Pasquale Di Bari

1
The path to neutrino mass , Aarhus, 3-6
September, 2007
Recent developments in leptogenesis

• Pasquale Di Bari
• (Max Planck, Munich)

2
Matter-antimatter asymmetry

• Symmetric Universe with matter- anti matter
  domains ? Excluded by CMB cosmic rays
• ) ?B (6.1 0.2) x 10-10 gtgt ?B
  
• (WMAP 2006)
• Pre-existing ? It conflicts with inflation !
  (Dolgov 97)
• ) dynamical generation (baryogenesis)
• A Standard Model Solution ? ?B ?B too
  low !

(Sakharov 67)
New Physics is needed!
3
Models of Baryogenesis

• 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

4
Neutrino masses m1 lt m2 lt m3
Tritium ? decay me lt 2.3 eV (Mainz 95 CL)
??0? m?? lt 0.3 1.0 eV (Heidelberg-Moscow
90 CL, similar result by CUORICINO )
using the flat prior (?01) CMBLSS ? mi lt
0.94 eV (WMAPSDSS) CMBLSS Ly? ? mi lt 0.17
eV (Seljak et al.)
5
Neutrinos and the Cosmological Puzzles
?infl
?B
?DM
?
m?
6
RH neutrinos and the see-saw limit
MR
m?
?B
7
Minimal RH neutrino implementation

• 3 limiting cases
• pure Dirac MR 0
• pseudo-Dirac MR ltlt mD
• see-saw limit MR gtgt mD

8
See-saw mechanism

• 3 light LH neutrinos
• N?2 heavy RH neutrinos N1,
  N2 ,

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

9
? 1 GeV

• gt ? ? high pivot see-saw scale ? heavy RH
  neutrinos

• lt ? ? low pivot see-saw scale ? light RH
  neutrinos

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The see-saw orthogonal matrix
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Basics of leptogenesis
(Fukugita,Yanagida 86)
M, mD, m? are complex matrices ? natural
source of CP violation
CP asymmetry
If ?i ? 0 a lepton asymmetry is generated from
Ni decays and partly converted into a baryon
asymmetry by sphaleron processes if Treh ? 100
GeV !
(Kuzmin,Rubakov,Shaposhnikov, 85)
efficiency factors ? of Ni decaying
out-of-equilibrium
12
Vanilla leptogenesis
Assume

• Unflavoured regime
• Semi-hierarchical heavy neutrino spectrum

13
N1 - dominated scenario
It does not depend on low energy phases !
14
Total CP asymmetry
(Flanz,Paschos,Sarkar95 Covi,Roulet,Vissani96
Buchmüller,Plümacher98)
(Davidson, Ibarra 02 Buchmüller,PDB,Plümacher03
PDB05 )
It does not depend on U !
15
Efficiency factor
(Buchmüller,PDB, Plümacher 04)
decay parameter
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z M1/ T
K1 tU(TM1)/?1
(Blanchet, PDB 06)
WEAK WASH-OUT
STRONG WASH-OUT
zd
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Dependence on the initial conditions
m1? msol
M1?1014 GeV
Neutrino mixing data favor the strong wash-out
regime !
18
Neutrino mass bounds
10-6 ( M1 / 1010 GeV)
Upper bound on the absolute neutrino mass scale
(Buchmüller, PDB, Plümacher 02)
0.12 eV
Lower bound on M1 (Davidson, Ibarra
02 Buchmüller, PDB, Plümacher 02)
3x109 GeV
Lower bound on Treh Treh ? 1.5 x 109
GeV (Buchmüller, PDB, Plümacher 04)
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Beyond the minimal picture

• M2 ? M3 ? ?1 ? ? (M1) evaded
• N2-dominated scenario
• beyond the hierarchical limit
• flavor effects

20
CP asymmetry bound revisited
If M3 ? M2
(Hambye,Notari,Papucci,Strumia 03 PDB05
Blanchet, PDB 06 )
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N2-dominated scenario
(PDB05)
Four things happen simultaneously
For a special choice of the see-saw orthogonal
matrix
?
The lower bound on M1 disappears and is
replaced by a lower bound on M2 that however
still implies a lower bound on Treh !
22
Beyond the hierarchical limit
(Pilaftsis 97, Hambye et al 03, Blanchet,PDB
06)
Different possibilities, for example

• partial hierarchy M3 gtgt M2 , M1

• M3 gtgt 1014 GeV

?
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3 Effects play simultaneously a role for ?2 ? 1

• Asymmetries add up

• Wash-out effects add up as well

• CP asymmetries get enhanced

For ?2 ? 0.01 (degenerate limit) the first two
effects saturate and
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Flavor effects
(Nardi,Roulet06Abada et al.06Blanchet,PDB06)
Flavour composition
Does it play any role ?
but for lower values of M1 the ?-Yukawa
interactions,
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 regime holds!
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Fully flavoured regime
Let us introduce the projectors
(Barbieri,Creminelli,Strumia,Tetradis01)
These 2 terms correspond to 2 different flavour
effects

• 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

Interestingly one has that now this additional
contribution depends on U !
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In pictures
1)
N1
2)
?
?
N1
?
?
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Classic Kinetic Equations in the fully flavored
regime
The asymmetries have to be tracked separately in
each flavour
conserved in sphaleron transitions !
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General scenarios (K1 gtgt 1)

• Alignment case
• Democratic (semi-democratic) case
• One-flavor dominance

and
and
Remember that
big effect!

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

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Lower bound on M1
semi-democratic
(Blanchet,PDB06)

• The lowest bounds independent of the
  initial conditions (at K1K) dont change!
  (Blanchet, PDB 06)

alignment
democratic
3x109
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.
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A relevant specific case
(Blanchet,PDB06)

• Consider

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

• For m10 (fully hierarchical light neutrinos)
• ?

? Semi-democratic case
Flavor effects represent just a correction in
this case !
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Is the upper bound on neutrino masses removed by
flavour effects ?
(Blanchet, PDB 06)
0.12 eV
EXCLUDED
(Abada, Davidson, Losada, Riotto06)
M1 (GeV)
FULLY FLAVORED REGIME
EXCLUDED
EXCLUDED
m1(eV)
Is the fully flavoured regime suitable to answer
the question ?
32
(Blanchet, PDB 06)
NO FLAVOR
N1
N1
F
l1
F
33
(Blanchet, PDB 06)
WITH FLAVOR
Lt
N1
F
Lµ
l1
N1
F
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When the fully flavored regime applies ?
(Blanchet,PDB,Raffelt 06)

• If the ?? is the rate of ,
  the condition ?? gt H (Nardi et al. 06 Abada
  et al. 06) is equivalent to T ? M1 ? 1012 GeV
  but is sufficient for the validity of the fully
  flavoured regime only in the weak wash-out regime
  where H gt ?ID . However flavour effects are
  relevant in the strong wash-out regime where the
  condition ?? gt ?ID is stronger than ?? gt H and
  is equivalent to
• If K1??K1 ? WID ? 1 ? M1 ? 1012
  GeV
• but if K1?ltlt K1 ? WID gtgt 1 ? much more
  restrictive !
• This is the one-flavor dominated scenario
  through which the upper bound on
  neutrino masses would be removed in the fully
  flavoured regime .

35
Is the upper bound on neutrino masses killed by
flavor effects ?
?
0.12 eV
M1 (GeV)
Condition of validity of a classic description
in the fully flavored regime
m1(eV)
A definitive answer requires a genuine quantum
kinetic calculation for a correct description of
the intermediate regime !
36
Leptogenesis from low energy phases ?
(Blanchet, PDB 06)
Let us now further impose ? real setting
Im(?13)0 ? ?1 0
M1min
traditional unflavored case
Majorana phases
?1 - ?/2 ?2 0 ? 0
Dirac phase

• 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)

37
?-Leptogenesis
(Anisimov, Blanchet, PDB, arXiv 0707.3024 )
In the hierarchical limit (M3gtgt M2 gtgt M1 )
In this region the results from the full flavored
regime are expected to undergo severe
corrections that tend to reduce the allowed
region
M1 (GeV)
?1 0 ?2 0 ? -?/2
sin?130.20
Here some minor corrections are also expected
?-leptogenesis represents another
important motivation for a full Quantum
Kinetic description !
38
Full degenerate limit M1? M2 ? M3

The maximum enhancement of the CP asymmetries is
obtained in so called resonant leptogenesis

• lower bound on sin ?13 and
• upper bound on m1

39
Unflavored versus flavored leptogenesis
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Can we detect RH neutrinos at LHC ?
Typically lowering the RH neutrino scale at TeV ,
the RH neutrinos decouple and they cannot
be efficiently produced in colliders
Different claimed possibilities to circumvent the
problem

• ? - resonant leptogenesis (Pilaftsis,
  Underwood 05)
• additional gauged U(1)B-L (King,Yanagida 04)

• Going beyond the usual type I see-saw
• leptogenesis with Higgs triplet
• (Ma,Sarkar 00 Hambye,Senjanovic 03
  Rodejohann04 Hambye,Strumia 05)
• leptogenesis with three body decays (Hambye 01)
  
• see-saw with vector fields (Losada,Nardi 07)
• ..

41
A wish-list for see-saw and leptogenesis

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

• Electroweak Baryogenesis non viable

• discovery of CP violation in neutrino mixing

• discovery of ??0?

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

• 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 ? )