1. Transversity and the PAX collaboration @ GSI Alessandro Drago University of Ferrara

2. About the PAX proposal for the new GSI Transversity distribution direct access to h 1 via A TT Sivers distribution testing: (Sivers) DY = - (Sivers) DIS

3. Yerevan Physics Institute, Yerevan, Armenia Department of Subatomic and Radiation Physics, University of Gent, Belgium University of Science & Technology of China, Beijing, P.R. China Department of Physics, Beijing, P.R. China Palaiseau, Ecole Polytechnique Centre de Physique Theorique, France High Energy Physics Institute, Tbilisi State University, Tbilisi, Georgia Nuclear Physics Department, Tbilisi State University, Georgia Forschungszentrum Jülich, Institut für Kernphysik Jülich, Germany Institut für Theoretische Physik II, Ruhr Universität Bochum, Germany Helmholtz-Institut für Strahlen- und Kernphysik, Bonn, Germany Physikalisches Institut, Universität Erlangen-Nürnberg, Germany Langenbernsodorf, UGS, Gelinde Schulteis and Partner GbR, Germany Department of Mathematics, University of Dublin,Dublin, Ireland Università del Piemonte Orientale and INFN, Alessandria, Italy Dipartimento di Fisica dell’Università and INFN, Cagliari, Italy Università dell’Insubria and INFN, Como, Italy Instituto Nationale di Fisica Nuclelare, Ferrara, Italy PAX Collaboration Spokespersons: Paolo Lenisa Paolo Lenisalenisa@mail.desy.de Frank Rathmann Frank Rathmann f.rathmann@fz-juelich.de

4. Dipartimento di Fisica Teorica, Universita di Torino and INFN, Torino, Italy Instituto Nationale di Fisica Nucleare, Frascati, Italy Andrej Sultan Institute for Nuclear Studies, Dep. of Nuclear Reactions, Warsaw, Poland Petersburg Nuclear Physics Institute, Gatchina, Russia Institute for Theoretical and Experimental Physics, Moscow, Russia Lebedev Physical Institute, Moscow, Russia Physics Department, Moscow Engineering Physics Institute, Moscow, Russia Laboratory of Theoretical Physics, Joint Institute for Nueclear Research, Dubna, Russia Laboratory of Particle Physics, Joint Institute for Nuclear Research, Dubna, Russia Laboratory of Nuclear Problems, Joint Institute for Nuclear Research, Dubna, Russia Budker Institute of Nuclear Physics, Novosibirsk, Russia High Energy Physics Institute, Protvino, Russia Institute of Experimental Physics, Slovak Academy of Science, Kosice Slovakia Department of Radiation Sciences, Nuclear Physics Division, Uppsala University, Uppsala, Sweden Collider Accelerator Department, Brookhaven National Laboratory, Broohhaven USA RIKEN BNL Research Center Brookhaven National Laboratory, Brookhaven, USA University of Wisconsin, Madison, USA Department of Physics, University of Virginia, USA 178 physicists 35 institutions (15 EU, 20 NON-EU) PAX Collaboration

5. The PAX proposal Jan. 04 LOI submitted 15.06.04 QCD PAC meeting at GSI 18-19.08.04 Workshop on polarized antiprotons at GSI 15.01.05 Technical Report submitted 14-16.03.05 QCD-PAC meeting at GSI Polarization enters in the core of FAIR

6. Principle of spin filter method P beam polarization Q target polarization k || beam direction σ tot = σ 0 + σ  ·P·Q + σ || ·(P·k)(Q·k) transverse case:longitudinal case: For initially equally populated spin states:  (m=+½) and  (m=-½) Unpolarized anti-p beam Polarized H target

7. Principle of spin filter method P beam polarization Q target polarization k || beam direction σ tot = σ 0 + σ  ·P·Q + σ || ·(P·k)(Q·k) transverse case:longitudinal case: For initially equally populated spin states:  (m=+½) and  (m=-½) Unpolarized anti-p beam Polarized H target Polarized anti-p beam

8. Meyer PRE 50 (1994) 1485 Rathmann et al. PRL 71(1993)1379

9. Polarization with hadronic pbar-p interaction Model A: T. Hippchen et al. Phys. Rev. C 44, 1323 (1991) P Kinetic energy (MeV) 10 100 10001 0.05 0.10 0.15 0.20 Model D: V. Mull, K. Holinde, Phys. Rev. C 51, 2360 (1995) P Kinetic energy (MeV) 10 100 10001 0.05 0.10 0.15 0.20

10. 0.1 0.2 0.3 0.4 Beam Polarization P(2·τ beam ) 10 T (MeV)100 EM only 5 10 30 20 40 Ψ acc =50 mrad 0 1 Filter Test: T = 23 MeV Ψ acc = 4.4 mrad Beam Polarization

11. Staging: Phase I (PAX@CSR) Physics:EMFF pbar-p elastic Experiment: pol./unpol. pbar on internal polarized target Independent from HESR running

12. Staging: Phase II (PAX@HESR) EXPERIMENT: 1. Asymmetric collider: polarized antiprotons in HESR (p=15 GeV/c) polarized protons in CSR (p=3.5 GeV/c) 2. Internal polarized target with 22 GeV/c polarized antiproton beam. Physics: Transversity

13. Transversity in Drell-Yan processes p p qLqL q l+l+ l-l- q 2 =M 2 qTqT PAX: Polarized antiproton beam → polarized proton target (both transverse) M invariant Mass of lepton pair

14. PAX: M 2 ~10-100 GeV 2, s~45-200 GeV 2,  =x 1 x 2 =M 2 /s~0.05-0.6 → Exploration of valence quarks (h 1 q (x,Q 2 ) large) A TT for PAX kinematic conditions RHIC: τ=x 1 x 2 =M 2 /s~10 -3 → Exploration of the sea quark content (polarizations small!) A TT very small (~ 1 %) A TT /a TT > 0.2 Models predict |h 1 u |>>|h 1 d |

15. Kinematics and cross section M 2 = s x 1 x 2 x F =2Q L /√s = x 1 -x 2 M (GeV/c 2 ) 22 GeV collider 2 k events/day

16. Energy for Drell-Yan processes "safe region": QCD corrections might be very large at smaller values of M: yes, for cross-sections, not for A TT K-factor almost spin-independent Fermilab E866 800 GeV/c H. Shimizu, G. Sterman, W. Vogelsang and H. Yokoya, hep-ph/0503270

17. s=30 GeV 2 s=45 GeV 2 s=210 GeV 2 s=900 GeV 2

18. J/ψ q q q l+l+ l–l– l+l+ l–l– all vector couplings, same spinor structure and, at large x 1, x 2 measure A TT also in J/ψ resonance region q Mauro Anselmino, V. Barone, A. D. and N. Nikolaev PLB 594 (2004) 97

19. Estimated signal for h 1 (phase II) 1 year of data taking Collider: L=2x10 30 cm -2 s -1 Fixed target: L=2.7x10 31 cm -2 s -1

20. Transversity in various quark models MIT CDM CQSM g 1 evol

21. Sivers functionusual parton distribution Direct access to Sivers function test QCD basic result: J. Collins usual fragmentation function process dominated by no Collins contribution same process at RHIC is dominated by Measuring the Sivers function Sivers function non-vanishing in gauge theories. Chiral models with vector mesons as gauge bosons can be used A.D. PRD71(2005)057501. (Sivers) u = -(Sivers) d in chiral models at leading order in 1/N c.

22. Conclusions PAX Collaboration proposal @ GSI: First experiment with a polarized antiproton beam Possibility of measuring h 1 in the valence region Possibility of testing the gauge-theory dictated rule (Sivers) DY = - (Sivers) DIS