1. 03/03/31 日本物理学会 1 HERMES による横偏極水素標的を 用いた quark transversity の測定 大須賀弘, 田中秀和, 宮地義之, 柴田利明, 他 HERMES Collaboration 東京工業大学 柴田研究室

2. 03/03/31 日本物理学会 2 Outline Transversity - What is the Transversity? - Motivation of the Transversity Measurement - How to Access the Transversity HERMES Experiment ( 27.6 GeV e + + N Deep Inelastic Scattering) A UL (φ) Single-Spin Asymmetry and Transversity (analyzed) A UT (φ) Single-Spin Asymmetry and Transversity (in progress) Conclusion

3. 03/03/31 日本物理学会 3 Notation Quark Number Density: q(x) ⇒ F 1 (x) Quark Helicity: Δq(x) ⇒ g 1 (x) Quark Transversity: δq(x) ⇒ h 1 (x) introduced by Jaffe and Ji in their classification Phys. Rev. Lett. 71 (1993) 2547

4. 03/03/31 日本物理学会 4 What is the Transversity? Quark Number Density: q(x) Quark Helicity: Δq(x) Quark Transversity: δq(x)

5. 03/03/31 日本物理学会 5 Motivation The difference between helicity distribution Δq and transversity distribution δq ⇒ measure of the relativistic effects for quarks inside the nucleon Relativistic Effects for Quarks inside the Nucleon for non-relativistic quarks

6. 03/03/31 日本物理学会 6 Characteristics of Transversity for relativistic quarks : transversity distribution CHIRAL ODD Bounds: ( Soffer Bound ) q and q contribute with opposite sign to the transversity ⇒ predominantly sensitive to valence quark polarization

7. 03/03/31 日本物理学会 7 How to Access Transversity Collins Effect with Transverse Target - Cleanest method is - effect already visible using a longitudinally polarized target sinφ moment : Azimuthal Asymmetry with Transversely Polarized Target : U: Unpolarized Beam T: Transversely Polarized Target along Beam Direction Azimuthal Angle : the angle between lepton scattering plane and hadron production plane : Collins Fragmentation Function (T-odd, Chiral odd)

8. 03/03/31 日本物理学会 8 HERMES at DESY-HERA target: gas target in internal storage cell PID: RICH, TRD, Preshower, Calorimeter 8 m e + beam 27.6 GeV

9. 03/03/31 日本物理学会 9 Transversity Measurement at HERMES HERMES 1995-2000 HERMES 2002- Longitudinally Polarized Target Transversely Polarized Target ⇒ Quark Helicity Distribution: Δq ⇒ Glimpse on Quark Transversity Distribution: δq ⇒ Quark Transverse Distribution: δq (analyzed) (in progress)

10. 03/03/31 日本物理学会 10 Azimuthal Asymmetry with Longitudinal Polarized Target (analyzed) Longitudinal Target Spin Asymmetry: significant sinφ dependence observed for π + and π 0 sin 2φ moment consistent with zero for all pions π0π0 π-π- π+π+ π 0 : Phys. Rev. D64 (2001) 097101 π ± : Phys. Rev. Lett. 84 (2000) 4047-4051

11. 03/03/31 日本物理学会 11 Sinφ Moment of the Azimuthal Asymmetry (analyzed) HERMES: Phys. Rev. D64 (2001) 097101 S L (T) : component of the longitudinal (transverse) target polarization in the virtual photon frame zxp ⊥ (GeV) sinφ moment of the azimuthal asymmetry: π0π0 π+π+ π-π-

12. 03/03/31 日本物理学会 12 Transversity Measurement at HERMES HERMES 1995-2000 HERMES 2002- Longitudinally Polarized Target Transversely Polarized Target ⇒ Quark Helicity Distribution: Δq ⇒ Glimpse on Quark Transversity Distribution: δq ⇒ Quark Transverse Distribution: δq (analyzed) (in progress)

13. 03/03/31 日本物理学会 13 Target Magnet Transverse target ( B = 0.295 T ) Transversely polarized hydrogen Target polarization above 80%

14. 03/03/31 日本物理学会 14 Azimuthal Asymmetries with Transversely Polarized Target (unpolarized beam) : Collins Angle : Angle between Target Spin Vector and Scattering Plane : Collins Fragmentation Function Azimuthal Asymmetry with Transversely Polarized Target (in progress)

15. 03/03/31 日本物理学会 15 Integrated Deep Inelastic Scattering events 0 100 200 300 Total DIS : 512K Day of Year (2002) 5000 4000 3000 2000 1000 0 ×10 2 Number of DIS events 2002: 512 K DIS events (accumulated) Up to Spring 2003: 1.3 M DIS events (in progress)

16. 03/03/31 日本物理学会 16 Conclusion HERMES is a deep inelastic scattering experiment using HERA 27.6 GeV positron beam Transversity is the distribution of the quark’s transverse spin in a transversely polarized nucleon The transversity measurement can provide a measure of the relativistic effects for quarks inside the nucleon HERMES suggests both δq and significantly non-zero HERMES is taking data with transversely polarized hydrogen target Spring 2003: 1.3 Million DIS events expected HERMES will do the first determination of transverse u-quark distribution

17. 03/03/31 日本物理学会 17 How to Access Transversity Drell - Yan Process Λ-hyperon Semi-Inclusive Deep Inelastic Scattering Collins Effect with Transverse Target - Cleanest method is - effect already visible using a longitudinally polarized target sinφ moment Azimuthal Asymmetry with Transversely Polarized Target U: Unpolarized Beam T: Transversely Polarized Target along Beam Direction

18. 03/03/31 日本物理学会 18 Sinφ Moment of the Single Spin Asymmetry HERMES, Phys. Rev. D64 (2001) 097101 Larger for π +,π 0 than π - ⇒ u-quark dominance in case of proton target Peak around x=0.3 ⇒ valence quark dominance S L (T) : component of the longitudinal (transverse) target polarization in the virtual photon frame

19. 03/03/31 日本物理学会 19 Deep Inelastic Scattering (DIS) lepton nucleon γ hadron hadronization fragmentation Inclusive Semi-inclusive

20. 03/03/31 日本物理学会 20 SSA with Longitudinal Polarized Target Longitudinally polarized in experiment (along beam direction) L/T polarized in theory (along virtual gamma direction)

21. 03/03/31 日本物理学会 21 Motivation quark (u,d,s) gluon SzSz Spin Structure of the Nucleon Contribution from the quark spin 1988: EMC 1988-2000: SLAC, CERN, DESY

22. 03/03/31 日本物理学会 22 Motivation HERMES 1995-2000 HERMES 2002- Longitudinally Polarized Target Transversely Polarized Target ⇒ Quark Helicity Distribution: Δq ⇒ Remaining Quark Transverse Distribution: δq

23. 03/03/31 日本物理学会 23 History of Transversity The concept was Introduced by Ralston and Soper (1979) via Drell - Yan Production with polarized beams LO anomalous dimensions were first calculated by Baldracchini et al. (1981) Also calculated (for g 2 evolution) - Kodaira et al. (1979) - Antoniadis and Kounnas (1981) - Bukhvostov et al. (1985) - PGR (1986) Re-calculated by Artru and Mekhfi (1990)

24. 03/03/31 日本物理学会 24 Twist-2 Quark Distribution Functions ・ Functions Surviving on Integration over Transverse Momenta The others are sensitive to intrinsic in the nucleon and in the fragmentation process

25. 03/03/31 日本物理学会 25 How Access Transversity Collins Effect with Transverse Target Λ-hyperon SIDIS Drell - Yan Process - Cleanest method is - effect already visible using a longitudinally polarized target - Method requires significant spin transfer from quark to Λ in fragmentation process… - low rate of quark fragmentation into Λ-particle ( ～ 2%)