Pasquale Di BariPasquale Di Bari

(INFN, Padova)(INFN, Padova)

Dark Matter Dark Matter

from from

Heavy Right-HandedHeavy Right-Handed

Neutrino MixingNeutrino Mixing(see A.Anisimov, PDB, (see A.Anisimov, PDB, arXiv:0812.5085 [hep-ph]arXiv:0812.5085 [hep-ph] ))

NuHoRIzons 09Harish-Chandra Research Institute, Allahabad, India, January 7-9,

2009

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.)

Neutrino masses: mNeutrino masses: m11 < m < m22 < < mm33

Neutrinos are much lighter than all other fermions !

Type I See-Saw MechanismType I See-Saw Mechanism

mmDD

An impossible task ?An impossible task ?Is it possible reconstruct mIs it possible reconstruct mDD

and M from low energy and M from low energy neutrino experiments measuring mneutrino experiments measuring mi i and Uand UPMNS PMNS ??

Parameter counting: Parameter counting:

On the other hand neutrino experiments give information only On the other hand neutrino experiments give information only on the 9 parameters contained in on the 9 parameters contained in

we need some complementary information !we need some complementary information !

Puzzles of Modern Puzzles of Modern CosmologyCosmology

1.1. Dark matterDark matter

2.2. Matter - antimatter asymmetryMatter - antimatter asymmetry

3.3. InflationInflation

4.4. Accelerating UniverseAccelerating Universe

clash between the SM and CDM !

Can the see-saw help cosmology in solving the puzzles and Can the see-saw help cosmology in solving the puzzles and (vice-versa) (vice-versa) can cosmology complement neutrino physics can cosmology complement neutrino physics providing the missing information to reconstruct mproviding the missing information to reconstruct mD D and M ? and M ?

• 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

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 (Foot and Volkas ’97; PDB,Lipari,Lusignoli ‘99)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 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)

RH neutrinos as Warm Dark RH neutrinos as Warm Dark Matter ? Matter ?

(Seljak et al. ’06)

`heavy’ RH neutrinos if M1 » ~ (1-100) GeV

How heavy are the heavy RH neutrinos ?How heavy are the heavy RH neutrinos ?

GeVm ldu )1001(~max,,

`light’ RH neutrinos if « M1 (1-100) GeV

one expects one expects m mDDmaxmax ~ (1-100) GeV ~ (1-100) GeV as well as well

1)1) The see-saw works without introducing The see-saw works without introducing newnew ad-hocad-hoc (small) fundamental scales (small) fundamental scales to explain neutrino masses:to explain neutrino masses:

mmDD~ M~ Mewew , , M~MM~MGUTGUT

2)2) LeptogenesisLeptogenesis:: heavy RH neutrino decays heavy RH neutrino decays can can generate the matter-antimatter asymmetry generate the matter-antimatter asymmetry

… …but also 2 drawbacks:but also 2 drawbacks: Difficult to prove the existence of heavy RH neutrinosDifficult to prove the existence of heavy RH neutrinos Difficult to explain Dark MatterDifficult to explain Dark Matter

Heavy RH neutrinos (M>>Mew)2 solid motivations:2 solid motivations:

mm ~ m~ mDD22/M ~ 0.1 eV/M ~ 0.1 eV

Heavy RH neutrino DM ?Heavy RH neutrino DM ?

It is a challenging task ! Let us impose that It is a challenging task ! Let us impose that NNii (with i=1,2 or 3)(with i=1,2 or 3)

is the DARK MATTER particle (we also indicate it with is the DARK MATTER particle (we also indicate it with NNDMDM))Introducing the Introducing the effective neutrino masseffective neutrino mass,,

one has:one has:

Imposing Imposing , one finds then:, one finds then:

Notice that :Notice that :

From here one can also easily see that: From here one can also easily see that:

thermalize ! thermalize !

This means that the abundance of NThis means that the abundance of Nj j becomes becomes surely surely comparable to that of photons when Tcomparable to that of photons when T~ M~ Mjj

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 Indeed any mechanism based on the simple type I seesaw SM extension leads at most toseesaw SM extension leads at most to

Which mechanism for the Which mechanism for the

production ?production ?

Q: Can for example Nji Nsource NDM Ni oscillations produce the right NDM- abundance ?

After all, it is enough to convert just a small After all, it is enough to convert just a small fraction of Nfraction of Nsource source neutrinos into Nneutrinos into NDM DM neutrinos !neutrinos !

Failure of the minimal model Failure of the minimal model Consider the case when only the two lightest RH Consider the case when only the two lightest RH neutrinos (Nneutrinos (N1 1 and Nand N22) mix while the heaviest (N) mix while the heaviest (N33) ) does not (this corresponds to take does not (this corresponds to take ωω=1=1))

There are two possibilities:There are two possibilities:

1) N1) N11=N=NDM DM andand N N22=N=NSS

2) N2) N11=N=NS S andand N N22=N=NDMDM

Imposing again Imposing again one finds:one finds:

The RH neutrino mixing can be conveniently described in theThe RH neutrino mixing can be conveniently described in the„„Yukawa basis“ (the analogous of the flavour basis for LH neutrinos):Yukawa basis“ (the analogous of the flavour basis for LH neutrinos):

UR describes the RH neutrino mixing matrix !

In our case we have:In our case we have:

Can the tiny mixing angle Can the tiny mixing angle θθ be sufficient to be sufficient to have enough production of Nhave enough production of NDM DM ? ?

The hope is that The hope is that „matter effects“ „matter effects“ cancan enhance the mixing !enhance the mixing !

Matter effects are in this case due to the propagation of theMatter effects are in this case due to the propagation of themass eigenstates RH neutrinos in the bath of leptons and Higgsmass eigenstates RH neutrinos in the bath of leptons and Higgsand they are described by an effective potential given by: and they are described by an effective potential given by:

The relevant hamiltonian for oscillations is thenThe relevant hamiltonian for oscillations is then

For For MMSource Source > M> MDMDM there is a MSW resonance at there is a MSW resonance at

M3

M2

M1

M

2- M

1

M1

thermalized “source” RH neutrino NS

Dark Matter RH neutrino (stable) NDM

Therefore one can hope that with this set-upTherefore one can hope that with this set-up

the right DM abundance would be produced by non-adiabatic MSW the right DM abundance would be produced by non-adiabatic MSW conversions. Using the conversions. Using the Landau-Zener approximationLandau-Zener approximation::

Where Where γγresres is the is the adiabaticity parameter at the resonance:adiabaticity parameter at the resonance:

IT FAILS BY MANY ORDERS OF MAGNITUDE !IT FAILS BY MANY ORDERS OF MAGNITUDE !

The condition for the resonance does not change !The condition for the resonance does not change !

Add to the Add to the Lagrangian a dim-5 effective operator:Lagrangian a dim-5 effective operator:

This operator induces matter effects that are notThis operator induces matter effects that are notdiagonal in general in the diagonal in general in the “Yukawa“ basis“Yukawa“ basis

It turns out that for It turns out that for MMDM DM δδ221/41/4 ~ 10~ 10-13-13 ΛΛeffeff ξξ ((ξξ(h(hBB/v)/v)3/2/3/2/λλABAB) )

it is possible to produce the right Dark Matter abundance ! it is possible to produce the right Dark Matter abundance !

Example: Example: ΛΛeff eff ~ M~ MPl Pl M MDM DM ~ 10~ 103 3 TeV TeV

A way out ! A way out !

The 5-dim operator however also induces new decay channels The 5-dim operator however also induces new decay channels And cosmologically stability implies to And cosmologically stability implies to MMDMDM 10 1055 TeV TeV

Conclusions Conclusions

1.1. Heavy RH neutrino as DM within a simple type I seesawHeavy RH neutrino as DM within a simple type I seesaw mechanism encounters severe difficultiesmechanism encounters severe difficulties

2. Introducing a dim-5 operator it is possible to enhance2. Introducing a dim-5 operator it is possible to enhance the mixing among RH neutrinos wihthout changing usualthe 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 just3. This is possible because it is enough to convert just a small fraction of „source“ RH neutrinos into Darka small fraction of „source“ RH neutrinos into Dark Matter RH neutrinosMatter RH neutrinos

4.4. Decays introduce constraints but could also be 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 satelliteat high energies measured by the PAMELA satellite