Z' physics with early LHC data

We discuss the prospects for setting limits on or discovering spin-1 $Z'$ bosons using early LHC data at 7 TeV. Our results are based on the narrow width approximation in which the leptonic Drell-Yan $Z'$ boson production cross-section only depends on the $Z'$ boson mass together with two parameters $c_u$ and $c_d$. We carefully discuss the experimental cuts that should be applied and tabulate the theoretical next-to-next-to-leading order corrections which must be included. Using these results the approach then provides a safe, convenient and unbiased way of comparing experiment to theoretical models which avoids any built-in model dependent assumptions. We apply the method to three classes of perturbative $Z'$ boson benchmark models: $E_6$ models, left-right symmetric models and sequential standard models. We generalise each class of model in terms of {mixing angles which continuously parametrize} linear combinations of pairs of generators and lead to distinctive orbits in the $c_u-c_d$ plane. We also apply this method to the strongly coupled four-site benchmark model in which two $Z'$ bosons are predicted. By comparing the experimental limits or discovery bands to the theoretical predictions on the $c_u$-$c_d$ plane, we show that the LHC at 7 TeV with integrated luminosity of 500 pb$^{-1}$ will greatly improve on current Tevatron mass limits for the benchmark models. If a $Z'$ is discovered our results show that measurement of the mass and cross-section will provide a powerful discriminator between the benchmark models using this approach.