LHC constraints on ^W′,^Z′ that couple mainly to third generation fermions

We use the results of CMS and ATLAS searches for resonances that decay to τν or tb and τ⁺τ^- or tt¯ final states to constrain the parameters of non-universal W^′ and Z^′ gauge bosons that couple preferentially to the third generation. For the former we consider production from cb¯ annihilation and find very weak constraints on the strength of the interaction and only for the mass range between 800 and 1100 GeV from the pp→τhpTmiss channel. The constraints on the latter are much stronger and arise from both tt¯ and τ⁺τ^- production. Treated separately, we find that the weak constraints on the W^′ still permit an explanation of the R(D^(⋆)) anomalies with a light sterile neutrino whereas the stronger constraints on the Z^′ exclude significant light sterile neutrino contributions to the K→ πνν¯ rates. Within specific models the masses of W^′ and Z^′ are of course related and we briefly discuss the consequences.