Villa Olmo (Como), 7−10th. September 2005 9/19/2018 Transverse Double Spin Asymmetries in Drell-Yan processes with antiprotons Marco Guzzi Università di Lecce, Università dell’Insubria (collaboration with V.Barone, A. Cafarella, C. Corianò, P.G.Ratcliffe) “Transversity 2005“ Villa Olmo (Como), 7−10th. September 2005 19/09/2018 M. Guzzi M. Guzzi

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. 19/09/2018 M. Guzzi

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). 19/09/2018 M. Guzzi

This is the program of the PAX experiment at GSI 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. ‾ 19/09/2018 M. Guzzi

is found to be of order of 30% (Anselmino et al. 2004; 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 19/09/2018 M. Guzzi

and the hard scattering term is 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 (y is the rapidity variable and Ф is the azimuthal angle of the dilepton pair) 19/09/2018 M. Guzzi

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) 19/09/2018 M. Guzzi

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) 19/09/2018 M. Guzzi

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”) 19/09/2018 M. Guzzi

NLO ATT with M integrated from 4 to 7 GeV using GRV input with the minimal bound δf(x, μ) = Δf(x, μ). The asymmetry gets larger at larger M (but the cross section goes down rapidly) 19/09/2018 M. Guzzi

NLO vs. LO LO vs. NLO asymmetries generated using GRV input with the minimal bound at M=4 GeV and s=45 GeV² 19/09/2018 M. Guzzi

LO vs. NLO asymmetries generated using GRV input with the minimal bound at M=4 GeV and s=200 GeV² 19/09/2018 M. Guzzi

NLO ATT/âTT integrated over M from 2 up to 3 GeV. Setting the constraint δf(x, μ) = Δf(x, μ) at 1 GeV gives slightly larger asymmetries 19/09/2018 M. Guzzi

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. ‾ ‾ 19/09/2018 M. Guzzi

The helicity structure of the asymmetries is preserved. Replacing the couplings: 19/09/2018 M. Guzzi

transversity the condition h1u(x)>>h1d(x) holds. Hence one gets 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/Ψ asymmetry is 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. ‾ 19/09/2018 M. Guzzi

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. 19/09/2018 M. Guzzi

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/Ψ production at 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! 19/09/2018 M. Guzzi

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) 19/09/2018 M. Guzzi

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. 19/09/2018 M. Guzzi

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. 19/09/2018 M. Guzzi

NLO vs. LO transversely polarized cross section with M=4 GeV and s= 45 GeV² 19/09/2018 M. Guzzi