Search for tZ' associated production induced by tcZ' couplings at the LHC

The $P'_5$ and $R_K$ anomalies, recently observed by the LHCb collaboration in $B \to K^{(*)}$ transitions, may indicate the existence of a new $Z'$ boson, which may arise from gauged $L_\mu - L_\tau$ symmetry. Flavor-changing neutral current $Z'$ couplings, such as $tcZ'$, can be induced by the presence of extra vector-like quarks. In this paper we study the LHC signatures of the induced right-handed $tcZ'$ coupling that is inspired by, but not directly linked to, the $B \to K^{(*)}$ anomalies. The specific processes studied are $cg \to tZ'$ and its conjugate process each followed by $Z'\to\mu^+\mu^-$. By constructing an effective theory for the $tcZ'$ coupling, we first explore model-independently the discovery potential of such a $Z'$ at the 14 TeV LHC with 300 and 3000 fb$^{-1}$ integrated luminosities. We then reinterpret the model-independent results within the gauged $L_\mu - L_\tau$ model. In connection with $tcZ'$, the model also implies the existence of a flavor-conserving $ccZ'$ coupling, which can drive the $c \bar c \to Z' \to \mu^+\mu^-$ process. Our study shows that existing LHC results for dimuon resonance searches already constrain the $ccZ'$ coupling, and that the $Z'$ can be discovered in either or both of the $cg \to tZ'$ and $c \bar c \to Z'$ processes. We further discuss the sensitivity to the left-handed $tcZ'$ coupling and find that the coupling values favored by the $B \to K^{(*)}$ anomalies lie slightly below the LHC discovery reach even with 3000 fb$^{-1}$.