Strange quark asymmetry in the proton in chiral effective theory

We perform a comprehensive analysis of the strange-antistrange parton distribution function (PDF) asymmetry in the proton in the framework of chiral effective theory, including the full set of lowest order kaon loop diagrams with off-shell and contact interactions, in addition to the usual on-shell contributions previously discussed in the literature. We identify the presence of $\delta$-function contributions to the $\bar s$ PDF at $x=0$, with a corresponding valence-like component of the $s$-quark PDF at larger $x$, which allows greater flexibility for the shape of $s-\bar s$. Expanding the moments of the PDFs in terms of the pseudoscalar kaon mass, we compute the leading nonanalytic behavior of the number and momentum integrals of the $s$ and $\bar s$ distributions, consistent with the chiral symmetry of QCD. We discuss the implications of our results for the understanding of the NuTeV anomaly and for the phenomenology of strange quark PDFs in global QCD analysis.