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

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