1. Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami 2010 @ Fort Lauderdale, Dec. 14-19, 2010 University of Alabama Tuscaloosa, AL In collaboration with Zachary M. Burell (U. of Alabama) Paper in preparation

2. Problems in Standard Model The Standard Model (SM) is the best theory in describing the nature of elementary particle physics, which is in excellent agreement with almost of all current experimental results However, New Physics beyond SM is strongly suggested by both experimental & theoretical point of view

3. What is missing in the SM? 1. Neutrino masses and mixings Oscillation data Very small mass scale Large mixing angle

4. Existence of Dark Matter has been established! Wilkinson Microwave Anisotropy Probe (WMAP) satellite has established the energy budget of the present Universe with a great accuracy Dark Matter particle: non-baryonic electric charge neutral (quasi) stable 2. Dark Matter Problem No suitable DM candidates in the SM

5. Seesaw Mechanism Effective operator: If the seesaw scale  Naturally,  The seesaw scale lies in the intermediate scale or lower How to naturally incorporate tiny neutrino masses in the SM? Minkowski; Yanagida; Gell-Mann, Ramond & Slansky; Mohapatra & Senjanovic; others

6. SM singlet fermion Seesaw Mechanism We introduce right-handed neutrinos and Majorana masses Integrating the heavy Majorana neutrino Minkowski; Yanagida; Gell-Mann, Ramond & Slansky; Mohapatra & Senjanovic; others

7. What is the Majoranan mass scale? Broad range of Majorana mass is possible, depending on Dirac mass scale Example: What is the origin of MR?  We have added MR by hand

8. Minimal Gauged B-L Extension of the SM The model is based on  simple extension of the SM  we gauge an anomaly-free global (B-L) symmetry in the SM Particle Contents New fermions: New scalar:

9. gauge anomaly-free by the presence of right-handed neutrinos  responsible for the seesaw mechanism RH neutrino mass via B-L symmetry breaking B-L symmetry breaking via B-L gauge boson (Z’ boson) mass Majorana neutrino mass Mass scale is controlled by B-L Sym. Br. scale What is natural scale for B-L breaking?

10. DM candidate is still missing There have been many proposal for introduction of DM particles In fact, we do not need to add a new particle for DM physics, instead, we introduce a parity N.O & O. Seto, PRD 82:023507,2010 DM candidate  Two right-handed neutrinos are sufficient to fit all the neutrino oscillation data Z 2 odd right-handed neutrino can be a good WIMP DM candidate with mass range, O(100 GeV)-(1 TeV), consistent with WMAP data & others

11. Theoretical Problem in the SM and its extensions Gauge hierarchy problem: (extended) SM with Higgs field(s) suffers from this problem Instability of symmetry breaking scale  quadratic divergence of Higgs mass^2 corrections Supersymmetric Extension: promising way to solve the problem No quadratic divergence

12. SUSY B-L Extended SM Now, we consider SUSY extension of Minimal Gauged B-L SM It is straightforward to extend a model to its SUSY version Superfield formalism Matter & Higgs fields  chiral superfields Gauge fields  Vector superfields

13. Particle Content (Non-SUSY case)

14. Particle Content s (SUSY extension) Chiral superfield Chiral superfield:

15. Superpotential relevant to neutrino physics Because of Z_2 parity, N3 cannot have Dirac Yukawa Superpotential in Higgs sector

16. Introduction of SUSY breaking terms SUSY should be broken, otherwise  Superpartners have mass 100 GeV- 1 TeV We adopt the gravity mediation in our analysis, for simplicity: Universal gaugino masses: Universal sfermion masses: Unversal A-parameter : @ GUT scale

17. Interesting Features of the Model (A) Radiative B-L symmetry breaking B-L symmetry breaking naturally occurs at TeV scale  Z’ boson and RH neutrinos at TeV scale  LHC physics (B) R-party violation LSP neutralino is not stable anymore DM candidate is Z_2 odd RH neutrino (C) Relic abundance of RH neutrino Consistent with the observation  DM mass is fixed once Z’ mass fixed

18. (A) Radiative B-L symmetry Breaking In MSSM, EW symmetry is broken via radiative corrections due to interplay between the large top quark Yukawa coupling and SUSY breaking mass terms RGE running of SUSY breaking mass^2 for Higgs and squarks  negative @TeV scale

19. Higgs potential is changing its shape according to energy High Energy Low Energy Symmetric EW symmetry breaking Higgs VEV scale is O(sfermion mass)  EW scale

20. Similar to MSSM happens when Majorana Yukawa is large  negative

21. After potential analysis with, we find For fixed Radiative B-L symmetry breaking TeV Scale! Lower bound on BL scale by LEP experiment > 6 TeV

22. Z’ resonance hunting @ LHC Z’

23. CTEQ for pdf LHC @ 7 TeV or 14 TeV Z’ peak SM bkg Z’ peak

24. (B) R-parity Violation R-party violation Remember….. LSP neutralino is a DM candidate in the MSSM if R-parity is conserved In the present model, R-party is broken and thus, LSP neutralino is not stable any more Note that Z_2 odd RH neutrino is still stable and a good candidate for DM Fileviez Perez and Spinner, ``The Fate of R-Parity,'' arXiv:1005.4930 [hep-ph] In most of the parameter space, R-party is broken

25. (C ) Relic Density of Z_2 Odd RH Neutrino DM Z’ Boltzmann equation Annihilation process: Annihilation process is not efficient Need Z’ resonance WMAP data

26. Summary We have proposed Supersymmetric B-L Extended Standard Model 3 right-handed neutrinos are introduced to make the model free from all gauge & gravitational anomalies Associated with B-L symmetry breaking, right-handed neutrinos acquire masses and Seesaw Mechanism is naturally implemented Raidative B-L symmetry breaking occurs by the interplay between large Majorana Yukawa coupling and SUSY breaking masses B-L symmetry breaking is naturally at TeV scale, so that Z’ boson and right- handed neutrino masses around TeV  accessible by LHC R-parity is also broken  LSP neutralino is no longer DM candidate Z_2 odd right-handed neutrino is the DM candidate whose relic density is consistent with the observation if