LHC $\tau$-rich Tests of Lepton-specific 2HDM for $(g-2)_\mu$

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 $\tan\beta$. This scenario leads to $\tau$-rich signatures, such as $3\tau$, $4\tau$ and $4\tau+W/Z$, 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 $\lambda_{hAA}$ and $\xi_h^l$ which determine the 125 GeV Higgs boson decays $h\to \tau^+\tau^-$ and $h\to AA/AA^*(\tau^+\tau^-)$, 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 $\tau$-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 $g-2$.