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

2. 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

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

4. short notation

5. The E-L equation then reads:
using stationarity equations

6. Suppose
. Then:

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

8. 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

9. 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

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