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