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We calculate the $\cos2\phi$ azimuthal asymmetry of the unpolarized$p\bar{p}$ Drell-Yan dilepton production process in the $Z$-resonance region atthe Tevatron kinematic domain. Such an azimuthal asymmetry can provideadditional information about a spin-related new parton distribution function,i.e., the Boer-Mulders function of the proton, compared to the $pp$ process.Therefore the available data of unpolarized proton-antiproton collision atTevatron can contribute to our study on the spin structure of the nucleon.

The $\cos2\phi$ azimuthal asymmetry of unpolarized $p\bar{p}$ collisions at Tevatron