Pasquale Di Bari

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COSMO 06, Tahoe Lake, September 25-29, 2006
Flavor effects in leptogenesis
Reference paper S. Blanchet, PDB hep/ph 0607330

• Pasquale Di Bari
• (Max Planck, Munich)

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Outline

• From the see-saw mechanism to leptogenesis
• The traditional picture
• Beyond the traditional picture
• Flavor effects
• General implications on leptogenesis bounds
• Role of Majorana phases
• ? testing leptogenesis at low energies ?
• Conclusions

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From the see-saw mechanism to

• Compared to any other baryogenesis model,
  leptogenesis relies on a piece of new physics
  that has been already observed
• neutrino masses
• 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 gtgt mD
• 3 light LH neutrinos
• 3 heavy RH neutrinos N1 , N2 , N3
  

,
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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
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Kinetic Equations
Wash-out term from inverse decays
CP violation in decays
decay parameters

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

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The traditional picture

• flavor composition of leptons is neglected
• hierarchical heavy neutrino spectrum
• asymmetry generated from lightest RH
• neutrino decays (N1-dominated scenario)
  

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N1 - dominated scenario
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Dependence on the initial conditions
m1? msol
M1?1014 GeV
Neutrino mixing data favor the strong wash-out
regime !
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Neutrino mass bounds
? M1
m10
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Beyond the traditional picture

• beyond the hierarchical limit
• N2-dominated scenario
• flavor effects

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Flavor effects
(Barbieri et a l. 01 Endo et al. 04
Pilaftsis,Underwood 05 Nardi,Roulet06Abada et
al.06Blanchet,PDB06)
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 play !
It is then necessary to track the asymmetries
separately in each flavor
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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 !
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NO FLAVOR
Nj
F
L
Le
Lµ
Ni
Lt
F
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WITH FLAVOR
Nj
F
Le
Lµ
Lt
Ni
F
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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
potentially big effect!
and
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Lower bound on M1
semi-democratic

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

• Let us consider

• Since the projectors and flavored asymmetries
  depend 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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The role of Majorana phases

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

?1 0
?1 - ?
m1matm? 0.05 eV
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Leptogenesis testable at low energies ?
Let us now further impose ? real setting
Im(?13)0
M1min
traditional unflavored case

• 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)
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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)
  

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Neutrino masses m1lt m2 lt m3
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z M1/ T
K1 tU(TM1)/?1
WEAK WASH-OUT
STRONG WASH-OUT
zd
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Beyond the hierarchical limit
(Pilalftsis 97, Hambye et al 03, Blanchet,PDB
06)
Assume

• partial hierarchy M3 gtgt M2 , M1

• heavy N3 M3 gtgt 1014 GeV

3 Effects play simultaneously a role for ?2 ? 1

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N2-dominated scenario
(PDB05)
See-saw orthogonal matrix
?
For
The lower bound on M1 disappears and is
replaced by a lower bound on M2. The lower bound
on Treh remains