Nuclear Shadowing in the Structure Function $F_3(x)$

Nuclear modification of the structure function $F_3$ is investigated. Although it could be estimated in the medium and large $x$ regions from the nuclear structure function $F_2^A$, it is essentially unknown at small $x$. The nuclear structure function $F_3^A$ at small $x$ is investigated in two different theoretical models: a parton-recombination model with $Q^2$ rescaling and an aligned-jet model. We find that these models predict completely different behavior at small $x$: {\it antishadowing} in the first parton model and {\it shadowing} in the aligned-jet model. Therefore, studies of the ratio $F_3^A\mathrm{/}{F}_3^D$ at small $x$ could be useful in discriminating among different models, which produce similar shadowing behavior in the structure function $F_2$. We also estimate currently acceptable nuclear modification of $F_3$ at small $x$ by using $F_2^A\mathrm{/}{F}_2^D$ experimental data and baryon-number conservation.