EFT and 2 HDM Tree level matching up
- Slides: 10
EFT and 2 HDM Tree level matching up to D=8 Duarte Fontes September 6, 2016
Overview R I 1 st Lagrangean Start with a theory, like the SM Introduce a very massive field ( ) in theory 2 nd 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 3 rd Lagrangean Ascertain the results in the Higgs interactions 2
O R I We add a second Higgs doublet ( ) to the SM 2 nd Lagrangean in the Higgs basis: stationarity conditions: 3
O R I short notation 4
Integrate out O The E-L equation using stationarity equations R then reads: 5
Integrate out O Suppose R . Then: 6
Integrate out O R Replacing this expression in the 2 nd , we get: D=6 D=8 3 rd Lagrangean has been integrated out 7
O I Results We can ascertain results: new interactions Let us start with Thus, at . We find: , one has: corrections to the mass corrections to the trilinear coupling corrections to the coupling between and fermions 8
O Results I There are no corrections either to Since we have both and or to , then CP violation This is the only source of CP Violation at 9
O I At Results , the relevant terms are: thus have the same type of corrections 10
