The Physics Case for Polarized Protons at HERA

Several important and unique measurements, within the standard model and of possible physics beyond it, could be made with {\em polarized HERA} in which both the proton and the electron beams are polarized. With a $\sim$820 GeV proton beam and a $\sim$27.6 GeV electron beam, the polarized HERA will enable $\vec{e}-\vec{p}$ collisions with $\sqrt{s} \sim 300$ GeV and access spin variables in the kinematic range, $10^{-5} \le x_{\rm Bj} \le 0.6$ and $0 \le Q^{2} \le 10^{5}$, using the H1 and ZEUS detectors at DESY. This will be an increase of two orders of magnitude in both $x$ and $Q^{2}$ range compared to the presently explored range from fixed target experiments at CERN, SLAC and DESY. No other approved or planned spin experiment or accelerator facility will access the low $x$ and high $Q^{2}$ regions possible with HERA. Measurements performed with the polarized HERA collider will include the polarized structure function $g_{1}(x,Q^{2})$ at very low $x$, the polarized gluon distribution $\Delta G(x,Q^{2})$ from pQCD analysis of $g_{1}$, and from the production of di-jet events and high-p$_{T}$ hadrons in photon gluon fusion process and in photoproduction, the weak structure functions, the valence quark distribution functions from semi-inclusive asymmetries, parton distributions inside polarized photon, and information on helicity structure of possible new physics beyond the standard model. With such a rich and broad physics program possible for HERA,not polarizing the proton beam would be a great opportunity lost.