  Deep Inelastic scattering experiments using transversely polarised targets
yield information on the structure function $g_2$. By means of a free-field
analysis, we study the operator structure of $g_2$ and demonstrate the need for
retaining the twist three mass terms in order to maintain current-conservation.
We show that the structure function $g_T=g_1+g_2$ has a much simpler operator
structure as compared to $g_2$, in spite of the fact that, like $g_2$, $g_T$
has a twist-three component. We demonstrate factorisation of the hadronic
tensor into hard and soft parts for the case of $g_T$. We show that the first
moment of the gluonic contribution to $g_T$ vanishes, and discuss possible
physical applications.
