Perturbative QCD contribution to transverse single spin asymmetries in the Drell-Yan process and SIDIS

In a previous publication [Benić et al., Phys. Rev. D 104, 094027 (2021)], we have computed the perturbative QCD contribution to transverse single spin asymmetries (SSAs) in semi-inclusive deep inelastic scattering (SIDIS) involving the $g_T(x)$ distribution. In this paper, we first present a more efficient derivation of the asymmetries which is applicable to both transverse and longitudinal SSAs and correct some inconsistencies in our previous calculation. We then adapt the method to compute transverse SSAs in the Drell-Yan process proportional to $g_T(x)$ and its gluonic counterpart and discuss the crossing symmetry between the results for SIDIS and the Drell-Yan process. Finally, we present numerical results for various asymmetries measurable at the EIC, RHIC, COMPASS, and Fermilab (SpinQuest), including also part of the genuine twist-three corrections to $g_T(x)$ from a recent global analysis. We find that the asymmetries can reach percent-level magnitude, if the kinematics predominantly probes the large-$x$ (valence) region of the polarized proton, but remain at subpercent levels otherwise.

Figure 1

A class of one-loop diagrams in the $q\overline{q}\to g{\gamma }^{*}$ channel that contain imaginary parts. The short blue fermion lines denote the lepton pair from the virtual photon via ${\gamma }^{*}\to l^{+}{l}^{-}$.

Figure 2

A class of one-loop diagrams in the $qg\to q{\gamma }^{*}$ channel that contain imaginary parts. The short blue fermion lines denote the lepton pair from the virtual photon via ${\gamma }^{*}\to l^{+}{l}^{-}$.

Figure 3

$x{g}_T(x)$ for $u$ (left) and $d$ (right) quarks in the three different scenarios defined in (110) and (111). The blue and magenta bands roughly match the blue and magenta bands on Fig. 2 in [10].

Figure 4

$x^{2}d{g}_T(x)/dx$ for $u$ and $d$ quarks in the three different scenarios defined in (110) and (111).

Figure 5

The $P_{h\perp }$ dependencies of all the SIDIS asymmetries for the EIC kinematics at $\sqrt{S_{ep}}=45\mathrm{GeV}$ in the WW, EOM, and LIR scenarios. Left (right) is for ${\pi }^{+}$ (${\pi }^{-}$).

Figure 6

The $x_B$ dependencies of all the SIDIS ${\pi }^{+}$ asymmetries for the EIC kinematics at $\sqrt{S_{ep}}=20\mathrm{GeV}$. Left: different lower $P_{h\perp }$ cutoffs in the WW scenario. Right: different scenarios.

Figure 7

The $q_{\perp }$ dependencies of all the Drell-Yan asymmetries for the $\sqrt{s}=200\mathrm{GeV}$ RHIC kinematics. Here, we have fixed $y=3$ and $Q=2\mathrm{GeV}$ (left) and $Q=4\mathrm{GeV}$ (right).

Figure 8

The $x_F$ dependencies of all the Drell-Yan asymmetries for the $\sqrt{s}=200\mathrm{GeV}$ RHIC kinematics. We have fixed $Q=2\mathrm{GeV}$ and $q_{\perp }=2(5)\mathrm{GeV}$ left (right).

Figure 9

The asymmetries $A_{UT}$’s as functions of $q_T$ for the COMPASS kinematics at $\sqrt{s}=18.9\mathrm{GeV}$. On the left panel, we have fixed $Q=5.3\mathrm{GeV}$ and integrated over the rapidity $y$ of the Drell-Yan pair. On the right panel, the results are obtained for $Q=2.0\mathrm{GeV}$ and $y=1.0$.

Figure 10

The asymmetries $A_{UT}$’s as functions of $q_T$ for the Fermilab SpinQuest collision energy $\sqrt{s}=15.5\mathrm{GeV}$. We have taken $y=-0.5$, $Q=4.0\mathrm{GeV}$ (left) and $y=1.0$, $Q=2.0\mathrm{GeV}$ (right).