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

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Supersymmetric B-L Extended Standard Model

with Right-Handed Neutrino Dark Matter

Nobuchika Okada

University of Alabama

Tuscaloosa, AL

In collaboration with Zachary M. Burell (U. of Alabama)

Paper in preparation

Miami 2010 @ Fort Lauderdale, Dec. 14-19, 2010


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


New Physics beyond SMis 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 scale

Large mixing angle


2. Dark Matter Problem

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

No suitable DM candidates in the SM


How to naturally incorporate tiny neutrino masses in the SM?

Seesaw Mechanism

Effective operator:

If the seesaw scale 

Minkowski; Yanagida; Gell-Mann, Ramond & Slansky; Mohapatra & Senjanovic; others


The seesaw scale lies in the intermediate scale or lower


Seesaw Mechanism

Minkowski; Yanagida; Gell-Mann, Ramond & Slansky; Mohapatra & Senjanovic; others

We introduce right-handed neutrinos and Majorana masses

Integrating the heavy Majorana neutrino

SM singlet fermion


What is the Majoranan mass scale?

Broad range of Majorana mass is possible, depending on Dirac mass scale


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-freeby the presence ofright-handed neutrinosresponsible fortheseesaw 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 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

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 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

Low Energy

High Energy


EW symmetry breaking

Higgs VEV scale is O(sfermion mass)

 EW scale


After potential analysis with , we find



Lower bound on BL scale by LEP experiment > 6 TeV

Radiative B-L symmetry breaking

TeV Scale!


LHC @ 7 TeV or 14 TeV

CTEQ for pdf

Z’ peak

Z’ peak

SM bkg

SM bkg


(B) R-parity Violation

Fileviez Perez and Spinner,

``The Fate of R-Parity,\'\' arXiv:1005.4930 [hep-ph]

In most of the parameter space, R-party is broken




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


(C ) Relic Density of Z_2 Odd RH Neutrino DM

Annihilation process:

Boltzmann equation


Annihilation process is not efficient

Need Z’ resonance

WMAP data



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