Lensing mechanism meets small-<math><mi>x</mi></math> physics: Single transverse spin asymmetry in <math><msup><mi>p</mi><mo>↑</mo></msup><mo>+</mo><mi>p</mi></math> and <math><msup><mi>p</mi><mo>↑</mo></msup><mo>+</mo><mi>A</mi></math> collisions

We calculate the single transverse spin asymmetry in polarized proton-proton (p↑+p) and polarized proton-nucleus (p↑+A) collisions (AN) generated by a partonic lensing mechanism. The polarized proton is considered in the quark-diquark model while its interaction with the unpolarized target is calculated using the small-x/saturation approach, which includes multiple rescatterings and small-x evolution. The phase required for the asymmetry is caused by a final-state gluon exchange between the quark and diquark, as is standard in the lensing mechanism of Brodsky, Hwang, and Schmidt [Phys. Lett. B 530, 99 (2002)]. Our calculation combines the lensing mechanism with small-x physics in the saturation framework. The expression we obtain for the asymmetry AN of the produced quarks has the following properties: (i) The asymmetry is generated by the dominant elastic scattering contribution and the 1/Nc2 suppressed inelastic contribution (with Nc the number of quark colors). (ii) The asymmetry grows or oscillates with the produced quark’s transverse momentum pT until the momentum reaches the saturation scale Qs, and then only falls off as 1/pT for larger momenta. (iii) The asymmetry decreases with increasing atomic number A of the target for pT below or near Qs, but is independent of A for pT significantly above Qs. We discuss how these properties may be qualitatively consistent with the data on AN published by the PHENIX Collaboration [Phys. Rev. Lett. 123, 122001 (2019)] and with the preliminary data on AN reported by the STAR Collaboration [Proc. Sci., DIS2016 (2016) 212 [arXiv:1805.08875] ].