The quark quasi Sivers function and quasi Boer-Mulders function in a spectator diquark model

Chentao Tan; Zhun Lu

doi:10.1103/PhysRevD.106.094003

paper

The quark quasi Sivers function and quasi Boer-Mulders function in a spectator diquark model

arXiv:2206.06937 · doi:10.1103/PhysRevD.106.094003

Abstract

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

arXiv comment13 pages, 5 figures, match the journal version

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