Z' Coupling Information from the LHeC

If the LHC discovers a $Z'$-like state the extraction of its couplings to the particles of the Standard Model becomes mandatory in order to determine the nature of the underlying new physics theory. It has been well-known for some time that the direct measurements performed at the LHC in the Drell-Yan channel cannot determine these parameters uniquely in a model-independent manner even if large integrated luminosities, $\sim 100 fb^{-1}$, become available and the $Z'$ is relatively light $\lsim 1.5$ TeV. Here we examine the possibility that a proposed $e_{L,R}^\pm p$ collider upgrade at the LHC, the LHeC, with $\sqrt s=1.5-2$ TeV could be helpful with such coupling determinations in the years before a Linear Collider is constructed. We show that the polarization and charge asymmetries constructed from the cross sections for these processes can be useful in this regard depending upon the specific values of the particular $Z'$ model parameters.