1. New Constraints on the Squark Mass Matrices of the MSSM
Andreas Crivellin and Ulrich Nierste
“Supersymmetric renormalization of the CKM matrix and
new constraints on the Squark Mass Matrices of the MSSM”
[arXiv:hep-ph/0811XXX]
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2. Outline: The SUSY flavour problem and the squark mass matrix
Non-decouling flavour-changing SQCD self-energies
CKM renormalization and constraints from a fine-tuning argument
Flavour-changing self-energies and FCNC processes (D, Bs, Bd, K mixing and b→sγ)
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3. SUSY flavour problem
Squark mass matrices are not necessarily diagonal in the same basis as the quark mass matrices
Quark-squark-gluino vertex is in general flavour-changing
Dangerously large flavour-mixing in
FCNC processes because of the strong coupling
constant.
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4. Helicity flipping, flavour-diagonal, but Ο(1) for large tan(β)
Squark mass matrix
Helicity conserving, flavour non-diagonal
Helicity flipping and flavour non-diagonal
Helicity flipping, flavour-diagonal, but Ο(1) for large tan(β)
tan(β)=vu/vd
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5. Squark mass matrix is hermitian Parameterization:
In the convention of: F. Gabbiani, E. Gabrielli, A. Masiero and L. Silvestrini,
Nucl. Phys. B 477 (1996) 321 [arXiv:hep-ph/ ].
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6. Mass insertion approximation (L. J. Hall, V. A. Kostelecky and S
Mass insertion approximation (L.J. Hall, V.A. Kostelecky and S. Raby, Nucl. Phys. B 267 (1986) 415.)
Diagonalize the quark mass matrices:
Carry out the same rotation on the squark fields
super-CKM basis
Render the vertices flavour-diagonal and treat the off-diagonal elements as perturbations.
Define dimensionless quantity:
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7. Flavour-changing self energy:
Mass insertion approximation
Exact diagonalization
dimensonless
∑(0)~MSUSY for constant δ
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8. Renormalization of the CKM matrix
In the SM: A. Denner and T. Sack, RENORMALIZATION OF THE QUARK MIXING MATRIX, Nucl. Phys. B 347 (1990) 203.
Antihermitian correction
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9. Constraints from fine tuning
Large accidental cancellations are unlikely and from the theoretical point of view undesirable.
Corrections to the CKM matrix should not
exceed the experimentally measured values
Because of the V-A structure of the W vertex only is directly constrained for j>i
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10. Constraints on from Vub
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11. Constraints on from Vub
For large helicity flipping elements, for example mbμ tan(β), also can be constrained. Strongest for :
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12. Existing results: FCNC bounds (decoupling):
M. Ciuchini et al. [arXiv:hep-ph/ ]
F. Borzumati, C.Greub, T.Hurth and D.Wyler[arXiv:hep-ph/ ]
D. Becirevic et al. [arXiv:hep-ph/ ]
M. Ciuchini et al. [arXiv:hep-ph/ ] …
Vacuum stability bounds (non-decoupling):
J.A.Casas and S.Dimopoulos,
Stability bounds on flavor-violating trilinear soft terms in the MSSM, Phys. Lett. B387 (1996) 107 [arXiv:hep-ph/ ]
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13. Results and comparison
quantity
our bound
bound from FCNC
bound from vacuum stability
0.0011
0.006, K mixing
0.001
0.15, Bd mixing
0.005
0.01
0.06, b→sγ
0.05
0.032
0.5, Bd mixing --
0.0047
0.016, D mixing
0.0012
0.027
0.22
0.27
Bounds calculated with msquark=mgluino=1000GeV
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14. Improvement of FCNC analysis nessecary:
Self energies can be of Ο(1) in the flavour conserving case, and have to be resummed.
M.S.Carena, D.Garcia, U.Nierste and C.E.M.Wagner, [arXiv:hep-ph/ ].
They are still of Ο(1) in the flavour violating case, when the mixing angle is divided out.
Two- or even three-loop processes can be of the same order as the LO process!
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15. Effect of including the self energies in ΔF=2 processes
for
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16. Allowed range for NP in ΔF=2 processes
Results taken for: UTfit Collaboration:
Example: Bs mixing
M.Bona et al. [UTfit Collaboration],
``First Evidence of New Physics in b <--> s Transitions,'' [arXiv: hep-ph/ ].
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17. Constraints on (δLR)23 from Bs mixing
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18. Constraints on δLR from D, B, and K mixing
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19. Two-loop effects enter only if also mbμ·tan(β) is large.
b→sγ
Two-loop effects enter only if also mbμ·tan(β) is large.
Behavior of the branching ratio for
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20. Constraints on δ23 from b→sγ
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21. Conclusions
Flavour-changing SQCD self-energies lead to antihermitian corrections to the CKM matrix
Strong constraints on and are obtained if the absence of accidental cancellations is assumed.
Flavour-changing self-energies have to be included in the analysis of FCNC processes and lead to large effects for non-degenerate squark masses
The constraints from the CKM renormalization are still stronger than the FCNC bounds for MSUSY≈ 1Tev
Soft SUSY breaking as the only source of flavour violation?
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