Duarte Fontes September 6, 2016 EFT and 2HDM Tree level matching up to D=8 Duarte Fontes September 6, 2016

Start with a theory, like the SM 1st Lagrangean Start with a theory, like the SM Introduce a very massive field ( ) in the theory 2nd Lagrangean Integrate out : Write the Euler-Lagrange eqs. for Suppose (where is the mass squared of ) Use this (in the E-L) to find Plug the expression of back in the Lagrangean 3rd Lagrangean Ascertain the results in the Higgs interactions

We add a second Higgs doublet ( ) to the SM 2nd Lagrangean in the Higgs basis: stationarity conditions:

short notation

The E-L equation then reads: using stationarity equations

Suppose . Then:

Replacing this expression in the 2nd , we get: 3rd Lagrangean D=8 has been integrated out

We can ascertain certain results: new interactions Let us start with . We find: Thus, at , one has: corrections to the mass corrections to the trilinear coupling corrections to the coupling between and fermions

There are no corrections either to or to Since we have both and , then CP violation This is the only source of CP Violation at

At , the relevant terms are: thus have the same type of corrections