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LHC $τ$-rich Tests of Lepton-specific 2HDM for $(g-2)_μ$

The lepton-sepcific (or type X) 2HDM (L2HDM) is an attractive new physics candidate explaining the muon $g-2$ anomaly requiring a light CP-odd boson $A$ and large $\tanβ$. This scenario leads to $τ$-rich signatures, such as $3τ$, $4τ$ and $4τ+W/Z$, which can be readily accessible at the LHC. We first study the whole L2HDM parameter space to identify allowed regions of extra Higgs boson masses as well as two couplings $λ_{hAA}$ and $ξ_h^l$ which determine the 125 GeV Higgs boson decays $h\to τ^+τ^-$ and $h\to AA/AA^*(τ^+τ^-)$, respectively. This motivates us to set up two regions of interest: (A) $m_A \ll m_{H} \sim m_{H^\pm}$, and (B) $m_A \sim m_{H^\pm} \sim {\cal O}(100) \mbox{GeV} \ll m_H$, for which derive the current constraints by adopting the chargino-neutralino search at the LHC8, and then analyze the LHC14 prospects by implementing $τ$-tagging algorithm. A correlated study of the upcoming precision determination of the 125 GeV Higgs boson decay properties as well as the observation of multi-tau events at the next runs of LHC will be able to shed light on the L2HDM option for the muon $g-2$.