LHC constraints on $W^{\prime },Z^{\prime }$ that couple mainly to third generation fermions

Abstract

We use the results of CMS and ATLAS searches for resonances that decay to $\tau \nu$ or $tb$ and ${\tau }^{+}{\tau }^{-}$ or $t\bar{t}$ final states to constrain the parameters of non-universal $W^{\prime }$ and $Z^{\prime }$ gauge bosons that couple preferentially to the third generation. For the former we consider production from $c\bar{b}$ 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 $pp\to {\tau }_h{p}_T^{\mathrm{miss}}$ channel. The constraints on the latter are much stronger and arise from both $t\bar{t}$ and ${\tau }^{+}{\tau }^{-}$ production. Treated separately, we find that the weak constraints on the $W^{\prime }$ still permit an explanation of the $R(D^{(\star )})$ anomalies with a light sterile neutrino whereas the stronger constraints on the $Z^{\prime }$ exclude significant light sterile neutrino contributions to the $K\to \pi \nu \bar{\nu }$ rates. Within specific models the masses of $W^{\prime }$ and $Z^{\prime }$ are of course related and we briefly discuss the consequences.

Comments: 20 pages, 10 figures, matches version accepted for EPJC