Pasquale Di BariPasquale Di Bari

(INFN, Padova)(INFN, Padova)

Melbourne Neutrino Theory Workshop, 2-4 June 2008Melbourne Neutrino Theory Workshop, 2-4 June 2008

New Aspects New Aspects ofof

Leptogenesis Leptogenesis

Neutrino Mass Bounds Neutrino Mass Bounds (work in collaboration with Steve Blanchet to appear soon)

OutlineOutline

The minimal picture (‘vanilla’ leptogenesis)The minimal picture (‘vanilla’ leptogenesis)

Beyond the minimal picture: Beyond the minimal picture:

Extra-term in the total CP asymmetryExtra-term in the total CP asymmetry

Adding flavor to vanilla leptogenesisAdding flavor to vanilla leptogenesis

Beyond the hierarchical limitBeyond the hierarchical limit

NN2 2 – dominated scenario– dominated scenario

1) Minimal see-saw mechanism

3 light LH neutrinos: 3 light LH neutrinos:

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

mn

M

SEE-SAW

The see-saw orthogonal matrix

Total CP asymmetries If i 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-equilibriumdecaying out-of-equilibrium

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

mD is complex in general natural source of CP violation

(Fukugita,Yanagida ’86)(Fukugita,Yanagida ’86)2) Unflavoured leptogenesis

Total CP asymmetries(Flanz,Paschos,Sarkar’95; Covi,Roulet,Vissani’96; Buchmüller,Plümacher’98)

It does not depend on U !

(Davidson, Ibarra ’02; Buchmüller,PDB,Plümacher’03;Hambye et al ’04;PDB’05 )

) Upper bound on the CP asymmetry of the lightest RH neutrino

3) Semi-hierarchical heavy neutrino spectrum

N3 does not interfere with N2-decays:

It does not depend on U!

4) N1 - dominated scenario

Efficiency factordecay parameter

1

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

A first interesting coincidence !

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; Giudice,Notari,Raidal,Riotto,Strumia’04)

Neutrino mass bounds~ 10-6 ( M1 / 1010 GeV)

The lower boundson M1 and Treh

becomes more stringent whenm1 increases(PDB’04)

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

= 1

M

1 (G

eV)

m1 (eV)

Nin

N1

= 0

A second interesting coincidence

eVmatm 10 5 eVmatm 10eVmatm 05.0

A very hot Universe for leptogenesis ?

Notice also that such large MNotice also that such large M1 1 values are a problem in many models (e.g. SO(1O))values are a problem in many models (e.g. SO(1O))

Beyond vanilla leptogenesisBeyond vanilla leptogenesis

1.1. Extra-term in the total CP asymmetryExtra-term in the total CP asymmetry

2.2. Adding flavor to vanilla leptogenesisAdding flavor to vanilla leptogenesis

3.3. Beyond the hierarchical limitBeyond the hierarchical limit

4.4. NN2 2 - leptogenesis - leptogenesis

1) CP asymmetry bound revisited1) CP asymmetry bound revisited

If M3 M2 3M1:

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

= R12(12) R13(13)R23(23) M3 >> M2 = 3 M1

If R23 is switched off the extra-term does not help to relax the bounds !

|ij| < 1 |23| < 10

(Nardi,Roulet’06;Abada, Davidson, Josse-Michaux, Losada, Riotto’06, Blanchet,PDB, Raffelt’06

Flavour composition:

Does it play any role ?

are fast enough to break the coherent evolution of

But for M1 1012 GeV , -Yukawa interactions,

2) Flavor effects

()

andand

Imposing a more restrictive condition:Imposing a more restrictive condition:

If If M1 109 GeV then also - Yukawas are in equilibrium 3 - flavor regime

2 -2 -

(( and a overposition of and a overposition of + e + e))

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 now this additional contribution depends on U !

Fully flavoured regime

(( = = , , +e)+e)

– Alignment case

– Democratic (semi-democratic) case

– One-flavor dominance

and

and

big effect!Remember that:

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

General cases (K1 >> 1)

consider first |ij|1 and m1<< matm:

Flavor effects do not relax the lower bound on M1 and Treh !

Numerically:Numerically:

MM11(

GeV

)(G

eV)

KK11

Analytically:Analytically:

unfla

vore

d

unfla

vore

d

flavored

flavored

Do flavour effects relax the bounds on neutrino masses ?MM

11(G

eV)

(GeV

)

A new effect for large |ij|

It dominates for |It dominates for |ijij||1 but is upper 1 but is upper

bounded because of bounded because of orthogonality: orthogonality: It is usually neglected but since it is It is usually neglected but since it is not upper bounded by orthogonality, not upper bounded by orthogonality, for for ||ijij||11 it can be important it can be important

The usualThe usuallower boundlower boundgets relaxedgets relaxed

Red:

Green:

Arbitrary

Blue :

= R13PMNS phases off

0.12 eV

EXCLUDED

m1(eV)

M1 (GeV)

EXCLUDED

Is the fully flavoured regime suitable to answer the question ?

FULLY FLAVOREDREGIME

EXCLUDED

(Abada,Davidson, Losada, Riotto’06; Blanchet, PDB’06)(Abada,Davidson, Losada, Riotto’06; Blanchet, PDB’06) ?

Condition of validity of aclassic description inthe fully flavored regime

No ! There is an intermediate regime where a full quantum kinetic description is necessary !(Blanchet,PDB,Raffelt ‘06) (Blanchet,PDB,Raffelt ‘06)

INTERMEDIATE REGIME

Neutrino mass bounds

Red:

Green:

Blue :

Let us now further impose real

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) (difficult) and more realistically in neutrino mixing (Dirac phase)

1= - ¼/22= 0 = 0

Majorana phases

Dirac phase

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

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 !

(Anisimov, Blanchet, PDB, arXiv 0707.3024 )(Anisimov, Blanchet, PDB, arXiv 0707.3024 )

sin13=0.20

1= 02= 0 = -/2

Dirac phase leptogenesis

Full degenerate limit: M1 M2 M3

The maximum enhancement of the CP asymmetries is obtainedin so called resonant leptogenesis:

lower bound on sin 13 and upper bound on m1

Some remarks on -leptogenesis :• there is no theoretical motivation

• …however, within a generic model where all 6 phases are present, it could be regarded as an approximate scenario if the contribution from dominates it is interesting to know that something we could discover in neutrino mixing experiments is sufficientto explain (in principle) a global property of the Universe

• On the other hand notice that: if we do discover CP violation in neutrino mixing it does not prove leptogenesis

not dis

Different possibilities, for example:

• partial hierarchy: M3 >> M2 , M1

M3 & 3 M

2

M2

M1

M

2- M

1

M1

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

3) Beyond the hierarchical limit

• M3 >> 1014 GeV :

3 Effects play simultaneously a role for 2 1 :1. Asymmetries add up

2. Wash-out effects add up as well

3. CP asymmetries get enhanced

For 2 0.01 (degenerate limit) the first two effects saturate and:

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 =R23

4) N2-dominated scenario

Four things happen simultaneously:

Equivalent

to assume:

An analytical summarizing expression

heavy neutrino flavor index

lepton flavor index

CP asmmetry enhancement for degenerate RH neutrinos

Extra-term violatingthe ‘usual’ CP asymmetryupper bound Contribution from heavier RH neutrinos

FLAVOREFFECTS

Vanilla leptogenesis

ConclusionsConclusions1.1. The minimal scenario (vanilla leptogenesis) grasps the main The minimal scenario (vanilla leptogenesis) grasps the main

features of leptogenesis neutrino mass bounds but there are features of leptogenesis neutrino mass bounds but there are important novelties introduced by various effects beyondimportant novelties introduced by various effects beyond

2.2. A lower bound on the reheating temperature is a solid feature A lower bound on the reheating temperature is a solid feature in the hierarchical limit. However, flavor effects introduce a in the hierarchical limit. However, flavor effects introduce a new possibility that, though at expenses of a mild tuning, can new possibility that, though at expenses of a mild tuning, can relax the lower bound from 10relax the lower bound from 1099 GeV down to 10 GeV down to 1088 GeV GeV

3.3. The upper bound on neutrino masses needs a final answer The upper bound on neutrino masses needs a final answer from a full density matrix approachfrom a full density matrix approach

4.4. Flavor effects make possible a scenario (Dirac phase Flavor effects make possible a scenario (Dirac phase leptogenesis) where the final asymmetry stems only from the leptogenesis) where the final asymmetry stems only from the same source of CP violation (sin same source of CP violation (sin 13 13 sin sin ) that is testable in ) that is testable in

neutrino mixing neutrino mixing 5.5. The NThe N2 2 - dominated scenario is a good option with potential - dominated scenario is a good option with potential

interesting applicationsinteresting applications

FULLY FLAVORED REGIME

LµLτ

l1 N1Φ

Φ

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

R

In pictures:

1)

N1

2)

N1

++