Andreas Crivellin ITP Bern

1. Andreas Crivellin ITP Bern Chirally enhanced corrections in the MSSM

2. Outline: • Self-energies in the MSSM • Resummation of chirally-enhanced corrections • Effective higgsino and gaugino vertices • Effective Higgs vertices • Flavor-violation from SUSY

3. Introduction Sources of flavor-violation in the MSSM

4. Quark masses Top quark is very heavy. Bottom quark rather light, but Yb can be big at large tan(β) All other quark masses are very small sensitive to radiative corrections

5. Squark mass matrix hermitian: involves only bilinear terms (in the decoupling limit) The chirality-changing elements are proportional to a vev

6. Mass insertion approximation(L.J. Hall, V.A. Kostelecky and S. Raby, Nucl. Phys. B 267 (1986) 415.) • Useful to visualize flavor-changes in the squark sector off-diagonal element of the squark mass matrix • flavor indices 1,2,3 • chiralitys L,R

7. Self-energies in the MSSM

8. SQCD self-energy: Finite and proportional to at least one power of decoupling limit

9. Chargino self-energy:

10. Neutralino self-energy:

11. Decomposition of the self-energy(flavour-conserving part) into a holomorphic part proportional to an A-term non-holomorphic part proportional to a Yukawa Define dimensionless quantity which is independent of a Yukawa coupling

12. Decomposition of the self-energy(flavor-changing part) into a part independent of the CKM matrix part proportional to CKM element Define dimensionless quantity

13. Finite Renormalization and resummation of chirally enhanced corrections AC, Ulrich Nierste, arXiv:0810.1613 AC, Ulrich Nierste, arXiv:0908.4404 AC, arXiv:1012.4840 AC, L. Hofer and J. Rosiek, arXiv:1103.4272

14. Renormalization I • All corrections are finite; counter-term not necessary. • Minimal renormalization scheme is simplest. Mass renormalization • tan(β) is automatically resummed to all orders

15. Renormalization II important two-loop corrections A.C. Jennifer Girrbach 2010 • Flavour-changing corrections

16. Renormalization III • Renormalization of the CKM matrix: • Decomposition of the rotation matrices • Corrections independent of the CKM matrix • CKM dependent corrections

17. Effective gaugino and higgsino vertices • No enhanced genuine vertex corrections. • Calculate • Determine the bare Yukawas and bare CKM matrix • Insert the bare quantities for the vertices. • Apply rotations to the external quark fields. • Similar procedure for leptons (up-quarks)

18. Chiral enhancement • For the bottom quark only the term proportional to tan(β) is important.tan(β) enhancement • For the light quarks also the part proportional to the A-term is relevant. Blazek, Raby, Pokorski, hep-ph/9504364

19. Flavor-changing corrections • Flavor-changing A-term can easily lead to order one correction. A.C., Ulrich Nierste, hep-ph/08101613

20. Effect of including the self- energies in ΔF=2 processes for AC, Ulrich Nierste, arXiv:0908.4404

21. b→sγ Two-loop effects enter only if also mbμ·tan(β) is large. Behavior of the branching ratio for

22. Effective Higgs vertices AC, arXiv:1012.4840 AC, L. Hofer and J. Rosiek, arXiv:1103.4272

23. Higgs vertices in the EFT I new

24. Higgs vertices in the EFT II • Non-holomorphic corrections • Holomorphic corrections • The quark mass matrix is no longer diagonal in the same basis as the Yukawa couplingFlavor-changing neutral Higgs couplings

25. Effective Yukawa couplings • Final result: with Diagrammatic explanation in the full theory:

26. Higgs vertices in the full theory • Cancellation incomplete since Part proportional to is left over. A-terms generate flavor-changing Higgs couplings

27. Radiative generation of light quark masses and mixing angels AC, Ulrich Nierste, arXiv:0908.4404 AC, Jennifer Girrbach, Ulrich Nierste, arXiv:1010.4485 AC, Ulrich Nierste, Lars Hofer, Dominik Scherer arXiv:1104.XXXX

28. Radiative flavor-violation 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!

29. Features of the model Additional flavor symmetries in the superpotential. Explains small masses and mixing angles via a loop-suppression. 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 Can explain the Bs mixing phase

30. CKM generation in the down-sector • Constraints from b→sγ.Chirally enhanced corrections important • less constrained since they contribute to C7‘,C8‘. • can explain the CP phase in Bs mixing. (not possible in MFV)

31. Higgs effects: Bs→μμ • Constructive contribution due to

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

33. Correlations between Bs mixing andBs→μμ Allowed region from Bs mixing

34. 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

35. Effects in K→πνν • Verifiable predictions for NA62

36. Conclusions • Self-energies in the MSSM can be of order one. • Chirally enhanced corrections must be taken into account in FCNC processes. • A-terms generate flavor-changing neutral Higgs couplings. • Radiative generations of light fermion masses and mixing angles solves the SUSY flavor and the SUSY CP problem. It can explain Bs mixing.