Identifying a $Z^{\prime }$ behind $b\to s\ell \ell$ anomalies at the LHC

Abstract

Recent $b\to s\ell \ell$ anomalies may imply the existence of a new $Z^{\prime }$ boson with left-handed $Z^{\prime }bs$ and $Z^{\prime }\mu \mu$ couplings. Such a $Z^{\prime }$ may be directly observed at LHC via $b\bar{s}\to Z^{\prime }\to {\mu }^{+}{\mu }^{-}$, and its relevance to $b\to s\ell \ell$ may be studied by searching for the process $gs\to Z^{\prime }b\to {\mu }^{+}{\mu }^{-}b$. In this paper, we analyze the capability of the 14 TeV LHC to observe the $Z^{\prime }$ 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 $Z^{\prime }bs$ coupling saturates the latest $B_s-{\bar{B}}_s$ mixing limit from UTfit at around $2\sigma$. Besides, a tiny right-handed $Z^{\prime }bs$ 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 $Z^{\prime }bb$ coupling as large as the $Z^{\prime }bs$ coupling. This scenario enables discovery of the $Z^{\prime }$ in both modes with milder effects on the $B_s-{\bar{B}}_s$ mixing, but obscures the relevance of the $Z^{\prime }$ to $b\to s\ell \ell$. Discrimination between the $Z^{\prime }bs$ and $Z^{\prime }bb$ couplings may come from the production cross section for the $Z^{\prime }b\bar{b}$ final state. However, we do not find the prospect for this to be promising.

Comments: explanations and references added, matches with the published version