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

2. 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.
SUSY 2010

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; A.C., Ulrich Nierste 2008
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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 chirality flipping.
Possible solutions:
Flavor symmetries
Minimal flavor-violation
Radiative flavor-vioation
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5. 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
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6. Chirality-flipping self energy:
Chirally enhanced part:
non-decoupling
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7. 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
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8. 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
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9. 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!
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10. 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
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11. 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)
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12. 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
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13. Verifiable predictions for NA62
Effects in K→πνν
Verifiable predictions for NA62
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14. 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!
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15. Possible effect in Vub
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16. Effect of a right-handed W-coupling on the determination Vub
inklusive
CKM unitarity
B→τν
B→πlν
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17. 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.
SUSY 2010