Sivers distribution functions of sea quarks in a proton with the chiral Lagrangian

We propose a mechanism for the Sivers distribution function in a proton with the chiral Lagrangian. By introducing the gauge link of the vector meson, the transverse momentum dependent distribution of a pion in the nucleon is redefined, which is locally SU(2)V invariant as the Lagrangian. The eikonal propagator is generated from the gauge link, and this scenario is proven to be equivalent to the final state interaction. By combining the calculated splitting function and the valence q¯ distribution in π from the recent fit, the sea quark Sivers function in a proton is obtained. We find reasonable numerical results for the first momentum xΔNfq¯(1)(x) without any fine tuning of the free parameters.