Lepton Electric Dipole Moments in Supersymmetric Type II Seesaw Model

1. Lepton Electric Dipole Moments in Supersymmetric Type II Seesaw Model Takayuki Kubo (KEK, Graduate University for Advanced Studies) Toru Goto, Takayuki Kubo and Yasuhiro Okada, “Lepton electric dipole moments in supersymmetric type II seesaw model,” [arXiv:1001.1417].

2. Outline • Introduction: electric dipole moment (EDM) • SUSY type II seesaw model • A new source of CP violation • Lepton EDMs: previous study • Lepton EDMs: our results • Summary

3. Introduction(1) The electric dipole moments (EDMs) of leptons , nucleons and atoms are important probe for new physics. • Until now no EDM has been observed. • Upper limits on EDMs strongly constrain CP violating parameters.

4. Introduction(2) The ratio of the muon EDM to electron EDM is important in order to suggest necessary sensitivity for future experiments of muon EDM. • The previous study for lepton EDMs in SUSY type II seesaw model (Chun, Masiero, Rossi and Vempati, phys. Lett. B 622 (2005) 112) suggest • This implies that if the electron EDM lies just below the present limit, muon EDM is given by (for the normal hierarchy of neutrino masses)

5. Introduction(3) • However we found additional contributions which should be taken into account. • We will show that the ratio is given by in a wide region of parameter space. • The ratio does not depend on the neutrino parameters or unknown parameters.

6. SUSY Type II Seesaw Model (1): superpotential • Superpotential of the model • Exchange of heavy SU(2)L triplets generates small neutrino masses: the seesaw mechanism.

7. SUSY Type II Seesaw Model (2): neutrino masses • Integrating out the heavy SU(2)L triplets, we obtain neutrino masses as follows: • The matrix mνis diagonalized by the MNS matrix and we have • YT is directly related to mν and UMNS.

8. SUSY Type II Seesaw Model (3): soft SUSY breaking terms and assumptions • Soft SUSY breaking terms of the model • Soft SUSY breaking squared-mass parameters are universal (m02) at MG=2×1016GeV. • Gaugino masses are also universal (m1/2) at MG. • A-terms are proportional to corresponding Yukawa couplings (AE=a0YE) at MG.

9. BT as a new source of CP violation(1) • There still remains three CP violating phases, namely μ, a0 and BT. • Effects of μ and a0 have been studied very well. • Here we study the effects of BT as a new source of CP violation and assume that μand a0 are real.

10. BT as a new source of CP violation(2) • The BT contribute to the scalar trilinear couplings and the gaugino masses through the threshold correction at MT.

11. BT as a new source of CP violation(3) • The BT contribute to the scalar trilinear couplings , the gaugino masses and soft squared-masses through the threshold correction at MT.

12. Lepton EDMs: previous study • In the previous study (Chun, Masiero, Rossi and Vempati, phys. Lett. B 622 (2005) 112), the contributions fromδM1and δM2are missing. • They estimate lepton EDMs di as follows:

13. Lepton EDMs: previous study • In the previous study (Chun, Masiero, Rossi and Vempati, phys. Lett. B 622 (2005) 112), the contributions fromδM1and δM2are missing. • They estimate lepton EDMs di as follows: • Their result implies

14. Lepton EDMs: previous study • But we must include contributions fromδM1and δM2. • ex) Diagram shown below contribute to EDMs:

15. Lepton EDMs: our results(1) de dμ λ2 blows up dtau YT blows up

16. Lepton EDMs: our results(2) We can see that the ratio is around 200 except for the lower end of λ2 .

17. Summary • We studied lepton EDMs in the SUSY type II seesaw model. • All contributions generated by one-loop threshold corrections at MT through the BT term are included. • We showed that the ratios of lepton EDMs are given by those of the lepton masses: • Since the upper bound of de is at the level of 10-27 ecm, muon EDM search at the level of 10-24-10-25 are important.

18. Note

19. Lepton EDMs: our results(2) Next we fix the λ2 and MT. • λ2=0.03 • MT=1012 GeV Other parameters are fixed at • λ1=0 • tanβ=3, 30 • a0=0 GeV • m1/2=300, 600 GeV • ReBT=ImBT=100 GeV

20. Lepton EDMs: our results(2-1) dμ de dtau

21. Lepton EDMs: our results(2-2) We can see that the ratio is around 200, independent of the values of tanβ, m1/2 and mass of the lightest charged slepton. We vary m0 with in 100GeV < m0 < 1000GeV. The horizontal axis represents mass of the lightest charged slepton.

22. Lepton EDMs: our results(3) We can see that the ratio is around 17 except for the lower end of λ2 .

24. Lepton EDMs: our results(1) • In the numerical calculation, we evaluated the following diagrams: We fix the parameters as follows: • tanβ= 3 , 30 • λ1= 0 • m0 = m1/2 = 300 GeV • a0= 0 GeV • ReBT= ImBT= 100 GeV

25. Comments on EDMs(1) grow at small values of λ2 (large valus of YT).

26. Comments on EDMs(2) mass of the lightest slepton which couples to muon rather than electron rapidly decrease due to the large YT.

27. Comments on LFV decays • Branching ratios of LFV decays are given by • Ratio between the branching ratios is for s13=0, δ=0

28. Comparison with SUSY type I seesaw type II type I

30. SUSY seesaw models • SUSY type I seesaw model • SUSY type II seesaw model • U(1)B-L extended MSSM • …. • ….

32. Electric dipole moments as probes of new physics • Non-relativistic Hamiltonian for the interaction of an electric dipole moment (EDM) with an electric field: • The relativistic generalization: • Until now no EDM has been observed. • ex) electron and muon EDM

33. electron EDM

34. Motivation(2): seesaw mechanism Seesaw mechanism explains the observed tiny neutrino masses: