We examine the lepton-specific 2HDM as a solution of muon g−2 anomaly under
various theoretical and experimental constraints, especially the direct search
limits from the LHC and the requirement of a strong first-order phase
transition in the early universe. We find that the muon g-2 anomaly can be
explained in the region of 32 <tanβ< 80, 10 GeV <mA< 65 GeV, 260 GeV
<mH< 620 GeV and 180 GeV <mH±< 620 GeV after imposing the joint
constraints from the theory, the precision electroweak data, the 125 GeV Higgs
data, the leptonic/semi-hadronic τ decays, the leptonic Z decays and
Br(Bs→μ+μ−). The direct searches from the h→AA channels can
impose stringent upper limits on Br(h→AA) and the multi-lepton event
searches can sizably reduce the allowed region of mA and tanβ (10 GeV
<mA< 44 GeV and 32 <tanβ< 60). Finally, we find that the model can
produce a strong first-order phase transition in the region of 14 GeV <mA<
25 GeV, 310 GeV <mH< 355 GeV and 250 GeV <mH±< 295 GeV, allowed by
the explanation of the muon g−2 anomaly.Comment: 24 pages, 8 figures, 3 Tables, matches published versio