1. 1 Transversity Experiments Experimental probes for transversity Current experimental status on transversity and other related distribution and fragmentation functions Outstanding issues and future prospect Jen-Chieh Peng SIR2005, Jefferson Lab, May 18-20, 2005 University of Illinois

2. 2 Remaining frontier of k T – independent structure functions Connections to many other k T – dependent distribution and fragmentation functions Major experimental challenges to measure transversity. Opportunities for lepton and hadron beams. Active interaction between theory and experiment WHY Transversity ?

3. 3 Transversity Some characteristics of transversity: –δq(x) = Δq(x) for non-relativistic quarks –δq and gluons do not mix → Q 2 -evolution for δq and Δq are different –Chiral-odd → not accessible in inclusive DIS Chiral-quark soliton model Quark – diquark model (solid) and pQCD-based model (dashed) Similar to helicity distributions B. –Q. Ma, I. Schmidt and J. –J. Yang, PRD 65, 034010 (2002) hep-ph/0101300

4. 4 How to measure transversity? Transversely Polarized Drell-Yan Semi-Inclusive DIS –Single-hadron (Collins fragmentation function) –Two hadrons (Interference fragmentation function) –Vector meson polarization –Λ - polarization Chiral-odd → not accessible in DIS Require another chiral-odd object

5. 5 Polarized Drell-Yan in p-p collision (RHIC-spin) Well understood reaction mechanism. Clear interpretation An unique method to extract sea-quark transversity Small effect due to the expected small sea quark transversity Transverse double-spin asymmetry for Drell-Yan PHENIX, s 1/2 =200GeV, 320 pb -1 hep-ph/9902250

6. 6 Collider: L=2x10 30 cm -2 s -1 Fixed target: L=2.7x10 31 cm -2 s -1 GSI Polarized Antiproton eXperiment (PAX) Phase I: 2013-2017, Phase II: 2018 - DIS2005 talk by Lenisa

7. 7 Leading-Twist Quark Distributions No K ┴ dependence K ┴ - dependent, T-odd K ┴ - dependent, T-even ( A total of eight distributions) Simi-inclusive DIS can access all leading-twist quark distributions

8. 8 All Eight Quark Distributions Are Probed in Semi-Inclusive DIS Unpolarized Polarized target Polarzied beam and target S L and S T : Target Polarizations; λe: Beam Polarization Sivers Transversity

9. 9 Observation of Single-Spin Azimuthal Asymmetry Longitudinally polarized target ep → e’πxHERMES ~ 0.15 Collins effect: Correlation between the quark’s transverse spin with pion’s p T in the fragmentation process. Sivers effect: Correlation between the transverse spin of the proton with the quark’s transverse momentum. Other higher twist effects could also contribute. Origins of the azimuthal asymmetry (correlation between the target nucleon transverse spin and the pion transverse momentum)?

10. 10 Comparison with HERMES longitudinal SSA data Proton data Deuteron data Efremov et al. shows that Chiral-quark soliton model can describe the SSA data (by including only the transversity / Collins term) hep-ph/0206267

11. 11 Comparison with HERMES longitudinal SSA data proton data Anselmino et al. showed that the Hermes SSA data for longitudinally polarized data can be explained by Sivers effect alone (without the transversity / Collins effect). hep-ph/0412316

12. 12 A UT sin(  ) from transv. pol. H target Simultaneous fit to sin(  +  s ) and sin(  -  s ) Talk by Schnell „Collins“ moments hep-ex/0408013

13. 13 Collins asymmetry from COMPASS COMPASS 2002-2004 data: ~ factor of 4 in statistics hep-ex/0503002 Talk by Bressan Transversely polarized 6 LiD target Cover smaller x Consistent with 0

14. 14 Comparison between HERMES and COMPASS Results Cancellation between p and n asymmetries?

15. 15 JLab Hall-A proposal for 3 He ↑ (e,e’π - )x Beam –6 GeV polarized e -, 15 μA, helicity flip at 60 Hz Target –Optically pumped Rb spin-exchange 3 He target, 50 mg/cm 2, ~42% polarization, transversely polarized with tunable direction Electron detection –BigBite spectrometer, Solid angle = 60 msr, θ Lab = 30 0 Charged pion detection –HRS spectrometer, θ Lab = -16 0

16. 16 Transversity measurements at JLab 12 GeV upgrade Projected sensitivity at CLAS12

17. 17 Measuring transversity using two-hadron production in SIDIS SSA for π+π- production in SIDIS

18. 18 Mass dependence of the π+π- interference FF Jaffe et al. hep-ph/9709322 Hermes data for longitudiannly polarized deuterium target hep-ex/0501009 New results from Hermes and Compass for transversely polarized target (talks by Schnell and Bressan)

19. 19 “Byproduct” of the transversity experiments “Sivers“ moments A UT sin(  ) from Hermes transv. pol. H target First measurement of Sivers asymmetry Sivers function nonzero  orbital angular momentum of quarks Sivers moments from HERMES and COMPASS (Talks by Schnell and Bressan)

20. 20 Extraction of Sivers functions from the Sivers moment measurements Fits to the Hermes data“Prediction” of the Compass data Anselmino et al. hep/ph/0501196

21. 21 Is the Hermes A UL data consistent with A UT data? A combined analysis of the A UL and the A UT data Contributions from Collins and Sivers Higher-twist contribution Data Elschenbroich et al. hep-ex/0504025

22. 22 Transverse SSA in p-p collision ++ -- 00 Result from STAR New data at forward and backward X F presented at DIS2005 (talk by Perdekamp)

23. 23 Comparing An for  + and  -  N = -0.08 +- 0.005 +- [0.02] in 0.17 < x F < 0.32  N = +0.05 +- 0.005 +- [0.015] in 0.17 < x F < 0.32  +  -. Polarization was ~42% for  + measurements and ~38% for  -. syst error on P ~ 20- 30%. Improve in final analysis of CNI and Gas Jet data. New A N data from BRAHMS DIS2005 Talk by Videbaek

24. 24 BRAHMS preliminary This corresponds to negative x F, and is consistent with 0 as expected. Negative X F data from BRAHMS A unified picture for SSA with hadron and lepton beams?

25. 25 SSA with Transversely Polarized Drell-Yan Prediction by Anselmino, D’Alesio, Murgia (hep-ph/0210371) for a negative A N. |A N | increases with rapidity, y, and with dilepton mass, M. Analysing power (A N ) is sensitive to Sivers function Sivers function in Drell-Yan is expected to have a sign opposite to that in DIS! (Brodsky, Hwang, Schmidt, hep-ph/0206259; Collins, hep-ph/0204004) p↑ + p → l + l - + X √s = 200 GeV ANAN y Is this measurement feasible at RHIC?

26. 26 Expected statistical sensitivity for Drell-Yan A N Might be feasible to determine the sign of the Sivers function at RHIC Should consider fixed-target polarized Drell-Yan too Assuming 400 pb -1 50% polarization 6 < M < 10 GeV p↑ + p → l + l - + x √s = 200 GeV

27. 27 Cos2Ф Dependence in Unpolarized Drell-Yan RHIC would provide unpolarized p-p Drell- Yan data too Fixed-target unpolarized p-p Drell-Yan data also exist Large cos2Ф dependences have been observed in π – induced Drell-Yan This azimuthal dependence could arise from a product of K T -dependent distribution function h 1 ┴ ( Boer, hep-ph/9902255; Boer, Brodsky, Hwang, hep-ph/0211110) In quark-diquark model, h 1 ┴ is identical to Sivers function No Cos2Ф depenence for unpolarized p-p Drell-Yan has been reported yet (The effect from h 1 ┴ is expected to be smaller)

28. 28 Unpolarized p-p and p-d dimuon production Fermilab E866, √s = 38.8 GeV J/Ψ Ψ’Ψ’ Υ ~ 2.5 x 10 5 Drell-Yan events Talk by Reimer

29. 29 Sin2Φ moment of single-spin asymmetry CLAS EG1b preliminary (Probing Collins function) Talk by Bosted

30. 30 Summary Exciting time for physics of transversity and related topics. Still a long way from measuring the transversity. However, the journey might be as interesting as the destination. Look forward to the talks on new experimental results and the discussion on theoretical interpretations.