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What is missing in the SM? 1. Neutrino masses and mixings Oscillation data Very small mass scale Large mixing angle
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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
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
What is missing in the SM?
1. Neutrino masses and mixings
Oscillation data
Very small mass scaleLarge mixing angle
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
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
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
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
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:
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?
DM candidate is still missingThere 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 82:023507,2010DM candidate
Two right-handed neutrinos are sufficient to fit all the neutrino oscillation data
Z2 odd right-handed neutrino can be a good WIMP DM candidate with mass range, O(100 GeV)-(1 TeV), consistent with WMAP data & others
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
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
Particle Content (Non-SUSY case)
Particle Content s (SUSY extension)
Chiral superfield
Chiral superfield:
Superpotential relevant to neutrino physics
Because of Z_2 parity, N3 cannot have Dirac Yukawa
Superpotential in Higgs sector
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
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
(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
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
Similar to MSSM happens when Majorana Yukawa is large
negative
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
Z’ resonance hunting @ LHC
Z’
CTEQ for pdfLHC @ 7 TeV or 14 TeV
Z’ peak
SM bkgSM bkg
Z’ peak
(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
(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
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