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${}^{\text{â}}\text{ˆ}\text{’}$ or $t\overline{t}$ 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 $c\overline{b}$ 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→τ${}_h$p${}_T^{miss}$ channel. The constraints on the latter are much stronger and arise from both $t\overline{t}$ and τ${}^{+}$τ${}^{\text{â}}\text{ˆ}\text{’}$ production. Treated separately, we find that the weak constraints on the W′ still permit an explanation of the R(D${}^{\left(\text{â}\text{‹}\text{†}\right)}$) anomalies with a light sterile neutrino whereas the stronger constraints on the Z′ exclude significant light sterile neutrino contributions to the K→π$\nu \overline{\nu }$ rates. Within specific models the masses of W′ and Z′ are of course related and we briefly discuss the consequences.