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

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-

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

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

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

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

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!

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.

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

Effects in K→πνν Verifiable predictions for NA62

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

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

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

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

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

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-