Effects of Large Threshold Corrections in SUSY type-I Seesaw Model

1. Effects of Large Threshold Corrections in SUSY type-I Seesaw Model IV International Workshop on the Interconnection between Particle Physics and Cosmology National University Library Torino, Italy 12-16 July 2010 Sin Kyu Kang (Seoul National University of Technology) Based on arXiv :1005.1354 in collaboration with Morozumi and Yokazaki)

2. Outline • Introduction • Threshold corrections to soft SUSY breaking terms in SUSY type-I seesaw • Effects of the threshold corrections on • Numerical calculation and results • Summary - Relic abundance of neutralino dark matter - Lepton flavor violation

3. I. Introduction • Main purpose of this talk : to show how - Brs of LFV radiative decays - the relic abundance of Neutralino dark matter can be significantly affected by large threshold corrections mediated by gauge singlet neutrino superfields in SUSY type-I Seesaw Model • Smallness of neutrino masses • Stabilizing EW scale without fine-tuning • Providing a natural candidate for a dark matter • Grand unification of SU(3)xSU(2)xU(1) • introducing gauge singlet RH neutrino superfields • SUSY version of type I seesaw model :

4. Issue on this work • In SUSY type I seesaw model with hierarchical RH neutrino mass spectrum, we allow the B-term , to be large, which leads to large mass splitting of RH sneutrinos • Effects of B-term have been studied by Farzan ’03, Kato,SKK,Morozumi, Yokozaki ‘09, Giudice, Paradisi, Strumia, ‘10 • Large mass splitting leads to large threshold corrections to affect the minimization condition for the Higgs potential the fine-tuning can bereduced(Kato, SKK, Morozumi, Yokozaki) • Such a large mass splitting affects relic abundance of the DM and leads to additional source of LFV slepton masses as well • While large threshold corrections give rise to large LFV, they lower the abundance of the neutralino DM

5. II. Threshold corrections • Superpotential of type-I SUSY seesaw • Soft SUSY breaking terms :

6. Mass spectrum of RH neutrinos & sneutrinos • For heavy RH neutrinos NRi : • For heavy RH sneutrinos :

7. Without threshold corrections • RGEs for slepton masses and H2 mass • Assuming that soft SUSY breaking parameters are universal at high energy scale like GUT scale. • Integrating RGEs between RG corrections

8. Decoupling RH neutrino superfields at threshold scales, terms of RGEs leading to threshold corrections

9. Integrating those RGE terms for , and using the relations, • we can obtain threshold corrections : • Assuming universal soft breaking terms,

10. Similarly, the threshold corrections to up-type Higgs mass • There also exist finite contributions of threshold corrections calculable by diagrammatic method, but they are much smaller than the above contributions. • The above results are consistent with the results obtained by the method of analytic continuation into superspace (Giudice, Paradisi, Strumia ‘10, see aslo Arkani-Hamed, Giudice, Luty, Rattazzi ‘98, Matssura, Nakano, Yoshioka ’06)

11. III. Effects of threshold corrections

12. m Parameter via Higgs mass • Minimization condition of the Higgs potential : • Corrections to • When the threshold corrections become large, • compensates large top-stop corrections, then the size m parameter becomes small. • This lowers the relic abundance of neutralino dark matter compared to that of MSSM thresholds RG effects

13. In SUSY seesaw based on mSUGRA, the radiative corrections drive more negative than that in MSSM if we do not include the threshold corrections. • However, if we include large threshold corrections, is driven less negative which leads to smaller |m|. • So, the portion of higgsino in the lightest neutralino state becomes large, the allowed parameter space leading to right amount of relic density of neutralino DM becomes shifted compared to MSSM. EW symmetry breaking requires |m| to be larger than that in MSSM.

14. Lepton Flavor Violation • The radiative LFV decays Branching ratios The : proportional to Including the threshold corrections Both contributions cancel each other when they are comparable. thresholds

15. As BN becomes large, threshold corrections get dominant over RG effects. Giving rise to large lepton flavor violation Lowering the relic abundance of neutralino dark matter So, it is possible to obtain right amount of even in the parameter space excluded by WMAP in MSSM

16. IV. Numerical calculation and Results • Soft breaking parameters are universal at the high E scale like GUT scale • Deriving weak scale values of SSB parameters by using RGEs. • Software : SuSpect, micrOMEGAs with appropriate modifications. • The upper bounds on • WMAP result for relic abundance of the cold DM :

17. Assumptions in the Neutrino Sector • No LFV in charged Lepton sector • MR are hierarchical • Yn and MR can be diagonalized simultaneously (A) Normal hierarchical spectrum of light neutrinos

18. Thanks to as a function of BN

19. as a function of universal soft scalar mass m0

20. (B) Inverted hierarchical spectrum of light neutrinos • In the case of Comparing to NH : Therefore, threshold corrections to up-type Higgs mass are much smaller than in the NH case, which lead to large relic abundance • even other cases, it is difficult to satisfy the constraints on BR and relic density

21. (C) Quasi-degenerate spectrum of light neutrinos • is larger than that in NH, which makes the prediction of substantially enhanced compared to NH, and thus the constraint of becomes more severe when we consider the constraint of the relic abundance simultaneously.

22. V. Summary • In type-I SUSY seesaw model, large mass splitting of heavy sneutrinos leads to large threshold corrections to slepton masses and up-type Higgs mass. • Large threshold corrections affect the relic abundance of neutralino dark matter and give rise to large BRs of the LFV decays. • Large threshold corrections can reduce fine-tuning in MSSM and make the allowed region of the soft parameter space shifted.

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