# Sivers distribution functions of sea quark in proton with chiral Lagrangian

## TL;DR

This paper introduces a chiral Lagrangian-based mechanism to calculate the sea quark Sivers distribution in the proton, linking gauge links, vector mesons, and final state interactions to produce reasonable numerical results.

## Contribution

It presents a novel approach using chiral Lagrangian and gauge links to compute the sea quark Sivers function in the proton, incorporating vector mesons and final state interactions.

## Key findings

- Reasonable numerical results for sea quark Sivers function
- No fine tuning needed for free parameters
- Method links gauge links with chiral Lagrangian

## 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.