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We consider the production of $W$ and $Z / \gamma^{*}$ gauge bosons inproton-proton collisions at a center-of-mass energy of $\sqrt{s} = 510\mbox{GeV}$ available at RHIC at BNL, operating at high luminosity. We stressthe importance of measuring the transverse double-spin asymmetries $A_{TT}$, inconnection with available transversely polarized beams with a high degree ofpolarisation. We will discuss some theoretical issues related to the predictedasymmetries. These studies are contrasted to the 2017 RHIC running operation oftransversely polarized beams of mid-rapidity $W$ and $Z$ boson production at acenter-of-mass energy of $\sqrt{s}=510\,$GeV along with long-term prospectsbeyond 2020 at RHIC.

Transverse double-spin asymmetries for electroweak gauge-boson production in high-energy polarized $p^{\uparrow} + p^{\uparrow}$ collisions