Slide 1: Overview

Slide 2: particle content of the MSSM

Slide 3: listing of complex parameters in the MSSM;
         where can CPV effects occur?

Slide 4: stop/sbottom sector of the MSSM incl. complex parameters

Slide 5: not all phases are physical! Listing of possible physical combinations

Slide 6: chargino/neutralino sector of the MSSM incl. complex parameters

Slide 7: Higgs sector of the MSSM with real parameters

Slide 8: Higgs sector of the MSSM with complex parameters

Slide 9: No CPV in the Higgs sector at tree-level.
         How can we get rid of the phases? 
         PQ-Transformation, A-Tadpole = 0.

Slide 10: Generic SUSY contributions to EDMS => possibly too large!

Slide 11: example for experimental restrictions on phases

Slide 12: overview about the MSSM constraints on phases:
          where do they appear? Why can the effects be large

Slide 13: CP-even Higgs sector at tree-level, mass formulas, mh < MZ

Slide 14: how to evaluate higher-order corrections to the CP-even 
          Higgs sector for masses and mixings

Slide 15: listing of complex parameters in the MSSM;
          effects enter Higgs sector via loop corrections;
          CP-even and CP-odd fields mix => 3 neutral Higgs bosons mix;
          h1, h2, h3 with M_h1 < M_h2 < M_h3

Slide 16: how to evaluate higher-order corrections to the neutral
          Higgs sector (mixed CP-even and -odd) for masses and mixings

Slide 17: M_h1 as a function of phi_At at the one-loop and two-loop level
 
Slide 18: M_h1 as a function of phi_Mgluino at the two-loop level

Slide 19: Higgs boson mixings: examples for external Higgs bosons;
          => important to ensure on-shell properties of the 
             external Higgs bosons!

Slide 20: Introduction of the Z-Matrix that ensures these on-shell properties

Slide 21: Higgs boson mixings: examples for internal Higgs bosons;
          => important to ensure unitarity of the mixing matrix.

Slide 22: two possibilities for a unitary mixing matrix:
          p^2 on-shell: U-Matrix
          p^2 = 0     : R-Matrix

Slide 23: Limit p^2 -> 0 of the Z-Matrix yields the U-Matrix
          => important consistency check

Slide 24: comparison of U- and R-Matrix: two checks proposed:
          1) comparison with full calculation (Z-Matrix)
          2) how well describe U and R pure CP-even or -odd states?

Slide 25: example for test (2) => U-Higgs can be better
          However: U-Higgs has problems with decoupling properties

Slide 26: comparison of Z-, U- and R-Higgs for external Higgs bosons
          => Z-Higgs = full result, U-Higgs closer, R-Higgs a bit more far away

Slide 27: summary of the treatment of higher-order corrections for
          external and internal Higgs bosons

Slide 28: CPV effects on Higgs searches: example of CPX scenario at LEP;
          comparison of various Higgs final states

Slide 29: LEP results in the CPX scenario for two m_top values
          => unexcluded areas for low M_h1 values (CPX holes), 
             e.g. at M_h1 = 45 and tan_beta = 8.

Slide 30: new theoretical developments: 
          - new two-loop corrections for masses and mixings incl. complex par.
          - new one-loop calculation for h2 -> h1 h1 decay

Slide 31: re-evaluation of CPX holes using HiggsBounds
          => holes confirmed

Slide 32: chapter 3: Higgs in decays - renormalization;
          repitition of slide 15.

Slide 33: phases enter in tree-level couplings of Higgses to scalar fermions;
          existing analyses restricted to tree-level results;
          => full one-loop calculation needed.

Slide 34: full one-loop calculation needed:
          overview about 2-body decay channels;
          => all sectors of the MSSM enter

Slide 35: list of renormalizations included for the various sectors 

Slide 36: example of renormalization of complex parameters: 
          At, theta_stop, Ab, theta_sbot, M1, M2, mu

Slide 37: list of channels that have been evaluated;
          no numerical results yet. :-( 

Slide 38: conclusions 

Slide 39: back-up starts 

Slide 40: comparison of Z-, U- and R-Higgs as a function of phi_Xt 

Slide 41: example of effects of imaginary parts of Higgs self-energies

Slide 42: comparison of U_33^2 and R_33^2