Impact of a CP Violating Higgs: from LHC to Baryogenesis

We observe a generic connection between LHC Higgs data and electroweak baryogenesis: the particle that contributes to the CP odd $hgg$ or $h \gamma \gamma$ vertex would provide the CP violating source during a first order phase transition. It is illustrated in the 2HDM that a common complex phase controls the lightest Higgs properties at the LHC, electric dipole moments and the CP violating source for electroweak baryogenesis. We perform a general parametrization of Higgs effective couplings and a global fit to the LHC Higgs data. Current LHC measurements prefer a nonzero phase for $\tan \beta \lesssim 1$ and EDM constraints still allow an order one phase for $\tan\beta\sim1$, which gives sufficient room to generate the correct cosmic baryon asymmetry. We also give some prospects in the direct measurements of CP violation in the Higgs sector at the LHC.