Polarised deep inelastic scattering accompanied by a forward jet as a probe of the ln²(1/x) resummation

We argue that the production of forward jets in polarised deep inelastic scattering can be a useful tool for probing the double $ln^2(1/x)$ resummation effects which control the polarised deep inelastic scattering for small values of the Bjorken parameter $x$. We solve the corresponding integral equations generating the double $ln^2(1/x)$ resummation and calculate the differential structure function describing the forward jet production in the small $x$ regime which can possibly be probed by the polarised HERA measurements. We show that these structure functions should exhibit the characteristic increase with decreasing $x/x_J$, where $x_J$ denotes the longitudinal momentum fraction of the parent proton carried by a jet, and we quantify this increase.