1. Measurements of quark transversity and orbital motion in hard scattering
Yoshiyuki Miyachi
Tokyo Institute of Technology

2. Contents Proton spin problem
Transverse momentum dependent parton distribution functions
TMD in semi-inclusive measurements of DIS
Single hadron measurement: HERMES, COMPASS
Hadron pair measurement: HERMES, COMPASS
Summary

3. Proton spin problem Orbital angular momentum Quark spin: Gluon Spin:
EMC, Nucl.Phys.B328:1,1989 (Cited 1092 times)
Phys.Lett.B206:364,1988 (Cited 1274 times)
Quark spin:
- g1 NLO QCD analysis:
ΔΣ ~ 0.2
- Flavor decomposition
with SIDIS measurements
unpol. sea quark
1 2 = 1 2 𝐺𝐿
Gluon Spin:
- g1 NLO QCD analysis: ΔG > 0
- DIS: high-pt hadron pair, Open charm: moderate ΔG>0 ?
- RHIC spin: pion, direct photon, jet productions.
Orbital angular
momentum

4. Single Spin Asymmetries in hard scattering
𝑝  𝑝𝑋
STAR
HERMES
𝑒 𝑝  𝑒′𝑋
𝐴 𝑈𝐿 sin 𝑥
Transverse motion of parton:
Sivers effect:
correlation between parton transverse momentum and nucleon polarization
Collins effect:
correlation between parton polarization and transverse momentum in fragmentation.. Pt

5. Extension of parton distribution
Semi-inclusive DIS measurement
HERMES, AUL
𝐴 𝑈𝐿 𝑥 k⊥
Inclusive DIS measurement
Transverse momentum dependent PDF
Hard exclusive production
HERMES, DVCS
Off-forward
x dependent PDF
Generalized Parton Distribution

6. Transverse momentum dependent parton distribution functions
Unpolarized
Long. polarized
Trans. polarized
Nucleon
Number
density
Sivers
naïve T-odd
𝑓 1 =𝑞
These survive after
integration over k⊥.
𝑓 1T ⊥
Unpol.
Nucleon
Parton
Helicity
Long. pol.
𝑔 1L =𝑞
𝑔 1T
Parton
Chira-odd
requires chiral-odd partner
naïve T-odd
Transversity
ℎ 1T =𝑞
Trans. polarized
ℎ 1 ⊥
ℎ 1L ⊥
ℎ 1T ⊥

7. Semi-inclusive measurement of single hadron
in Deep Inelastic Scattering
𝑙𝑁𝑙′ℎ𝑋

8. Azimuthal angles in SIDIS
𝑆 𝐿  h
Lepton
Polarized target
Hadron

9. Eight PDFs accessible in DIS - single hadron semi-inclusive measurement -
Nucleon
Unpolarized:
𝑒 2 𝑓 1 𝐷 1
Density distribution
Parton
cos2  ℎ  𝑒 2 ℎ 1 ⊥1 𝐻 1 ⊥
Polarized target |S| :
∣ 𝑆 𝐿 ∣sin2  ℎ  𝑒 2 ℎ 1L ⊥1 𝐻 1 ⊥
∣ 𝑆 𝑇 ∣sin  ℎ   𝑠  𝑒 2 ℎ 1T 𝐻 1 ⊥
Transversity
∣ 𝑆 𝑇 ∣sin  ℎ −  𝑆  𝑒 2 𝑓 1T ⊥1 𝐷 1
Siverse distribution
∣ 𝑆 𝑇 ∣sin3  ℎ −  𝑆  𝑒 2 ℎ 1T ⊥2 𝐻 1 ⊥
Polarized beam λ and target |S| :
∣ 𝑆 𝐿 ∣ 𝑒 2 𝑔 1L 𝐷 1
Helicity distribution
∣ 𝑆 𝑇 ∣cos  ℎ −  𝑆  𝑒 2 𝑔 1T 1 𝐷 1

10. Chiral odd fragmentation function
𝑒   𝑒 −  ℎ 1  ℎ 2 𝑋
𝑑∝𝐵𝑦cos  1   2  𝐻 1 ⊥1  𝑧 1  𝐻 1 ⊥1  𝑧 1  𝐵𝑦 = cm sin 2 
 1
 2 −
𝑒 −
𝑒 
ℎ 1
ℎ 2
Preliminary
→ A. Ogawa

11. HERMES at DESY HERA: pol. electron/positron @ 27.5GeV
gas targets:
unpol. (H, D, Ne, Kr, Xe)
long. pol. (H, D)
trans. pol. (H)
DESY
HERA:
pol. 27.5GeV
polarization about 55%

12. HERMES Spectrometer and target
Transversely Polarized
Hydrogen target:
2002 ~ 2005

13. AUT with the trans. pol. p target - HERMES -
𝑒 𝑝  𝑒′𝑋
sin  ℎ   𝑠  𝑒 2 ℎ 1T ⋅ 𝐻 1 ⊥
sin  ℎ −  𝑆  𝑒 2 𝑓 1T ⊥1 ⋅ 𝐷 1
HERMES, Phys. Rev. Lett. 94 (2005) and updated results
→ T.-A. Shibata

14. AUT with the trans. pol. d target - COMPASS -
   𝑑  ′ℎ𝑋
Transversely polarized 6LiD target
Phys.Rev.Lett.94:202002,2005
Sivers
Collins
→ T. Iwata

15. Sivers extraction from asymmetries
M. Anselmino, M. Boglione, U. D'Alesio, A. Kotzinian, F. Murgia, A. Prokudin, hep-ph/
 𝑁 𝑓 𝑞 1 𝑥=− 𝑓 1T ⊥1𝑞 𝑥

16. Fit Collins and transversity
by Anselmino, Transversity 2005,
Sept. 7-10, Como

17. Semi-inclusive measurement of pion pair in Deep Inelastic Scattering
𝑙𝑁𝑙′     − 𝑋

18. Semi-inclusive measurement of π+ + π- in DIS
𝑙𝑁𝑙′     − 𝑋
𝐴 𝑈𝑇   𝑅⊥ ,  𝑆 = 1 𝑆 ⊥ 𝑁    𝑅⊥ ,  𝑆 − 𝑁 −   𝑅⊥ ,  𝑆  𝑁    𝑅⊥ ,  𝑆  𝑁 −   𝑅⊥ ,  𝑆 
~sin  𝑅⊥   𝑆  𝑒 2 sin⋅ ℎ 1T ⋅ 𝐻 1 ∢
After integration over hadron transverse momentum:
→ no convolution integral involved.
There is no Sivers contribution.

19. Interference fragmentation function - models -
(1) Jaffe, Jin, Tang, Phys. Rev. Lett. 80 (1998) 1166
π-π phase shift (data)
Phys. B79, 301 (1974)
𝐻 1 ∢ 𝑧,cos, 𝑀  2 = 𝐻 1 ∢,𝑠𝑝 𝑧, 𝑀  2 cos 𝐻 1 ∢,𝑝𝑝 𝑧, 𝑀  2 
𝐻 1 ∢,𝑠𝑝 𝑧, 𝑀  2 =sin  0 sin  1 sin  0 −  1  𝐻 1 ∢,𝑠𝑝′ 𝑧
(2) Radici, Jakob, Bianconi, PRD 65,
𝐻 1 ∢ z
𝐴 sin

20. → T. Iwata → T. Kobayashi 𝑒 𝑝  𝑒′     − 𝑋
   𝑑  ′ ℎ   ℎ − 𝑋
𝐴 𝑈𝑇 sin  𝑅⊥   𝑆 sin ~ 𝑒 2 ℎ 1T ⋅ 𝐻 1 ∢
𝐴 𝑈𝑇 sin  𝑅𝑆 
→ T. Kobayashi
→ T. Iwata

21. Prediction for IFF
by M. Transversity 2005

22. Summary Proton spin structure
Quark motions inside nucleon take an important role for the understanding “Spin structure of proton”
TMD PDF, GPD
Quark transversity and Sivers measurements in SIDIS
Experimental results: non-zero contributions from such TMD PDSs and FFs (HERMES, COMPASS)
SSAs in single hadron semi-inclusive measurements
Collins FF
SSAs in double hadron semi-inclusive measurements
Interference FF