Transverse momentum dependent gluon fragmentation functions from J/ψ π production at e^+ e^- colliders

The back-to-back J/ψ and π 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. With a spinless pion, unpolarized and linearly polarized gluon TMD fragmentation functions can be defined. It is found that at parton level the hadronic tensor can be described by three independent structure functions. As a result, there are three independent angular distributions, of which the cos2ϕ azimuthal asymmetry is sensitive to the linearly polarized gluon fragmentation function.