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

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 ${\tilde{f}}_{1T}^{\perp }(x,k_T^2;P_z)$ and the quasi Boer-Mulders function ${\tilde{h}}_1^{\perp }(x,k_T^2;P_z)$. 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 $f_{1T}^{\perp }(x,k_T^2)$ and $h_1^{\perp }(x,k_T^2)$ 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 ${\tilde{f}}_{1T}^{\perp (1)}(x,P_z)$ 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 $P_z\ge 2.5-3$ 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.

13 pages, 5 figures, match the journal version

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Cited by in corpus (1)

• Generalized quasi, Ioffe-time, and pseudo quark distributions of the pion in the Nambu--Jona-Lasinio model