The polarised gluon density from di-jet events in DIS at a polarised HERA

We present a possible direct measurement of the polarised gluon density $\Delta G(x)$ in LO from di-jet production in polarised deep inelastic ep scattering, assuming the kinematics of the HERA collider. We show the sensitivity to the x-dependence of $\Delta G(x)$ and to the first moment $\int \Delta G(x) dx$ in the range $0.002< x <0.2$, assuming the electron and proton beam of HERA being polarised to 70% and an integrated luminosity of at least 200 pb$^{-1}$. We include in our study hadronisation and higher order effects, as well as realistic detector smearing and acceptance. We find that the statistical and systematic uncertainties are small enough to distinguish between different parametrizations for $\Delta G(x)$, which all are in accordance with present data. We stress that at HERA an x-range could be measured, that is not accessible to any other present or proposed experiment.