A study of the polarized structure function $g_{1}^{p}(x,Q^{2})$ and the polarized gluon distribution $\Delta g(x,Q^{2})$ at HERA

We present estimates of possible data on spin-dependent asymmetries in inclusive scattering of high energy polarized electrons by high energy polarized protons at HERA with their statistical errors and discuss systematic errors. We show that these data will provide important information on the low-x behavior of the polarized structure function g_1, and will reduce the uncertainty in the determination of the first moment of the polarized gluon distribution Delta g(x,Q^2) obtained from the QCD analysis of g_1 in NLO. Furthermore, using asymmetries for di-jet events from a polarized HERA would substantially reduce the uncertainty in the shape of Delta g(x,Q^2). Using the information on Delta g(x,Q^2) from the di-jet analysis in conjunction with the NLO QCD analysis of g_1 will provide an accurate determination of Delta g(x,Q^2) and its first moment.