Transversely polarized Drell-Yan asymmetry $A_{TT}$ at NLO

We present the first fully differential next-to-leading order QCD calculation for lepton production in transversely polarized hadronic collisions, $p\uparrow p\uparrow \to {\ell }^{\pm }X$, where the lepton arises from the decay of an electroweak gauge boson. The calculation is implemented in the Monte-Carlo like code che that already includes the unpolarized and longitudinally polarized cross sections and may be readily used to perform a comparison to experimental data and to extract information on the related parton distributions. We analyze the perturbative stability of the cross-section and double spin asymmetry $A_{TT}$ at RHIC kinematics. We find that the QCD corrections are non-negligible even at the level of asymmetries and that they strongly depend on the lepton kinematics. Furthermore, we present two scenarios for transversely polarized parton distributions, based on the de Florian-Sassot-Stratmann-Vogelsang (DSSV) set of longitudinally parton densities and fully evolved to NLO accuracy, that can be used for the evaluation of different observables involving transverse polarization.

Figure 1

Feynman diagrams for $Z$, $\gamma$ production with leptonic decay: (a) leading-order, (b) NLO virtual correction, (c) NLO real emission. Crossed diagrams are not shown.

Figure 2

Left: Next-to-leading order $xu(x,Q)$ evaluated at the scale $Q=91.2\mathrm{GeV}$ for the unpolarized MSTW [34] distributions (solid), helicity DSSV [5, 6, 7] distribution (dashes), transversity maximally saturated (dashed-blue), and transversity-helicity distributions (dots-blue). Right: Same for $x\overline{u}(x,Q)$ (right-hand side).

Figure 3

Same as Fig. 2 but for the $xd(x,Q)$ and $x\overline{d}(x,Q)$ distributions.

Figure 4

Dilepton mass distribution for the transversely polarized cross section computed at NLO accuracy with the transversity maximally saturated (solid) and transversity-helicity (dotted) polarized densities.

Figure 5

Transverse momentum dependence of the NLO (solid) and LO (dashes) transversely polarized cross sections. The corresponding $K$-factors are shown in the inset plot.

Figure 6

Rapidity dependence of the NLO (solid) and LO (dashes) transversely polarized cross sections. The corresponding $K$-factors are shown in the inset plot.

Figure 7

Rapidity dependence of the NLO (solid) and LO (dashes) transversely polarized asymmetries for the two sets of the transversely polarized parton distribution functions defined above. The corresponding $K$-factors are shown in the inset plot.

Figure 8

Rapidity dependence of the NLO (solid) and LO (dashes) transversely polarized asymmetries for the two sets of the transversely polarized parton distribution functions, with a modified cut on the transverse momentum of the electron $p_T>20$. The corresponding $K$-factors are shown in the inset plot.