Pasquale Di BariPasquale Di Bari

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

COSMO 06, Tahoe Lake, September 25-29, 2006

Flavor effects in leptogenesis

Reference paper: S. Blanchet, PDB hep/ph 0607330

OutlineOutline

From the see-saw mechanism to leptogenesis From the see-saw mechanism to leptogenesis

The traditional picture The traditional picture

Beyond the traditional picture Beyond the traditional picture

Flavor effects Flavor effects

General implications on leptogenesis boundsGeneral implications on leptogenesis bounds

Role of Majorana phasesRole of Majorana phases

testing leptogenesis at low energies ?testing leptogenesis at low energies ?

ConclusionsConclusions

From the see-saw mechanism to …From the see-saw mechanism to … Compared to any other baryogenesis model, leptogenesis relies on a

piece of new physics that has been alreadyalready observed:

neutrino masses and on the simplest way to explain them:and on the simplest way to explain them:

the see-saw mechanism Adding to the SM (3) RH neutrinos with Yukawa couplings h and a Majorana mass M,

a usual Dirac mass mD = v * h is also generated after SSB. For M >> mD :

3 light LH neutrinos:3 light LH neutrinos:

3 heavy RH neutrinos: 3 heavy RH neutrinos: NN11 , N , N22 , N , N33

m

mD

M

SEE-SAW

,

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 factors ´ # of Ni decaying out-of-equilibrium

(Kuzmin,Rubakov,Shaposhnikov, ’85)

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

(Fukugita,Yanagida ’86)

… … leptogenesisleptogenesis

Kinetic Equations

``decay parameters´´

CP violation in decays Wash-out term from inverse decays

• Strong wash-out when Ki 3 • Weak wash-out when Ki 3

• flavor composition of leptons is neglected

• hierarchical heavy neutrino spectrum

• asymmetry generated from lightest RH neutrino decays (N1-dominated scenario)

The traditional pictureThe traditional picture

N1 - dominated scenario

Dependence on the initial conditions

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 !

Neutrino mass bounds

mm11=0=0

M1

• beyond the hierarchical limit

• N2-dominated scenario

• flavor effects

Beyond the traditional pictureBeyond the traditional picture

(Barbieri et a l. ’01; Endo et al. ’04; Pilaftsis,Underwood ’05; Nardi,Roulet’06;Abada et al.’06;Blanchet,PDB’06)

Flavor composition:

Does it play any role ? However for lower temperatures the charged lepton Yukawa couplings,

are strong enough to break the coherent evolution of the and of the , that are then projected on a flavor basis: ‘‘flavor’ is measured and comes into flavor’ is measured and comes into play !play !

Flavor effects

It is then necessary to track the asymmetries separately in each flavor:

How flavor effects modify leptogenesis? • The kinetic equations then become :

• First type of effect: inverse decays wash-out in each flavor is suppressed by the projectors:

• Second type of effect: additional contribution to the individual CP asymmetries:

Same as before!

(Nardi et al., 06)

(Nardi et al., 06)

Interestingly one has that this additional contribution depends on U !

L

NO FLAVOR

Nj

Φ

ΦLe

LµLτ

WITH FLAVOR

Nj

Φ

ΦLeLµLτ

General implications on the bounds• Upper bound on the individual CP asymmetries (Abada, et al., 06) :

Notice that it does not decrease when the active neutrino mass scale increases

This can potentially remove the upper bound on neutrino masses

• Possible general scenarios:– Alignment case (Nardi et al., 05)

– Democratic (semi-democratic) case (Blanchet, PDB, 06)

– One-flavor dominance (Blanchet, PDB, 06)

and

and

potentially big effect!

Lower bound on M1

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), but it can be much larger in the case of one flavor dominance.

A relevant specific case

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 !

The role of Majorana phases

•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= -

Leptogenesis testable at low energies ?

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) and neutrino mixing (Dirac phase) • Moreover considering the degenerate limit these lower bounds can be relaxed !

(Blanchet,PDB 06)

Conclusions• Leptogenesis is fastly developing in last

years becoming more and more quantitative; • The most interesting recent achievement is

represented by an account of flavor effects;• They typically reduce the range of the strong

wash-out regime without relaxing the lower bounds on M1 and on Treh (for this one needs to consider a degenerate heavy neutrino spectrum) but removing the upper bound on neutrino masses that holds in the unflavored case;

• Very interestingly they make possible to have successful leptogenesis just from low energy phases testable in neutrino experiments:

0 decay experiments (Majorana phases) and

neutrino mixing experiments (Dirac phase)

Neutrino masses: m1< m2 < m3

WEAK WASH-OUT

zz´ ´ MM11/ T/ T

zd

KK11´ ´ ttUU(T=M(T=M11)/)/

STRONG WASH-OUT

Beyond the hierarchical limit

Assume:• 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 :

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

For

The lower bound on M1 disappears and is replaced by a lower bound on M2. The lower bound on Treh remains

(PDB’05)(PDB’05) N2-dominated scenario

See-saw orthogonal matrix: