference FF Polarized Lambda FF Spin-1 FF : :)(xq  Inclusive DISSemi-inclusive DIS Not accessibleaccessible

6. Single-spin asymmetry of 2-hadron production Azimuthal single-spin asymmetries )()(sin)sin(~ 1 zHxq SR     Transversity Interference FF (chiral odd) describes interference between different production channels of pion pairs )( 1 zH (data taken in 2002 … 2004) can be extracted using measured by e + e - collider, BELLE )(xq  )( 1 zH beam spin target spin

7. : s-p wave interference in scattering theory R. L. Jaffe, Xuemin Jin, and Jian Tan, Phys. Rev. Lett. 80, 1166 (1998) P. Estabrooks and A. D. Martin, Nucl. Phys. B79, 301 (1974) Partial wave expansion Sign of the phase shift changes at might depend strongly on

8. Spectator model for fragmentation M. Radici et al., hep/ph-0110252 No strong dependence. Partial wave expansion

9. Single-spin asymmetry in 2-hadron production Single-spin asymmetries First observation of transverse asymmetries in interference process (no binning)

10. Fit with Single-spin asymmetry in 2-hadron production Single-spin asymmetries Amplitude of the asymmetry modulation

11. Positive asymmetry is observed around Asymmetry is fitted with Single-spin asymmetry in 2-hadron production If we look at dependence, ( : invariant mass of pion pair)

12. Spectator model for fragmentation Marco Radici at Como, 7 - 10 Sept 2005 Partial wave expansion

13. Conclusion Conclusion Single-spin asymmetry in production is measured with transversely polarized hydrogen target at HERMES. This is the first observation of transverse target spin asymmetry in interference process. modulation of is observed at 4 sigma level. Positive asymmetry is observed for measured invariant mass range. ( =0.25 - 2.0 [GeV/c 2 ])

14. Outlook Outlook 4~5 M more DIS events are expected in 2005, compared to 3.5 M DIS events in 2002~2004.

15. backup

16. Event selection Kinematic cuts : ≥ 1 GeV 2 ≥ 4 GeV 2 ≥ 0.023 0.1 < < 0.85 > 2.5 GeV (for DIS lepton) > 1 GeV (for Hadron) > 2 GeV, where SIDIS events with at least pion pair( ) appeared were analyzed. To cut exclusive channel. Data set : 2002~2004

17. Evaluate where is the average target polarization. ( ) What is measured

18. Positive asymmetry is observed around Asymmetry is fitted with binning :0.25, 0.40, 0.55, 0.77, 2.0 [GeV] Single-spin asymmetry in 2-hadron production : invariant mass of pion pair

19. spectrum With or without cut

20. spectrum With or without cut

21. double spin asymmetry Beam polarization don’t affect to the asymmetry Fit for both beam polarization. Beam polarization (%) No double spin asymmetry

22. Polarized cross section for 2 hadron SIDIS 2 hadron semi-inclusive DIS Single spin asymmetries

23. Polarized cross section for 2 hadron SIDIS 2 hadron semi-inclusive DIS In Wandzura-Wilzcek approx., function with tilde vanish.