We compute the leading-twist T-odd quasidistributions of the proton in a spectator model with scalar and axial-vector diquarks: the quasi-Sivers function ${\tilde{f}}_{1T}^{\perp }(x,{\mathit{k}}_T^2;P_z)$ and the quasi-Boer-Mulders function ${\tilde{h}}_1^{\perp }(x,{\mathit{k}}_T^2;P_z)$. We obtain the quark-quark correlators in the four-dimensional Euclidian space by replacing ${\gamma }^{+}$ and ${\sigma }^{i+}$ in the light-cone frame with ${\gamma }_z$ and ${\sigma }_{iz}$. We show by analytical calculation that the results of ${\tilde{f}}_{1T}^{\perp }$ and ${\tilde{h}}_1^{\perp }$ derived from the correlators can reduce to the expressions of the corresponding standard T-odd distributions $f_{1T}^{\perp }(x,{\mathit{k}}_T^2)$ and $h_1^{\perp }(x,{\mathit{k}}_T^2)$ in the limit $P_z\to \infty$. The numerical results for these quasidistributions and their first transverse moments for the $u$ and $d$ quarks in different $x$ and $P_z$ regions are also presented. We find that ${\tilde{f}}_{1T}^{\perp (1)}(x,P_z)$ and ${\tilde{h}}_1^{\perp (1)}(x,P_z)$ in the spectator model are fair approximations to the standard ones (within 20%–30%) in the region $0.1<x<0.5$ when $P_z\ge 2.5–3\mathrm{GeV}$. This supports the idea of using T-odd quasidistributions to obtain standard distributions in the region $P_z>2.5\mathrm{GeV}$ as fair approximation.

• Received 23 June 2022
• Accepted 17 October 2022

DOI:https://doi.org/10.1103/PhysRevD.106.094003

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Published by the American Physical Society