Identifying a $Z'$ behind $b \to s \ell \ell$ anomalies at the LHC

Recent $b\to s\ell\ell$ anomalies may imply the existence of a new $Z'$ boson with left-handed $Z'bs$ and $Z'\mu\mu$ couplings. Such a $Z'$ may be directly observed at LHC via $b \bar s \to Z' \to \mu^+\mu^-$, and its relevance to $b\to s\ell\ell$ may be studied by searching for the process $gs \to Z'b \to \mu^+\mu^- b$. In this paper, we analyze the capability of the 14 TeV LHC to observe the $Z'$ in the $\mu^+ \mu^-$ and $\mu^+\mu^- b$ modes based on an effective model with major phenomenological constraints imposed. We find that both modes can be discovered with 3000 fb$^{-1}$ data if the $Z'bs$ coupling saturates the latest $B_s-\bar B_s$ mixing limit from UTfit at around $2\sigma$. Besides, a tiny right-handed $Z'bs$ coupling, if it exists, opens up the possibility of a relatively large left-handed counterpart, due to cancellation in the $B_s-\bar B_s$ mixing amplitude. In this case, we show that even a data sample of $\mathcal{O}(100)$ fb$^{-1}$ would enable discovery of both modes. We further study the impact of a $Z'bb$ coupling as large as the $Z'bs$ coupling. This scenario enables discovery of the $Z'$ in both modes with milder effects on the $B_s-\bar B_s$ mixing, but obscures the relevance of the $Z'$ to $b \to s\ell\ell$. Discrimination between the $Z'bs$ and $Z'bb$ couplings may come from the production cross section for the $Z'b\bar{b}$ final state. However, we do not find the prospect for this to be promising.