Dark matter, $Z^{\prime }$, vector-like quark at the LHC and $b\to s\mu \mu$ anomaly

Abstract

Combining the $b\to s{\mu }^{+}{\mu }^{-}$ anomaly and dark matter observables, we study the capability of LHC to test dark matter, $Z^{\prime }$, and vector-like quark. We focus on a local $U(1{)}_{L_{\mu }-L_{\tau }}$ model with a vector-like $SU(2{)}_L$ doublet quark $Q$ and a complex singlet scalar whose lightest component $X_I$ is a candidate of dark matter. After imposing relevant constraints, we find that the $b\to s{\mu }^{+}{\mu }^{-}$ anomaly and the relic abundance of dark matter favor $m_{X_I}<350$ GeV and $m_{Z^{\prime }}<450$ GeV for $m_Q<$ 2 TeV and $m_{X_R}<$ 2 TeV (the heavy partner of $m_{X_I}$). The current searches for jets and missing transverse momentum at the LHC sizably reduce the mass ranges of the vector-like quark, and $m_Q$ is required to be larger than 1.7 TeV. Finally, we discuss the possibility of probing these new particles at the high luminosity LHC via the QCD process $pp\to D\bar{D}$ or $pp\to U\bar{U}$ followed by the decay $D\to s(b)Z^{\prime }{X}_I$ or $U\to u(c)Z^{\prime }{X}_I$ and then $Z^{\prime }\to {\mu }^{+}{\mu }^{-}$. Taking a benchmark point of $m_Q$=1.93 TeV, $m_{Z^{\prime }}=170$ GeV, and $m_{X_I}=$ 145 GeV, we perform a detailed Monte Carlo simulation, and find that such benchmark point can be accessible at the 14 TeV LHC with an integrated luminosity 3000 fb${}^{-1}$.

18 pages, 7 figures, 2 tables

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