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

2. Tritium  decay :m e <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 :  m i < 0.61 eV (WMAP5+SDSS) CMB+LSS + Ly  :  m i <0.17 eV (Seljak et al.) Neutrino masses: m 1 < m 2 < m 3

3. Neutrinos are much lighter than all other fermions !

4. Type I See-Saw Mechanism Type I See-Saw Mechanism mDmDmDmD

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

6. Puzzles of Modern Cosmology 1. Dark matter 2. Matter - antimatter asymmetry 3. Inflation 4. Accelerating Universe  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 m D and M ?

7. However the same flavor-mixing mechanism that produce the DM neutrinos also leads to their radiative decay: N 1   +   >> t 0  M 1  10 KeV (from X-ray) Moreover: SDSS Ly   M 1 > (10-14) KeV (Foot and Volkas ’97; PDB,Lipari,Lusignoli ‘99) RH neutrino production from the mixing with ordinary neutrinos is enhanced by matter effects in the early Universe and 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) If m 1 < 10 -5 eV and M 1 ~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) RH neutrinos as Warm Dark Matter ? (Seljak et al. ’06)

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

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

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

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

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

13. Failure of the minimal model Failure of the minimal model Consider the case when only the two lightest RH neutrinos (N 1 and N 2 ) mix while the heaviest (N 3 ) does not (this corresponds to take ω=1) There are two possibilities: 1) N 1 =N DM and N 2 =N S 2) N 1 =N S and N 2 =N DM Imposing again one finds:

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

15. The hope is that „matter effects“ can enhance 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 M Source > M DM there is a MSW resonance at

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

17. The condition for the resonance does not change ! Add to the Lagrangian a dim-5 effective operator: This operator induces matter effects that are not diagonal in general in the “Yukawa“ basis It turns out that for M DM δ 2 1/4 ~ 10 -13 Λ eff ξ (ξ  (h B /v) 3/2/ λ AB ) it is possible to produce the right Dark Matter abundance ! Example: Λ eff ~ M Pl  M DM ~ 10 3 TeV A way out ! A way out ! The 5-dim operator however also induces new decay channels And cosmologically stability implies to M DM  10 5 TeV

18. Conclusions Conclusions 1.Heavy RH neutrino as DM within a simple type I seesaw mechanism encounters severe difficulties mechanism encounters severe difficulties 2. Introducing a dim-5 operator it is possible to enhance the mixing among RH neutrinos wihthout changing usual the mixing among RH neutrinos wihthout changing usual seesaw outcome on neutrino masses and mixing. 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 a small fraction of „source“ RH neutrinos into Dark Matter RH neutrinos Matter RH neutrinos 4.Decays introduce constraints but could also be an opportunity to detect these RH neutrinos and an opportunity to detect these RH neutrinos and maybe they could explain the recent positron excess maybe they could explain the recent positron excess at high energies measured by the PAMELA satellite at high energies measured by the PAMELA satellite