1. Radiative Flavour Violation in the MSSM
Andreas Crivellin
ITP Bern
Radiative Flavour Violation in the MSSM
in collaboration with Lars Hofer, Ulrich Nierste and Dominik Scherer

2. Outline: Why radiative mass generation?
The SUSY flavor (CP) problem and the trilinear A-terms
Radiative flavour violation in the MSSM
Phenomenological consequences:
B→sγ
Kaon mixing
K →πνν
Bs mixing and Bs→μ+μ-

3. Radiative mass generation
The smallness of the Yukawa couplings of the first two generations (and the small off-diagonal CKM elements) suggest the idea that these quantities are loop-induced corrections.
SM: Weinberg, 1972;
SUSY:
Buchmüller, Wyler, 1983;
Banks 1988;
Borzumati, Farrar, Polonsky, Thomas 1998/1999;
Ferrandis, Haba 2004

4. SUSY flavor (CP) problem
The squark mass matrices are not necessarily diagonal (and real) in the same basis as the quark mass matrices.
Especially the trilinear A-terms can induce dangerously large flavor-mixing (and complex phases) because they are also chirality flipping.
Possible solutions:
Flavor symmetries
Minimal flavor-violation
Radiative flavor-violation

5. Chirality-flipping self-energy:
Chirally-enhanced part:
non-decoupling

6. Finite renormalization
Corrections to the mass:
Corrections to the CKM matrix:
important two-loop
corrections
A.C.; J. Girrbach 2010

7. The model
SU(2)³ flavor-symmetry in
the MSSM superpotential:
CKM matrix is the unit matrix.
Only the third generation Yukawa coupling is different from zero.
All other elements are generated via loops using the trilinear A-terms!

8. Features of the model
Additional flavor symmetries in the superpotential.
Explains small masses and mixing angles via a loop-suppression.
Minimally flavor-violating with respect to the first two generations (renormalization group invariant).
Deviations from MFV if the third generation is involved.
Solves the SUSY CP problem via a mandatory phase alignment between the masses and the A-terms. (Phase of μ enters only at two loops) Borzumati, Farrar, Polonsky, Thomas 1999.
The SUSY flavor problem reduces to the elements which are less constrained.

9. CKM generation in the up-sector:
Parameter regions compatible with Kaon mixing

10. Effects in K→πνν
Verifiable predictions for NA62

11. CKM generation in the down-sector:
Allowed regions from b→sγ. Chirally enhanced corrections must be taken into account. A.C., Ulrich Nierste 2009

12. Non-decoupling effects
Non-holomorphic self-energies induce flavour-changing neutral Higgs couplings.
Effect proportional to εb

13. Higgs effects: Bs→μ+μ-
Constructive contribution due to

14. Higgs effects: Bs mixing
Contribution only if due to Peccei-Quinn symmetry

15. Correlations between Bs mixing and Bs→μ+μ-
Br[Bs→μ+μ-]x10-9

16. Conclusions RFV solves the SUSY flavour and the SUSY CP problem.
Constraints from b→sγ and Kaon mixing satisfied for SUSY masses O(1 TeV)
Large effects in K→πνν possible
Can explain the Bs mixing phase and enhance Bs→μ+μ-