Speaker
Description
We apply the formalism developed earlier [1, 2] for studying transverse momentum dependent parton distribution functions (TMDs) at small Bjorken $x$ to construct the small-$x$ asymptotics of the quark Sivers function. First, we explicitly construct the complete fundamental “polarized Wilson line” operator to sub-sub-eikonal order. We then express the quark Sivers function in terms of dipole
scattering amplitudes containing various components of the “polarized Wilson line” and show that the dominant term which contributes to the quark Sivers function at small-$x$ is the spin-dependent odderon, confirming the recent results of Dong, Zheng and Zhou [3]. Our conclusion is also similar to the case of the gluon Sivers function derived by Boer, Eschevarria, Mulders and Zhou [4] (see also [5]). We thus obtain that $f_{1T}^{\perp q} (x, k_T^2) ∼ 1/x$ at small-$x$.
[1] Y. V. Kovchegov and M. D. Sievert, Phys. Rev. D99, 054032 (2019), arXiv:1808.09010 [hep-ph].
[2] Y. V. Kovchegov and M. D. Sievert, Phys. Rev. D99, 054033 (2019), arXiv:1808.10354 [hep-ph].
[3] H. Dong, D.-X. Zheng, and J. Zhou, Phys. Lett. B 788, 401 (2019), arXiv:1805.09479 [hep-ph].
[4] D. Boer, M. G. Echevarria, P. Mulders, and J. Zhou, Phys. Rev. Lett. 116, 122001 (2016), arXiv:1511.03485 [hep-ph].
[5] L. Szymanowski and J. Zhou, Phys. Lett. B760, 249 (2016), arXiv:1604.03207 [hep-ph].
