1. 1 Gauge-singlet dark matter in the left-right symmetric model with spontaneous CP violation 郭万磊 中国科学院理论物理研究所 CPS 2008, JiNan ， 08.09.20 W.L. Guo, L.M. Wang, Y.L. Wu, Y.F. Zhou and C. Zhuang, in preparation

2. 2 Outline  Left-right symmetric model  Motivation for gauge singlet dark matter  Gauge singlet dark matter in the LR model with one Higgs bi-doublet  Relic density  The dark matter direct detection  Two Higgs Bi-doublet Model  Summary

3. 3 Left-right symmetry model right-handed gauge bosons, right-handed neutrinos and 1. Spontaneous P and CP Violation

4. 4 2. Neutrino masses Type II Seesaw Left-Right Symmetry Model:

5. 5 TeV Physics VEV Seesaw Puzzle Introduce Z 2 symmetry: [ N.G. Deshpande et al ， PRD 44, 837 (1991)] VEV Seesaw Puzzle A pair of stable particles, Dark Matter? Z2Z2

6. 6 Current bounds ： Our results ： The DM annihilation cross section must be very large! W.L. Guo, L.M. Wang, Y.L. Wu and C. Zhuang, PRD

7. 7 Motivation for Singlet dark matter in LR model Dark matter candidate is always accompanied with some discrete symmetries which keep it stable!   R parity in SUSY model   T parity in little Higgs model   KK parity in extra dimensional model Some authors introduce the discrete symmetry Z 2 by hand! In the LR symmetric model, P and CP are exact symmetries of the theory at the high energy scale. P and CP may naturally be obtained by the spontaneous symmetry breaking. Whether the P and CP symmetries can give a stable WIMP particle or not?

8. 8 P and CP transformation in the LR model Unique way! P and CP require:

9. 9 Higgs potential related to the Singlet

10. 10 Mass spectrum for singlet After SSB, the mass matrix related to singlet is given by

11. 11 Z2Z2 Mass spectrum for Higgs multiplets

12. 12 Annihilation cross section

13. 13 Relic density Expanded in powers of x=m D /T Relic density: [ E.W. Kolb and M.S. Turner] [ M. Scrdnicki et al., NPB310, 693, (1988)] Freeze-out temperature

14. 14 Numerical results Input: Require:

15. 15 The dark matter direct detection For scalar interaction WIMP-nucleus cross section WIMP-nucleon cross section

16. 16 Numerical results Assume: In our scenario:

17. 17 Two Higgs Bi-doublet Model Quark masses ： More DM annihilation processes [ Y.L. Wu and Y.F. Zhou, arXiv:0709.0042]

18. 18 Summary  The left-right symmetric model may naturally produce the spontaneous P and CP violation.  Using the P and CP symmetries, one can obtain a stable WIMP in the LR model with a gauge singlet.  Our numerical results show that the observed relic density can be reproduced for a large parameter space.  We predict the spin-independent WIMP-nucleon cross section, which is far less than the current bounds.

19. 19 Thanks ！