Radiative Flavor Violation SUSY 2010, Bonn Andreas Crivellin TTP Karlsruhe Radiative Flavor Violation

Outline: Why radiative mass generation? The SUSY flavor (CP) problem and the trilinear A-terms Radiative flavor violation in the MSSM Phenomenological consequences: B→sγ Kaon mixing K →πνν Right-handed W-coupling and the determination of Vub. 27.08.2010 SUSY 2010

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; A.C., Ulrich Nierste 2008 27.08.2010 SUSY 2010

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 chirality flipping. Possible solutions: Flavor symmetries Minimal flavor-violation Radiative flavor-vioation 27.08.2010 SUSY 2010

Mass insertion parameterization (L. J. Hall, V. A. Kostelecky and S Mass insertion parameterization (L.J. Hall, V.A. Kostelecky and S. Raby, Nucl. Phys. B 267 (1986) 415.) off-diagonal element of the squark mass matrix flavor indices 1,2,3 chiralitys L,R Define dimensionless quantity: average squark mass 27.08.2010 SUSY 2010

Chirality-flipping self energy: Chirally enhanced part: non-decoupling 27.08.2010 SUSY 2010

Finite renormalization by flavor-changing self-energies Corrections to the Mass: Corrections to the CKM matrix: important two-loop corrections A.C. Jennifer Girrbach 2010 27.08.2010 SUSY 2010

Radiative mass-generation in the MSSM The quark masses of the first two generations can be easily generated with small values of Top is too heavy tree-level top Yukawa coupling 27.08.2010 SUSY 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 radiatively using the trilinear A-terms! 27.08.2010 SUSY 2010

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. (Phase of μ enters only at two loops) Borzumati, Farrar, Polonsky, Thomas 1999. The SUSY flavor problem reduces to the elements 27.08.2010 SUSY 2010

CKM generation in the down sector: Constraints from b→sγ. Chirally enhanced corrections must be taken into account. A.C., Ulrich Nierste 2009 less constrained since they contribute to C7‘,C8‘. can explain the CP phase in Bs mixing. (not possible in MFV) 27.08.2010 SUSY 2010

CKM generation in the up sector: Constraints from Kaon mixing. unconstrained from FCNC processes. can induce a sizable right-handed W coupling. A.C. 2009 27.08.2010 SUSY 2010

Verifiable predictions for NA62 Effects in K→πνν Verifiable predictions for NA62 27.08.2010 SUSY 2010

Genuine vertex- correction Corrections to the left-handed coupling suppressed because the hermitian part of the WFR cancels with the genuine vertex correction. Right-handed coupling not suppressed! 27.08.2010 SUSY 2010

Possible effect in Vub 27.08.2010 SUSY 2010

Effect of a right-handed W-coupling on the determination Vub inklusive CKM unitarity B→τν B→πlν 27.08.2010 SUSY 2010

Conclusions Radiative generations of light fermion masses and mixing angles solves the SUSY flavour and the SUSY CP Problem. Chirally enhanced corrections must be taken into account in FCNC processes. Constraints from b→sγ and Kaon mixing satisfied for SUSY masses O(1TeV) Large effects in K→πνν possible The MSSM can generate a sizeable right-handed W-coupling. 27.08.2010 SUSY 2010