Abstract
We propose a mechanism for the Sivers distribution function in proton with chiral Lagrangian. By introducing the gauge link of the vector meson, the transverse momentum dependent distribution of a pion in the nucleon is re-defined which is locally $SU(2)_V$ invariant as the Lagrangian. The eikonal propagator is generated from the gauge link and this scenario is proved to be equivalent to the final state interaction. By combining the calculated splitting function and the valence $\bar{q}$ distribution in $\pi$ from the recent fit, the sea quark Sivers function in proton is obtained. We find reasonable numerical results for the first momentum $x\Delta^Nf_{\bar{q}}^{(1)}(x)$ without any fine tuning of the free parameters.
Highlights
In the recent decades, the transverse partonic structure of hadrons has been the subject of a lot of theoretical and experimental investigations
We proposed a mechanism for the study of the Sivers distribution function with the chiral Lagrangian
The bilocal π operator is redefined with the gauge link of the vector meson which is locally SUð2Þ invariant
Summary
The transverse partonic structure of hadrons has been the subject of a lot of theoretical and experimental investigations. The colored gluon field introduced from the gauge link is not consistent with the framework of EFT which is formulated in terms of hadronic d.o.f. in this paper, we will provide a mechanism to generate the T-odd TMD PDFs with the chiral Lagrangian. The bilocal operator constructed for the splitting function is invariant under the flavor SUð2Þ symmetry instead of color gauge symmetry With this approach, we will calculate the sea quark Sivers distribution functions in a proton, which have not been estimated theoretically even in the quark models. The calculation here is for the Sivers functions of sea quarks in a proton, and it is straightforward to generally apply it to any T-odd distributions
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