What is the G$^{0}$W$^{0}$ band gap of ZnO?

Recently, there has been considerable attention on ZnO as a candidate material for low-cost transparent conducting oxides. Even in its natural wurtzite bulk phase, it is numerically difficult to evaluate $G^{0}W^{0}$ quasiparticle (QP) corrections for ZnO. Therefore we have a wide range of theoretical QP gaps quoted in the literature (from $\sim\!\!1.6$~eV to $\sim\!\!3.6$~eV to be compared with $3.44$~eV experimentally). Typically, many approximations are used \textit{en route}. To find the correct theoretical gap, we have performed calculations of unprecedented accuracy. First, we study the $G^{0}W^{0}$ band gap given different ground-state DFT starting point approximations (LDA and GGA) and the effect of including scalar-relativistic corrections. Second, we present a study of results for norm-conserving pseudopotentials vs. all-electron techniques (both PAW and FP-LAPW). Four different plasmon-pole models are compared with the more accurate contour-deformation approach. Finally, a Hubbard U parameter for the 3d-states of Zn is shown to depend on the exact details of application. This work shows that the band-gap of ZnO is indeed underestimated in the $G^{0}W^{0}$ approach.