Using recently derived results for one-loop hadronic splitting functions from a nonlocal implementation of chiral effective theory, we study the contributions from pseudoscalar meson loops to flavor asymmetries in the proton. Constraining the parameters of the regulating functions by inclusive production of , , and baryons in collisions, we compute the shape of the light antiquark asymmetry in the proton and the strange asymmetry in the nucleon sea. With these constraints, the magnitude of the asymmetry is found to be compatible with that extracted from the Fermilab E866 Drell-Yan measurement, with no indication of a sign change at large values of , and an integrated value in the range $\langle \bar d-\bar u \rangle \approx 0.09-0.17s-\bar sx
0x=0x\langle x (s-\bar s) \rangle \approx (0.9-2.5) \times 10^{-3}$.

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