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

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 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 Introduction(2) (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  Superpotential of the model  Exchange of heavy SU(2) L triplets generates small neutrino masses: the seesaw mechanism. SUSY Type II Seesaw Model (1): superpotential SU(3) c SU(2) L U(1) Y T T 2 1 3

7  Integrating out the heavy SU(2) L triplets, we obtain neutrino masses as follows:  The matrix m ν is diagonalized by the MNS matrix and we have  Y T is directly related to m ν and U MNS. SUSY Type II Seesaw Model (2): neutrino masses

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 (m 0 2 ) at M G =2×10 16 GeV.  Gaugino masses are also universal (m 1/2 ) at M G.  A-terms are proportional to corresponding Yukawa couplings (A E =a 0 Y E ) at M G.

9 B T as a new source of CP violation(1) There still remains three CP violating phases, namely μ, a 0 and B T. Effects of μ and a 0 have been studied very well. Here we study the effects of B T as a new source of CP violation and assume that μand a 0 are real.

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

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

12 Lepton EDMs: previous study  In the previous study ( Chun, Masiero, Rossi and Vempati, phys. Lett. B 622 (2005) 112 ), the contributions from δM 1 and δM 2 are missing.  They estimate lepton EDMs d i as follows:

13 Lepton EDMs: previous study  In the previous study ( Chun, Masiero, Rossi and Vempati, phys. Lett. B 622 (2005) 112 ), the contributions from δM 1 and δM 2 are missing.  They estimate lepton EDMs d i as follows:  Their result implies

14 Lepton EDMs: previous study  But we must include contributions from δM 1 and δM 2.  ex) Diagram shown below contribute to EDMs:

15 Lepton EDMs: our results(1) dede dμdμ d tau λ 2 blows up Y T blows up

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

17 Summary  We studied lepton EDMs in the SUSY type II seesaw model.  All contributions generated by one-loop threshold corrections at M T through the B T term are included.  We showed that the ratios of lepton EDMs are given by those of the lepton masses:  Since the upper bound of d e is at the level of ecm, muon EDM search at the level of are important.

18 Note

19 Lepton EDMs: our results(2) Next we fix the λ 2 and M T.  λ 2 =0.03  M T =10 12 GeV Other parameters are fixed at  λ 1 =0  tanβ=3, 30  a 0 =0 GeV  m 1/2 =300, 600 GeV  ReB T =ImB T =100 GeV

20 Lepton EDMs: our results(2-1) dede dμdμ d tau

21 Lepton EDMs: our results(2-2) We vary m 0 with in 100GeV < m 0 < 1000GeV. The horizontal axis represents mass of the lightest charged slepton. We can see that the ratio is around 200, independent of the values of tanβ, m 1/2 and 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 λ 2.

23

24  In the numerical calculation, we evaluated the following diagrams: We fix the parameters as follows:  tanβ= 3, 30  λ 1 = 0  m 0 = m 1/2 = 300 GeV  a 0 = 0 GeV  ReB T = ImB T = 100 GeV Lepton EDMs: our results(1)

25 Comments on EDMs(1) grow at small values of λ 2 (large valus of Y T ).

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

27 Comments on LFV decays  Branching ratios of LFV decays are given by  Ratio between the branching ratios is for s 13 =0, δ=0

28 Comparison with SUSY type I seesaw type IItype I

29

30 SUSY seesaw models  SUSY type I seesaw model  SUSY type II seesaw model  U(1) B-L extended MSSM  …. SU(3) c SU(2) L U(1) Y N i SU(3) c SU(2) L U(1) Y U(1) B-L N i Δ Δ SU(3) c SU(2) L U(1) Y T T 2 1 3

31

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: