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] 09.23.2008 Euroflavour 08, Durham

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) 09.23.2008 Euroflavour 08, Durham

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. 09.23.2008 Euroflavour 08, Durham

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 09.23.2008 Euroflavour 08, Durham

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/9604387]. 09.23.2008 Euroflavour 08, Durham

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: 09.23.2008 Euroflavour 08, Durham

Flavour-changing self energy: Mass insertion approximation Exact diagonalization dimensonless ∑(0)~MSUSY for constant δ 09.23.2008 Euroflavour 08, Durham

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 09.23.2008 Euroflavour 08, Durham

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 09.23.2008 Euroflavour 08, Durham

Constraints on from Vub 09.23.2008 Euroflavour 08, Durham

Constraints on from Vub For large helicity flipping elements, for example mbμ tan(β), also can be constrained. Strongest for : 09.23.2008 Euroflavour 08, Durham

Existing results: FCNC bounds (decoupling): M. Ciuchini et al. [arXiv:hep-ph/9808328] F. Borzumati, C.Greub, T.Hurth and D.Wyler[arXiv:hep-ph/9911245] D. Becirevic et al. [arXiv:hep-ph/0112303] M. Ciuchini et al. [arXiv:hep-ph/0703204] … 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/9606237] 09.23.2008 Euroflavour 08, Durham

Results and comparison quantity our bound bound from FCNC bound from vacuum stability 0.0011 0.006, K mixing 0.00015 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 09.23.2008 Euroflavour 08, Durham

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/9912516]. 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! 09.23.2008 Euroflavour 08, Durham

Effect of including the self energies in ΔF=2 processes for 09.23.2008 Euroflavour 08, Durham

Allowed range for NP in ΔF=2 processes Results taken for: UTfit Collaboration: www.utfit.org Example: Bs mixing M.Bona et al. [UTfit Collaboration], ``First Evidence of New Physics in b <--> s Transitions,'' [arXiv: hep-ph/0803.0659]. 09.23.2008 Euroflavour 08, Durham

Constraints on (δLR)23 from Bs mixing 09.23.2008 Euroflavour 08, Durham

Constraints on δLR from D, B, and K mixing 09.23.2008 Euroflavour 08, Durham

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 09.23.2008 Euroflavour 08, Durham

Constraints on δ23 from b→sγ 09.23.2008 Euroflavour 08, Durham

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? 09.23.2008 Euroflavour 08, Durham