Relating dark matter and radiative Seesaw neutrino mass scales without beyond SM gauge symmetry Xiao-Gang He 1. Introduction 2. Radiative seesaw and dark matter Masses 3. Dark matter with SM symmetry only 4. A model of radiative seesaw and DM with SM symmetry 5. Neutrino mixing and mass, and mu -> e gamma Work with Yi Cai, M. Ramesy-Musolf and Lu-Hsing Tsai

1. Introduction There is about 20% of the energy come from dark matter in our universe. What is the nature of DM is not known: WIMP, Axion, … What is DM mass, not known, a big range is allowed. DM must be stable, usually impose additional symmetry beyond SM symmetry, such as R-parity in susy, Z 2 symmetry in darkon model, …

Neutrinos have non-zero masses. In minimal SM, neutrinos do not have masses. Need to go beyond SM to explain why neutrinos have small but non-zero masses. Loop generation of neutrino masses, like Zee model… Also the Seesaw models, Type I, Type II and Type III, and other variations. All need to introduce new particles in the model. In general these new particles do not play a role of DM. It would be good to relate them.

2. Radiative seesaw and dark matter Masses E. Ma, PRD73:077301,2006 introduce right handed neutrinos N R and a new Higgs doublet h under Z 2 under Z 2 N R -> - N R N R -> - N R h -> - h h -> - h h no vev, Z 2 not broken. No usual seesaw h no vev, Z 2 not broken. No usual seesaw neutrino masses. One loop will generate them. neutrino masses. One loop will generate them. If neutral h is the lightest particle, it can be DM If neutral h is the lightest particle, it can be DM If one of the N is the lightest, it is the DM If one of the N is the lightest, it is the DM DM mass related to radiative seesaw neutrino mass scale. Can one get rid off the additional Z 2 symmetry? Just SM gauge symmetry can do the job?

3. Dark matter with SM symmetry only M. Cirelli, N. Fornengo and A. Strumia, NP B753,178(2006) Choose large SM representation with no color which cannot couple to SM fermions and Higgs with renormalizable terms. The neutral component stable, plays the role of DM Minimal Dark Matter Smallest representations: n = (1, 5, 0) Why? If n fermion, L: (1,2,-1/2), H: (1,2,1/2) -> L H: (1 + 3, 0), Smallest n: (1, 4, ½) or (1,5,0). If want Majorana mass term, not good to have (1,4,1/2). If n scalar, HH*H: ( , ½), to avoid n to couple to this term, The minimal should be (1,5,0)

The lightest n does not decay. Can be candidate for DM. Co-annihilation produce the right relic DM density Coupling is SU(2) coupling, known, the DM relic density will fix the DM mass Require n to produce the DM relic density, the mass can be determined.

4. A model of radiative seesaw and DM with SM symmetry Ma model + MDM A new model: No additional symmetries other than SM gauge symmetry!

Radiative seesaw at one loop level Needs more than one N R to get phenomenologically consistent neutrino masses.

Dark matter, assuming N R 1 is the lightest

From: M. Cirelli and A. Strumia, New J Phys. 11, (2009) Relic density: DM mass is about 9.6 TeV.

DM direct detection

Indirect Dark Matter booster factor 50

5. Neutrino mixing and mass, and mu -> e gamma

Discussions With appropriate choices of new fields in the SM, without additional symmetries other than the SM gauge symmetry, it is possible to have WIMP DM. The DM mass is determined by DM relic density. This mass scale also determines the radiative seesaw scale for generating non-zero neutrino masses. Dark matter mass scale is naturally related to the radiative seesaw neutrino mass scale. Relating Radiative Seesaw Neutrino And Dark Matter Mass Scales Since DM mass of order 10 TeV, not much can be done at LHC. Flavour physics, like mu to e gamma can constrain the neutrino mass parameters.