Pasquale Di BariPasquale Di Bari

(Max Planck, Munich)(Max Planck, Munich)

‘‘The path to neutrino mass’ , Aarhus, 3-6 September, 2007The path to neutrino mass’ , Aarhus, 3-6 September, 2007

Recent developments inRecent developments inLeptogenesisLeptogenesis

• Symmetric Universe with matter- anti matter domains ? Excluded by CMB + cosmic rays

) = (±x>>

(WMAP 2006)

• Pre-existing ? It conflicts with inflation ! (Dolgov ‘97)

) dynamical generation (baryogenesis)

• A Standard Model Solution ? ¿ : too low !

New Physics is needed! New Physics is needed!

CMB

SM CMB

(Sakharov ’67)

Matter-antimatter asymmetry

• From phase transitions:

-Electroweak Baryogenesis:

* in the SM

* in the MSSM

* …………….

• Affleck-Dine:

- at preheating

- Q-balls

- ……….

• From Black Hole evaporation

• Spontaneous Baryogenesis

• …………………………………

• From heavy particle decays:

- GUT Baryogenesis

- LEPTOGENESIS

Models of Baryogenesis

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+LSS : mi < 0.94 eV (WMAP+SDSS)CMB+LSS + Ly : mi < 0.17 eV(Seljak et al.)

Neutrino masses: m1 < m2 < m3

3 limiting cases :

• pure Dirac: MR= 0

• pseudo-Dirac : MR << mD

• see-saw limit: MR >> mD

Minimal RH neutrino implementation

3 light LH neutrinos: 3 light LH neutrinos:

NN2 heavy RH neutrinos: 2 heavy RH neutrinos: NN11, N, N22 , … , …

m

M

SEE-SAW

- the `see-saw’ pivot scale is then an important quantity to understand the role of RH neutrinos in cosmology

See-saw mechanism

* ~ 1 GeV

> * high pivot see-saw scale `heavy’ RH neutrinos

< * low pivot see-saw scale `light’ RH neutrinos

The see-saw orthogonal matrix

CP asymmetry

If i ≠ 0 a lepton asymmetry is generated from Ni decays and partly converted into a baryon asymmetry by sphaleron processes

if Tif Trehreh 100 GeV ! 100 GeV !

efficiency factorsefficiency factors ## of N of Ni i decaying out-of-decaying out-of-equilibriumequilibrium

(Kuzmin,Rubakov,Shaposhnikov, ’85)(Kuzmin,Rubakov,Shaposhnikov, ’85)

M, mD, m are complex matrices natural source of CP violation

(Fukugita,Yanagida ’86)(Fukugita,Yanagida ’86)

Basics of leptogenesis

• Unflavoured regime

• Semi-hierarchical heavy neutrino spectrum :

•

‘Vanilla’ leptogenesis

Total CP asymmetry(Flanz,Paschos,Sarkar’95; Covi,Roulet,Vissani’96; Buchm¨uller,Pl ¨umacher’98)

(Davidson, Ibarra ’02; Buchmüller,PDB,Plümacher’03;PDB’05 )

It does not depend on U !

Efficiency factor(Buchm¨uller,PDB, Pl ¨umacher ‘04)

WEAK WASH-OUT

zz´ ´ MM11/ T/ T

zd

KK11´ ´ ttUU(T=M(T=M11)/)/

STRONG WASH-OUT

(Blanchet, PDB ‘06)

10-2 10-1 100 101 102 103

10-2 10-1 100 101 102 103

10-5

10-4

10-3

10-2

10-1

100

10-5

10-4

10-3

10-2

10-1

100 weak wash-out

5

Nin

N1

=0

Nin

N1

=1

fin

1

K1

5

strong wash-out

no dependence on the initial abundance

dependence on theinitial abundance

m1 msol

M11014 GeV

Neutrino mixing data favor the strong wash-out regime !

Dependence on the initial conditions

0.12 eV

Upper bound on the absolute neutrino mass scale (Buchmüller, PDB, Plümacher ‘02)

3x109 GeV

Lower bound on M1 (Davidson,Ibarra ’02;Buchmüller, PDB, Plümacher ‘02)

Lower bound on Treh : Treh 1.5 x 109 GeV(Buchmüller, PDB, Plümacher ‘04)

Neutrino mass bounds

10-4 10-3 10-2 10-1 100

10-4 10-3 10-2 10-1 100

108

109

1010

1011

1012

1013

1014

1015

1016

108

109

1010

1011

1012

1013

1014

1015

1016

Nin

N1

= 0

M

1 (G

eV

)

m1 (eV)

Nin

N1

= 1

~ 10-6 ( M1 / 1010 GeV)

Need of a very hot Universe for Leptogenesis

• M2 M3

• N2-dominated scenario

• beyond the hierarchical limit

• flavor effects

Beyond the minimal pictureBeyond the minimal picture

A poorly known detail

If M3 M2 :

(Hambye,Notari,Papucci,Strumia ’03; PDB’05; Blanchet, PDB ‘06 )

The lower bound on M1 disappears and is replaced by a lower bound on M2 …that however still implies a lower bound on Treh !

(PDB’05)(PDB’05)

For a special choice of the see-saw orthogonal matrix:

N2-dominated scenario

Four things happen simultaneously:

Different possibilities, for example:

• partial hierarchy: M3 >> M2 , M1

M3 & 3 M

2

M2

M1

M

2- M

1

M1

• heavy N3: M3 >> 1014 GeV

3 Effects play simultaneouslya role for 2 1 :

(Pilaftsis ’97, Hambye et al ’03, Blanchet,PDB ‘06)(Pilaftsis ’97, Hambye et al ’03, Blanchet,PDB ‘06)

Beyond the hierarchical limit

(Nardi,Roulet’06;Abada et al.’06;Blanchet,PDB’06)

Flavour composition:

Does it play any role ?

are fast enough to break the coherent evolution of the and quantum states and project them on the flavour basis within the horizon potentially a fully flavored regimefully flavored regime holds!

but for lower values of M1 the -Yukawa interactions,

Flavor effects

Let us introduce the projectors (Barbieri,Creminelli,Strumia,Tetradis’01) :

1. In each inverse decay the Higgs interacts now with incoherent flavour eigenstates ! the wash-out is reduced and

2. In general and this produces an additional CP violating contribution to the flavoured CP asymmetries:

These 2 terms correspond to 2 different flavour effects :

Interestingly one has that this additional contribution depends on U !

Fully flavoured regime

In pictures:

1)

N1

2)

N1

The asymmetries have to be tracked separately in each flavour:

Classic Kinetic Equations in the fully flavored regime

conserved insphaleron transitions !

General scenarios (K1 >> 1)

– Alignment case

– Democratic (semi-democratic) case

– One-flavor dominance

and

and

big effect!Remember that:

the one-flavor dominance scenario can be realized if the P1 term dominates !

The lowest bounds independent of the initial conditions (at K1=K*) don’t change! (Blanchet, PDB ‘06)

3x109

alignment

democratic

semi-democratic

But for a fixed K1, there is a relaxation of the lower bounds of a factor 2 (semi-democratic)

or 3 (democratic) that can become much larger in the case of one flavor dominance.

(Blanchet,PDB’06)(Blanchet,PDB’06)

Lower bound on M1

Semi-democratic case

• Let us consider:

• For m1=0 (fully hierarchical light neutrinos)

•Since the projectors and flavored asymmetries depend on U one has to plug the information from neutrino mixing experiments

Flavor effects represent just a correction in this case !

A relevant specific case

•However allowing for a non-vanishing m1 the effects become much larger especially when Majorana phases are turned on !

m1=matm 0.05 eV

1= 0

1= - M1min (GeV)

K1

The role of Majorana phases

Is the upper bound on neutrino masses removed by flavour effects ?

0.12 eV

EXCLUDED

EXCLUDED

(Abada,(Abada,Davidson, Davidson, Losada, Losada, Riotto’06)Riotto’06)

m1(eV)

M1 (GeV)

(Blanchet,(Blanchet, PDB ’06)PDB ’06)

FULLY FLAVOREDREGIME

EXCLUDED

Is the fully flavoured regime suitable to answer the question ?

l1

NO FLAVOR

N1

Φ

Φ

(Blanchet, PDB ’06)(Blanchet, PDB ’06)

WITH FLAVOR

LµLτ

l1 N1Φ

Φ

R(Blanchet, PDB ’06)(Blanchet, PDB ’06)

(Blanchet,PDB,Raffelt ‘06) (Blanchet,PDB,Raffelt ‘06)

• Consider the rate of processes like • The condition > H (Nardi et al. ’06; Abada et al. ‘06) (Nardi et al. ’06; Abada et al. ‘06)

(equivalent to T M1 1012 GeV) is sufficient for the validity of the fully

flavored regime and of the classic Boltzmann equations only in the weak wash-out regime where H > ID , however all interesting flavour effects occur in the strong wash-out regime !!• In the strong wash-out regime the condition > ID is stronger than > H and is equivalent to:

• If K1K1 WID 1 M1 1012 GeV but if K1<< K1 WID >> 1 much more restrictive ! This applies in particular to the one-flavor dominated scenario through which the upper bound on neutrino masses would be removed in a classic description.

When the fully flavored regime applies ?

0.12 eV

A definitive answer requires a genuine quantum kinetic calculation A definitive answer requires a genuine quantum kinetic calculation for a correct description of the `intermediate regime’ ! for a correct description of the `intermediate regime’ !

?

Condition of validity of aclassic description inthe fully flavored regime

m1(eV)

M1 (GeV)

Is the upper bound on neutrino masses killed by flavor effects ?

Let us now further impose real setting Im(13)=0

traditional unflavored case

M1min

•The lower bound gets more stringent but still successful leptogenesis is possible just with CP violation from ‘low energy’ phases that can be tested in 0 decay (Majorana phases) (very difficult) and more realistically in neutrino mixing (Dirac phase)

1= - /22= 0 = 0

Majorana phases

Dirac phase

Leptogenesis from low energy phases ?(Blanchet, PDB ’06)(Blanchet, PDB ’06)

-Leptogenesis

M1 (GeV)

In the hierarchical limit (M3>> M2 >> M1 ): In this region the resultsfrom the full flavored regime are expected to undergo severe corrections that tendto reduce the allowed region

Here some minorcorrections are alsoexpected

• -leptogenesis represents another important motivation for a full Quantum Kinetic description• Going beyond the hierarchical limit these lower bounds can be relaxed :

(Anisimov, Blanchet, PDB, in preparation )(Anisimov, Blanchet, PDB, in preparation )

sin13=0.20

1= 02= 0 = -/2

Unflavored versus flavored leptogenesis

Unflavored

Flavored

Lowest bounds on M1 and Treh

~ 109 GeV Unchanged

Upper bound

on m1

0.12 eV ? (QKE needed)

N2 - dominated scenario

for ~ R23 Domain is enlarged but no

drastic changes

Leptogenesis from low energy phases

Non-viable Viable (only marginally in the HL DL is needed)

A wish-list for see-saw and leptogenesis

• SUSY discovery with the right features: - Electro-weak Baryogenesis non viable (this should be clear) - discovery of LFV processes, discovery of EDM’s

• Treh 100 GeV (improved CMB data ? Discovery of GW background ?)

• Electroweak Baryogenesis non viable

• discovery of CP violation in neutrino mixing

• normal hierarchical neutrinos

• discovery of 0

• discovery of heavy RH neutrinos: - dream: directly at LHC or ILC - more realistically: some indirect effect (EW precision measurements?, some new cosmological effect, [e.g. RH neutrinos as DM] ? …… )

• LeptogenesisLeptogenesis provides a strong motivation fro heavy RH neutrinos and flavor effects open new prospects to test it in

0 decay experiments (Majorana phases) and (more realistically) in neutrino mixing experiments (Dirac phase)

Summary• Cosmological observations CDM modelCDM model in conflict with the SM: 4 puzzles aiming at new physics

• Discovery of neutrino masses strongly motivates to search for solutions in terms of neutrino physics; adding RH neutrinos and taking the see-saw limit seems the simplest way to explain neutrino masses and to address in an attractive way some of the puzzles;• Between light and heavy RH neutrinos the second option appears currently more robustly motivated (things could change for example if a N 0 is discovered);

•A unified picture of leptogenesis and dark matter is challenging but maybe not impossible ! However a simultaneous solution of all puzzles seems to require a deeper SM extension like (at least) GUT’s