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We study the Collins function $H^\perp_{1}$ of the $\Lambda$ hyperon, whichdescribes the fragmentation of a transversely polarized quark into anunpolarized $\Lambda$ hyperon. We calculate $H^\perp_{1}$ for light quarks ofthe $\Lambda$ hyperon, in the diquark spectator model with a Gaussian formfactor for the hyperon-quark-diquark vertex. The model calculation includescontributions from both the scalar diquark and vector diquark spectators. Usingthe model result, we estimate the weighted $\cos2\phi_0$ asymmetry in theprocess $e^+e^- \to \Lambda\bar{\Lambda}X$ contributed by the coupling of twoCollins functions. The QCD evolution effects for the first $k_T$-moment of theCollins function and the unpolarized fragmentation function $D_1(z)$ are alsoincluded. The results show that asymmetry is sizable and measurable at thekinematical configurations of Belle and BaBar experiments. We also find thatthe evolution effects play an important role in the phenomenological analysis.

Double Collins effect in $e^+ e^-\to\Lambda \bar\Lambda X$ process in a diquark spectator model