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The odderon mechanism to generate Transverse Single Spin Asymmetries (TSSA) in high energy $q^\uparrow p$ and $q^\uparrow A$ collisions was originally suggested by Kovchegov and Sievert [1] and their results suggest significant nuclear suppression yielding a potentially strong ($A^{-7/6}$) suppression of TSSA in $p^\uparrow A$ vs $p^\uparrow p$ collisions. This is of interest in context of recent measurements of nuclear dependance of TSSA by the PHENIX and STAR collaborations [2,3]. In our previous work [4] we extended this computation taking into account a complete set of twist-3 parton distribution functions (PDF) on the polarized proton side. In the first step of our analysis, we have demonstrated that a partonic collinear divergence residing in the calculation of [1] gets completely cancelled by the kinematic twist-3 part of cross section. In fact, we have demonstrated that in the Wandzura-Wilczek [5] approximation the odderon mechanism cannot generate TSSA. In a follow-up study [Benić, Vivoda, in preparation] we are considering also diagrams containing dynamical twist-3 Efremov-Teryaev-Qiu-Sterman (ETQS) functions [6,7] which are known to give rise to pole contributions to TSSA [8]. Picking up instead a principal part from the hard factor, we have been able to identify a completely new contribution to the asymmetry that is proportional to the QCD odderon.
[1] Y. V. Kovchegov and M. D. Sievert, Phys. Rev. D 86, 034028 (2012).
[2] PHENIX Collaboration, C. Aidala et. al., Phys.Rev.Lett. 123, 122001 (2019).
[3] Star Collaboration, J. Adam et. al., Phys.Rev.D 103, 072005 (2021).
[4] S. Benić, D. Horvatić, A. Kaushik and E. A. Vivoda, Phys. Rev D 106, 114025 (2022).
[5] S. Wandzura and F. Wilczek, Phys. Lett. B 72, 195 (1977).
[6] A.V. Eferemov and O.V. Teryaev, Sov. J. Nucl. Phys. 36, 140 (1982).
[7] J. W. Qiu and G.F. Sterman, Phys. Rev. Lett. 67, 2264 (1991).
[8] Y. Hatta, B.-W. Xiao, S. Yoshida and F. Yuan, Phys. Rev. D 94, 054013 (2016).