Sivers effect in the Drell-Yan process at BNL RHIC

On the basis of a fit to the Sivers effect in deep-inelastic scattering, we make predictions for single-spin asymmetries in the Drell-Yan process at BNL RHIC.

Figure 1

The $u$-quark Sivers function $x{f}_{1T\mathrm{SIDIS}}^{\perp (1)u}(x)$ vs $x$ at a scale of about $2.5{\mathrm{GeV}}^2$, as obtained from a fit to the HERMES data [16]. Shown are the best fit and its 1-$\sigma$ uncertainty.

Figure 2

The azimuthal SSA $A_{\mathrm{UT}}^{\sin (\varphi -\varphi s)}$ in Drell-Yan lepton pair production, $p^{\uparrow }p\to l^{+}{l}^{-}X$, as function of y for the kinematics of the RHIC experiment with $\sqrt{s}=200\mathrm{GeV}$. The left plots show $Q^2=(4\mathrm{GeV}{)}^2$, and the right plots $Q^2=(20\mathrm{GeV}{)}^2$. The upper plots show the effects of varying the Sivers antiquark distributions within the range of model I—see Eqs. (10, 11). The lower plots show instead the results of model II. In all cases, the central estimates are based on our fit (4) for the Sivers quark distribution functions from the HERMES data [16]. The inner error band (solid lines) shows the 1-$\sigma$ uncertainty of the fit. The outer error bands (dashed lines) show the error from varying the Sivers antiquark distribution functions within the ranges specified in Eqs. (10, 11), model I for the upper plots, and model II for the lower plots. The $x$-region explored in the HERMES kinematics is indicated. For $Q=4\mathrm{GeV}$ we show the estimated statistical error for STAR and PHENIX. For $Q=20\mathrm{GeV}$ the statistical error at STAR and PHENIX is comparable to the asymmetry. See text and Table  for a discussion of the planned RHIC II.

Figure 3

a) The numerator and denominator, see Eqs. (15, 16, 17), for the azimuthal SSA $A_{\mathrm{UT}}^{\sin (\varphi -\varphi s)}$ in the DY process as functions of the dilepton transverse momentum $q_T$ for $1.2<y<2.4$ at RHIC with $\sqrt{s}=200\mathrm{GeV}$ and $Q^2=(4\mathrm{GeV}{)}^2$. The absolute numbers for the cross sections are somewhat altered by the assumption (13). b) The azimuthal SSA $A_{\mathrm{UT}}^{\sin (\varphi -\varphi s)}$ and its estimated statistical uncertainty as functions of the low-$q_T$ cut $q_{\min }$, i.e. the ratio of the numerator and denominator in Fig. 3a integrated, respectively, over $q_T\in [q_{\min },\infty ]$. Both the SSA and its uncertainty are normalized with respect to their values for $q_{\min }=0$.

Figure 4

The azimuthal SSA $A_{\mathrm{UT}}^{\sin (\varphi -\varphi s)}$ as function of $y$ in Drell-Yan lepton pair production in $p^{\uparrow }p\to l^{+}{l}^{-}X$ for the kinematics of the PAX fixed target experiment with $s=45{\mathrm{GeV}}^2$ and $Q^2=(2.5\mathrm{GeV}{)}^2$, and in Drell-Yan lepton pair production in $p^{\uparrow }p\to l^{+}{l}^{-}X$ for the kinematics of the COMPASS experiment with $s=400{\mathrm{GeV}}^2$ and $Q^2=20{\mathrm{GeV}}^2$, respectively. The estimates are based on the fit for the Sivers $q$-distribution functions, see Eq. (4), obtained from the HERMES data [16]. The inner error band (solid lines) shows the 1-$\sigma$ uncertainty of the fit. The outer error band (dashed lines) arises from assuming that the Sivers $\overline{q}$-distribution functions are proportional to the unpolarized antiquarks see Eqs. (10, 11). For the PAX experiment the uncertainty due to Sivers antiquarks is not visible on this scale. The $x$-region explored in the HERMES kinematics is shown.