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We apply the transverse momentum dependent factorization formalism toinvestigate the transverse single spin dependent Collins asymmetry with a$\sin(\phi_h+\phi_s)$ modulation in the semi-inclusive production of Kaon mesonin deep inelastic scattering process. The asymmetry is contributed by theconvolutions of the transversity distribution function $h_1(x)$ of the targetproton and the Collins function of the Kaon in the final state. We adopt theavailable parametrization of $h_1(x)$ as well as the recent extracted resultfor the Kaon Collins function. To perform the transverse momentum dependentevolution, the parametrization of the nonperturbative Sudakov form factor ofthe proton and final state Kaon are utilized. We numerically predict theCollins asymmetry for charged Kaon production at the electron ion colliderswithin the accuracy of next-to-leading-logarithmic order. It is found that theasymmetry is sizable and could be measured. We emphasize the importance ofplanned electron ion colliders in the aspect of constraining sea quarkdistribution functions as well as accessing the information of the nucleon spinstructure and the hadronization mechanism.

The Collins asymmetry in electroproduction of Kaon at the electron ion colliders within TMD factorization