Lepton-mediated electroweak baryogenesis, gravitational waves and the
  $4\tau$ final state at the collider
  An electroweak baryogenesis (EWBG) mechanism mediated by $\tau$ lepton
transport is proposed. We extend the Standard Model with a real singlet scalar
$S$ to trigger the strong first-order electroweak phase transition (SFOEWPT),
and with a set of leptophilic dimension-5 operators to provide sufficient CP
violating source. We demonstrate this model is able to generate the observed
baryon asymmetry of the universe. This scenario is experimentally testable via
either the SFOEWPT gravitational wave signals at the next-generation
space-based detectors, or the $pp\to h^*\to SS\to 4\tau$ process (where $h^*$
is an off-shell Higgs) at the hadron colliders. A detailed collider simulation
shows that a considerable fraction of parameter space can be probed at the
HL-LHC, while almost the whole parameter space allowed by EWBG can be reached
by the 27 TeV HE-LHC.
