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

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

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

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

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

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 ⊥

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

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

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

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 1 4 sin 2   1  2 − 𝑒 − 𝑒  ℎ 1 ℎ 2 Preliminary → A. Ogawa

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. electron/positron @ 27.5GeV polarization about 55%

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

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) 012002 and updated results → T.-A. Shibata

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

Sivers extraction from asymmetries M. Anselmino, M. Boglione, U. D'Alesio, A. Kotzinian, F. Murgia, A. Prokudin, hep-ph/0507181  𝑁 𝑓 𝑞 1 𝑥=− 𝑓 1T ⊥1𝑞 𝑥

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

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

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.

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, 074031 𝐻 1 ∢ z 𝐴 sin

→ 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

Prediction for IFF by M. Radici @ Transversity 2005

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