Marco Guzzi Università di Lecce, Università dell’Insubria (collaboration with V.Barone, A. Cafarella, C. Corianò, P.G.

1. Marco Guzzi Università di Lecce, Università dell’Insubria(collaboration with V.Barone, A. Cafarella, C. Corianò, P.G.Ratcliffe) Transverse Double Spin Asymmetries in Drell-Yan processes with antiprotons “Transversity 2005“ Villa Olmo (Como), 7−10th. September 2005 M. Guzzi

2. The missing piece in the leading twist QCD description of the nucleon is the transversity density δq(x) = qhh(x) - qhi(x) Given its chirally-odd nature, transversity may be accessed in collisions between two transversely polarized nucleons. Double polarized Drell-Yan production is the cleanest process that probes the transversity distributions. M. Guzzi

3. Double-spin transverse asymmetries depend on quark and antiquark transversity distributions only. Measurement of is planned at RHIC but this asymmetry is expected to be small (2-3%). (Barone, Calarco, Drago 1997; O. Martin et al. 1998) contains antiquark transversity distributions RHIC kinematics (√s=200 GeV, M<10 GeV, x1 x2=M²/s <3×10­³) probes the low x region where δq(x) is suppressed by QCD evolution compared to q(x). M. Guzzi

4. These problems may be avoided by measuring at lower center of mass energies. (Barone, Calarco, Drago 1997; Anselmino et al. 2004) This is the program of the PAX experiment at GSI (PAX Technical report, hep-ex/o5o5o54) s=30 GeV² or 45 GeV² (fixed target) up to 200 GeV ² (collider mode) GSI kinematics M>2 GeV τ = x1 x2 = M²/s >0.1 (M is the dilepton invariant mass) Double transverse pp Drell-Yan process probes the product δq ×δq of two quark distributions and the GSI kinematics is such that the asymmetries are dominated by valence. ‾ M. Guzzi

5. At leading order: is found to be of order of 30% (Anselmino et al. 2004; Efremov et al. 2004 ) - - - - - s=30 GeV² ____ s=45 GeV² M. Guzzi

6. At NLO the factorization formula for the cross section of transversely polarized proton-antiproton scattering with dilepton production is (O. Martin et al. 1999; Mukherjee et al. 2003) and the hard scattering term is (yis the rapidity variable and Ф is the azimuthal angle of the dilepton pair) M. Guzzi

7. To predict the asymmetries one has to make some assumption about the transversity distributions. For instance: Helicity = Transversity at low scale (as suggested by models) δf(x, μ) = Δf(x, μ) (“Minimal Bound”) Saturation of Soffer’s inequality 2 δf(x, μ) ≤ [ f(x, μ) + Δf(x, μ) ] We used GRV input distributions whose starting scale (at NLO) is μ0=0.63 GeV. The relations between transversity and the GRV distributions are set at this scale. The transversity densities have been evolved by solving the appropriate NLO DGLAP equations (Cafarella, Corianò 2004) M. Guzzi

8. We plot the ratio NLO ATT with M integrated from 2 to 3 GeV using GRV input with the minimal bound δf(x, μ) = Δf(x, μ) M. Guzzi

9. ATT at NLO with M integrated from 2 to 3 GeV using GRV input saturating the Soffer bound. (Systematically larger than ATT obtained with the “minimal bound”) M. Guzzi

10. NLO ATT with M integrated from 4 to 7 GeV using GRV input with the minimal bound δf(x, μ) = Δf(x, μ). The asymmetrygets larger at larger M (but the cross section goes down rapidly) M. Guzzi

11. NLO vs. LO LO vs. NLO asymmetries generated using GRV input with the minimal bound at M=4 GeV and s=45 GeV² M. Guzzi

12. LO vs. NLO asymmetries generated using GRV input with the minimal bound at M=4 GeV and s=200 GeV² M. Guzzi

13. NLO ATT/âTT integrated over M from 2 up to 3 GeV. Setting the constraint δf(x, μ) = Δf(x, μ)at1 GeV gives slightly larger asymmetries M. Guzzi

14. Dilepton production via J/Ψ resonance in the GSI regime To have a higher counting rate one can exploit the J/Ψ peak, where the cross section is two orders of magnitude larger. If the J/Ψ production is dominated by qq annhilation channel the corresponding asymmetry has the same structure as in the continuum region, since the J/Ψ is a vector particle and qq-J/Ψ coupling is similar to qq-γ* coupling (M. Anselmino et al. 2004). ‾ ‾ ‾ Old SPS data show that the pp cross section for J/ Ψ production at s=80 GeV² is about 10 times larger than the corresponding pp cross section, indicating the dominance of the qq annhilation mechanism. ‾ ‾ M. Guzzi

15. The helicity structure of the asymmetries is preserved. Replacing the couplings: M. Guzzi

16. In the region of large x1 x2 only the u and d valence quarks dominate and the coupling qq-J/Ψ is the same for u and d quarks. Thus the asymmetry for the pp process is ‾ ‾ We can have a further simplification since at large x in all the models for transversity the condition h1u(x)>>h1d(x) holds. Hence one gets The J/Ψasymmetryis essentially the DY asymmetry evaluated at MJ/Ψ This remains true at NLO (that is considering gluon radiation) as far as the gg fusion diagram can be neglected, as old pp data suggest. ‾ M. Guzzi

17. Threshold Resummation(Shimizu et al. 2005) Virtual and Real emission diagrams become strongly unbalanced (real-gluon emission is suppressed) z = τ/(x1 x2) ≤ 1 There are large logarithmic higher-order corrections to the partonic cross section of the form The region z≈1 is dominant in the kinematic regime relevant for GSI, hence large logarithmic contributions need to be resummed to all orders in αs, (“threshold resummation”). Resummation effects on ATT are less than 10% and rather dependent on the infrared cut-off in the soft gluon emission. M. Guzzi

18. Conclusions Drell-Yan double transverse asymmetries in the GSI regime are sizable (ATT/âTT ≈0.3). They are not spoiled by NLO (and resummation) effects. Transverse asymmetries for J/Ψproductionat moderate energies are expected to be similar (with the advantage of much higher counting rate). Transversely polarized antiproton experiments at GSI will provide an excellent window on the transversity of nucleons. THANK YOU! M. Guzzi

19. Bibliography [1] A. Cafarella, C. Corianò, V. Barone, M. Guzzi and P. Ratcliffe in preparation. [2] Shimizu, Sterman, Vogelsang and Yokoya, Phys. Rev. D 71, 114007 (2005) [3] O. Martin, A. Schäfer, M. Stratmann, and W. Vogelsang Phys. Rev. D 60 117502 (1999) [4] A. Mukherjee, M. Stratmann, and W. Vogelsang Phys. Rev. D 67 114006 (2003) [5] J. Soffer, Phys. Rev. Lett. 74 1292 (1995) [6] Proton-Antiproton scattering experiments with polarization (V. Barone et al.) hep-ex/0505054 [7] M. Anselmino, V. Barone, A. Drago, N.N. Nikolaev, Phys. Lett. B 594 97 (2004) M. Guzzi

20. NLO vs. LO asymmetries plotted using GRV input evolved up to 1 GeV and saturating the minimal bound with a fixed value of M=4 GeV. M. Guzzi

21. NLO transversely polarized cross section with M integrated from 2 to 3 GeV , with GRV input evolved up to 1 GeV and saturating the minimal bound. M. Guzzi

22. NLO vs. LO transversely polarized cross section with M=4 GeV and s= 45 GeV² M. Guzzi