SMEFT Matching to $Z^\prime$ Models at Dimension-8

Heavy neutral gauge bosons arise in many motivated models of Beyond the Standard Model Physics. Experimental searches require that such gauge bosons are above the TeV scale in most models which means that the tools of effective field theories, in particular the Standard Model Effective Field Theory (SMEFT), are useful. We match the SMEFT to models with heavy $Z^\prime$ bosons, including effects of dimension-8 operators, and consider the restrictions on model parameters from electroweak precision measurements and from Drell Yan invariant mass distributions and forward-backward asymmetry, $A_\text{FB}$, measurements at the LHC. The results demonstrate the model dependence of the resulting limits on SMEFT coefficients and the relatively small impact of including dimension-8 matching. In all cases, the limits from invariant mass distributions are stronger than from $A_\text{FB}$ measurements in the $Z^\prime$ models we consider.