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The back-to-back $J/\psi$ and $\pi$ associated production at $e^+ e^-$colliders is proposed to detect the gluon transverse momentum dependent(TMD)fragmentation functions. TMD factorization is assumed for this process. Withspinless pion, unpolarized and linearly polarized gluon TMD fragmentationfunctions can be defined. It is found at parton level the hadronic tensor canbe described by four structure functions. As a result, there are threeindependent angular distributions, of which a $\cos{2\phi}$ azimuthal asymmetryis sensitive to the linearly polarized gluon fragmentation function.

Transverse momentum dependent gluon fragmentation functions from $J/\psi\ \pi$ production at $e^+ e^-$ colliders