1. Generating Neutrino Mass & Electroweak Scale Radiatively
Amine AHRICHE
Department of Physics, University of Jijel,
Algeria
NCTS Annual Theory Meeting 2015: Particles, Strings & Cosmology

2. Outlines The Model Dark Matter Experimental Constraints
A. Ahriche, U. Jijel
NCTS Annual Theory Meeting 2015
Outlines
The Model
Dark Matter
Experimental Constraints
Numerical Results
Conclusion
based on A.A. & K.L. McDonald & S. Nasri, [hep-ph]

3. A. Ahriche, U. Jijel
NCTS Annual Theory Meeting 2015
The Model
The SM is very succesful, but ... ν ‘masses, gauge unification, hierarchy pb, BAU, DM, DE ..
Many extensions: gauge symmetry, particle content, space-time or introducing exotic ideas (SUSY, LH, UnParticle..)
A small ν ‘masses: Seesaw mechanism ... or Radiatively ... Zee, Babu-Zee ... etc
Our model is a simple (& economical) SM extension: SM + a real singlet scalar + two charged singlet scalar + 3 RH singlet fermions with a global Z2 symmetry. This leads to:
EWSB radiatively;
neutrino mass and mixing values given by the Exp;
DM candidate: relic density & direct detection Exp;
Higgs mass at 125 GeV;
Being in agreement with: LFV; muon anomalous magnetic moment; the Higgs decay h→γ γ; electroweak precision tests; the Higgs invisible decay.

4. Lagrangian Neutrino mass
A. Ahriche, U. Jijel
NCTS Annual Theory Meeting 2015
Lagrangian
Neutrino mass
These values have to be matched observed values
We do not know the neutrino mass hierarchy: normal or inverted? and the absolute neutrino mass (m1 ot m3) ?

5. EWSB A minimum with and exists on if and the tadpole conditions give
A. Ahriche, U. Jijel
NCTS Annual Theory Meeting 2015
EWSB
A minimum with and exists on if and the tadpole conditions give
where all field dependant masses can be written as
The vacuum stability is ensured by imposing the condition
with

6. Scalar spectrum We have two CP-even scalars with and
A. Ahriche, U. Jijel
NCTS Annual Theory Meeting 2015
Scalar spectrum
We have two CP-even scalars
with
and
where the charged scalar masses are given by
Here:
The quartic couplings , and are not free parameters: two of them are defined by the tadpole conditions and the third one by the Higgs (h1) mass.
The dilaton (h2) mass squared is always positive once the vacuum stability is imposed.
The dilaton mass, which is null at tree-level, is defined by the size of different radaitive contributions.

7. Dark Matter Relic density
A. Ahriche, U. Jijel
NCTS Annual Theory Meeting 2015
Dark Matter
Relic density
The relic density in the WIMP paradigm is given by:
with the freeze-out parameter
and is the thermally averaged annihilation cross-section of the DM candidate (the lightest RH fermion singlet N1 in our setup) into all kinematically accessible final state particles
In our setup, the DM candidate has the annihilation channels:

8. The charged leptons annihilation cross section is similar to KNT
A. Ahriche, U. Jijel
NCTS Annual Theory Meeting 2015
The charged leptons annihilation cross section is similar to KNT
and the scalar annihilation cross sections:
with

9. Direct detection The low-energy effective Lagrangian
A. Ahriche, U. Jijel
NCTS Annual Theory Meeting 2015
Direct detection
The low-energy effective Lagrangian
leads to the direct detection cross section
with is the nucleon mass and the baryon mass in the chiral limit.
This has to be in agreement with different direct detection experiments such as LUX

10. Experimental Constraints
A. Ahriche, U. Jijel
NCTS Annual Theory Meeting 2015
Experimental Constraints
Lepton flavor
Exp. Bounds:
Muon anomalous magnetic moment

11. Electroweak precision tests
A. Ahriche, U. Jijel
NCTS Annual Theory Meeting 2015
Electroweak precision tests
The Higgs is composite & existence of charged scalars => NEW contributions to S & T
Following Grimus, et al. NPB801(2008)81, the oblique parameters are given by:
with and the functions are given in the literature.
Higgs invisible decay
Higgs invisible decay is possible if , with
Then
However, is vanishing at tree-level due to SI symmetry.

12. The Higgs decay channel h → γγ
A. Ahriche, U. Jijel
NCTS Annual Theory Meeting 2015
The Higgs decay channel h → γγ
The Higgs is composite & existence of charged scalars => Modification in the Higgs decay channels: h → γγ , γZ as
with , , and
The ratio value should in agreement with

13. Numerical Results The dilation mass
A. Ahriche, U. Jijel
NCTS Annual Theory Meeting 2015
Numerical Results
In our numerical scan, we consider:
- The neutrino mass and mixing for normal or inverted hierarchy.
LFV constraints.
LEP constraints on light Higgs mass and mixing.
Relic density.
The dilation mass

14. The new Yukawa couplings
A. Ahriche, U. Jijel
NCTS Annual Theory Meeting 2015
The new Yukawa couplings
DM & charged scalars masses

15. Direct detection EWPT & h → γγ A. Ahriche, U. Jijel
NCTS Annual Theory Meeting 2015
Direct detection
EWPT & h → γγ

16. Thank you for your attention
A. Ahriche, U. Jijel
NCTS Annual Theory Meeting 2015
Conclusion
This model gives:
The neutrino mass and mixing data for normal and inverted hierarhy without beeing in conflict with Exp. constraints such as LFV procesess.
Right amount of the relic density without being in conflcit with detection experiemetns.
The Higgs mass at 125 GeV.
a possible enhancement on the Higgs decay channel h→ γγ while h→ γZ remains almost unchanged.
Possibly tested signals at both the ILC & LHC.
Thank you for your attention