We perform an analysis of $J/\psi$ decays into octet baryons using
the QCD factorisation framework. All decay amplitudes are calculated within the effective field theory approach. The subleading amplitude, which describes the decay of longitudinally polarised charmonia, is obtained for the first time using higher twist three-quark distribution amplitudes. A qualitative analysis of the experimental data is performed. It is found that the polarisation parameter $\alpha_B$ can be described with an accuracy $10-30\%$, which indicates that the pQCD contribution provides the dominant part for this observable.