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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

Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami Fort Lauderdale, Dec. 14-19, 2010 University

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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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Page 1: Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami Fort Lauderdale, Dec. 14-19, 2010 University

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

Page 2: Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami Fort Lauderdale, Dec. 14-19, 2010 University

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

Page 3: Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami Fort Lauderdale, Dec. 14-19, 2010 University

What is missing in the SM?

1. Neutrino masses and mixings

Oscillation data

Very small mass scaleLarge mixing angle

Page 4: Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami Fort Lauderdale, Dec. 14-19, 2010 University

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

Page 5: Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami Fort Lauderdale, Dec. 14-19, 2010 University

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

Page 6: Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami Fort Lauderdale, Dec. 14-19, 2010 University

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

Page 7: Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami Fort Lauderdale, Dec. 14-19, 2010 University

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

Page 8: Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami Fort Lauderdale, Dec. 14-19, 2010 University

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:

Page 9: Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami Fort Lauderdale, Dec. 14-19, 2010 University

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?

Page 10: Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami Fort Lauderdale, Dec. 14-19, 2010 University

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

Page 11: Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami Fort Lauderdale, Dec. 14-19, 2010 University

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

Page 12: Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami Fort Lauderdale, Dec. 14-19, 2010 University

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

Page 13: Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami Fort Lauderdale, Dec. 14-19, 2010 University

Particle Content (Non-SUSY case)

Page 14: Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami Fort Lauderdale, Dec. 14-19, 2010 University

Particle Content s (SUSY extension)

Chiral superfield

Chiral superfield:

Page 15: Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami Fort Lauderdale, Dec. 14-19, 2010 University

Superpotential relevant to neutrino physics

Because of Z_2 parity, N3 cannot have Dirac Yukawa

Superpotential in Higgs sector

Page 16: Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami Fort Lauderdale, Dec. 14-19, 2010 University

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

Page 17: Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami Fort Lauderdale, Dec. 14-19, 2010 University

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

Page 18: Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami Fort Lauderdale, Dec. 14-19, 2010 University

(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

Page 19: Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami Fort Lauderdale, Dec. 14-19, 2010 University

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

Page 20: Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami Fort Lauderdale, Dec. 14-19, 2010 University

Similar to MSSM happens when Majorana Yukawa is large

negative

Page 21: Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami Fort Lauderdale, Dec. 14-19, 2010 University

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

Page 22: Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami Fort Lauderdale, Dec. 14-19, 2010 University

Z’ resonance hunting @ LHC

Z’

Page 23: Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami Fort Lauderdale, Dec. 14-19, 2010 University

CTEQ for pdfLHC @ 7 TeV or 14 TeV

Z’ peak

SM bkgSM bkg

Z’ peak

Page 24: Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami Fort Lauderdale, Dec. 14-19, 2010 University

(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

Page 25: Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami Fort Lauderdale, Dec. 14-19, 2010 University

(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

Page 26: Supersymmetric B-L Extended Standard Model with Right-Handed Neutrino Dark Matter Nobuchika Okada Miami Fort Lauderdale, Dec. 14-19, 2010 University

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