Pasquale Di Bari (INFN, Padova)

1. NuHoRIzons 09 Harish-Chandra Research Institute, Allahabad, India, January 7-9, 2009 Pasquale Di Bari (INFN, Padova) Dark Matter from Heavy Right-Handed Neutrino Mixing (see A.Anisimov, PDB, arXiv:0812.5085 [hep-ph])

2. Neutrino masses: m1 < m2 < m3 Tritium  decay :me<2.3 eV (Mainz 95% CL) 0:m< 0.3 – 1.0 eV (Heidelberg-Moscow 90% CL, similar result by CUORICINO ) using the flat prior (0=1): CMB+BAO :  mi < 0.61 eV (WMAP5+SDSS) CMB+LSS + Ly : mi <0.17 eV (Seljak et al.)

3. Neutrinos are much lighter than all other fermions !

4. Type I See-Saw Mechanism mD

5. An impossible task ? Is it possible reconstruct mDand M from low energy neutrino experiments measuring mi and UPMNS ? Parameter counting: On the other hand neutrino experiments give information only on the 9 parameters contained in  we need some complementary information !

6. Dark matter Matter - antimatter asymmetry Inflation Accelerating Universe Puzzles of Modern Cosmology  clash between the SM and CDM ! Can the see-saw help cosmology in solving the puzzles and (vice-versa) can cosmology complement neutrino physics providing the missing information to reconstruct mD and M ?

7. RH neutrinos as Warm Dark Matter ? RH neutrino productionfrom the mixing with ordinary neutrinos is enhanced by matter effects in the early Universeand can be calculated with classic Boltzmann equations(Foot and Volkas ’97; PDB,Lipari,Lusignoli ‘99) . RH neutrinos can play the role of ‘warm’ DM if (Dodelson,Widrow’94;Dolgov,Hansen’01;Abazajian,Fuller,Patel 01) • However the same flavor-mixing mechanism that produce the DM neutrinos also leads to their radiative decay:N1   +   >> t0 M1  10 KeV (from X-ray) Moreover:SDSS Ly  M1 > (10-14) KeV • If m1< 10-5 eV and M1 ~O(KeV)the lightest RH neutrino can play the role of warm DM and at the same time the see-saw formula can explain neutrino masses(Asaka,Blanchet,Shaposhnikov’05) (Seljak et al. ’06)

8. How heavy are the heavy RH neutrinos ? one expects   mDmax ~ (1-100) GeV as well `heavy’ RH neutrinos if M1»  ~ (1-100) GeV `light’ RH neutrinos if  « M1  (1-100) GeV

9. Heavy RH neutrinos (M>>Mew) 2 solid motivations: • The see-saw works without introducing newad-hoc (small) fundamental scales to explain neutrino masses: mD~ Mew, M~MGUT • Leptogenesis: heavy RH neutrino decays can generate the matter-antimatter asymmetry …but also 2 drawbacks: • Difficult to prove the existence of heavy RH neutrinos • Difficult to explain Dark Matter m ~ mD2/M ~ 0.1 eV

10. Heavy RH neutrino DM ? It is a challenging task ! Let us impose that Ni(with i=1,2 or 3) is the DARK MATTER particle (we also indicate it with NDM) Introducing the effective neutrino mass, one has: , one finds then: Imposing

11. Notice that : From here one can also easily see that: thermalize ! This means that the abundance of Nj becomes surely comparable to that of photons when T~ Mj

12. Which mechanism for the production ? Which production mechanism ? The tough problem is then to find a way to produce an abundance: Indeed any mechanism based on the simple type I seesaw SM extension leads at most to Q: Can for example Nji  Nsource  NDM  Nioscillations produce the right NDM- abundance ? After all, it is enough to convert just a small fraction of Nsource neutrinos into NDM neutrinos !

13. Failure of the minimal model Consider the case when only the two lightest RH neutrinos (N1 and N2) mix while the heaviest (N3) does not (this corresponds to take ω=1) There are two possibilities: 1) N1=NDM and N2=NS 2) N1=NS and N2=NDM one finds: Imposing again

14. The RH neutrino mixing can be conveniently described in the „Yukawa basis“ (the analogous of the flavour basis for LH neutrinos): UR describes the RH neutrino mixing matrix ! In our case we have: Can the tiny mixing angle θ be sufficient to have enough production of NDM ?

15. The hope is that „matter effects“ canenhance the mixing ! Matter effects are in this case due to the propagation of the mass eigenstates RH neutrinos in the bath of leptons and Higgs and they are described by an effective potential given by: The relevant hamiltonian for oscillations is then For MSource > MDM there is a MSW resonance at

16. Therefore one can hope that with this set-up Dark Matter RH neutrino (stable) NDM thermalized “source” RH neutrino NS the right DM abundance would be produced by non-adiabatic MSW conversions. Using the Landau-Zener approximation: Where γres is the adiabaticity parameter at the resonance:  IT FAILS BY MANY ORDERS OF MAGNITUDE !

17. A way out ! Add to the Lagrangian a dim-5 effective operator: This operator induces matter effects that are not diagonal in general in the “Yukawa“ basis The condition for the resonance does not change ! It turns out that for MDM δ21/4~ 10-13Λeffξ(ξ(hB/v)3/2/λAB) it is possible to produce the right Dark Matter abundance ! Example: Λeff ~ MPl  MDM ~ 103 TeV The 5-dim operator however also induces new decay channels And cosmologically stability implies to MDM 105 TeV

18. Conclusions • Heavy RH neutrino as DM within a simple type I seesaw • mechanism encounters severe difficulties • 2. Introducing a dim-5 operator it is possible to enhance • the mixing among RH neutrinos wihthout changing usual • seesaw outcome on neutrino masses and mixing. • 3. This is possible because it is enough to convert just • a small fraction of „source“ RH neutrinos into Dark • Matter RH neutrinos • Decays introduce constraints but could also be • an opportunity to detect these RH neutrinos and • maybe they could explain the recent positron excess • at high energies measured by the PAMELA satellite