Bounds from leptogenesis

1
Bounds from leptogenesis
Workshop Early Universe Thermometers February
6-8, 2008, Padova, Italy

• Steve Blanchet
• Max-Planck-Institut für Physik, Munich

February 7, 2008
2
Outline

• Modern view of leptogenesis
• Unflavored leptogenesis
• Fully-flavored leptogenesis
• Transition regime
• Fully-flavored leptogenesis
• Bounds on M1 (Treh) and m1
• CP violation
• Dirac-phase leptogenesis (-leptogenesis)
• Conclusion

3
Modern view of leptogenesis

• Leptogenesis Fukugita and Yanagida, 1986 stands
  here for the generation of a lepton asymmetry by
  the decay of heavy right-handed neutrinos
  , and its subsequent conversion into a
  baryon asymmetry by the sphaleron processes
  Kuzmin, Rubakov, Shaposhnikov, 1985.

• Being the cosmological consequence of the see-saw
  mechanism, it offers an elegant and simple
  explanation to the puzzle of the baryon asymmetry
  of the Universe (BAU), i.e. why WMAP,06

• The extension of the Standard Model is given by

4
Modern view of leptogenesis

• Thanks to the Yukawa interaction , the
  heavy RH neutrinos decay and are repopulated by
  inverse decay , where we define the state
  as

• However, if the lepton-lepton interactions coming
  from are fast (i.e. in equilibrium
  , but also faster than the inverse decay
  rate when the asymmetry is produced SB, Di Bari,
  Raffelt, 06), they impose a different
  description of leptogenesis.

Nardi, Nir, Racker, Roulet, 06 Abada, Davidson,
Josse-Michaux, Losada, Riotto, 06
5
Modern view of leptogenesis

• Flavor starts to matter when the t Yukawa
  interaction enters equilibrium, at a temperature
  of 1012 GeV. The µ interaction enters
  equilibrium only much later, at 109 GeV.

• So, between 1012 GeV and 109 GeV, a 2-flavor
  problem must be tackled, with flavors denoted t
  and eµ.

l1 is the good quantum state Unflavored
leptogenesis applies.
1
The flavored states leµ and lt have to be
considered fully-flavored lep. applies.
2
6
1
NO FLAVOR EFFECTS
N1
N1
F
l1
F
7
2
WITH FLAVOR EFFECTS
lt
N1
F
leµ
l1
N1
F
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Fully-flavored leptogenesis
Nardi, et al., 06 Abada, et al., 06

• The (classical) Boltzmann equations are

Sphalerons conserve ?a !
CP violation
Out-of-equilibrium condition

• The CP violation parameter is given by

• , the important decay parameter.

9
Fully-flavored leptogenesis

• The projectors Barbieri, Creminelli, Strumia,
  Tetradis, 99 are given by

New source of CP violation!

• The flavored CP asymmetries can indeed be written
  as

Even when the total CP asymmetry, , is 0, the
flavored ones can be non-zero Nardi, et al.,
06.
This new source of CP violation depends on the
lepton mixing matrix, contrary to !
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Fully-flavored leptogenesis

• Main scenarios in fully-flavored leptogenesis for
  a N1-dominated scenario
• Alignment case Nardi et al., 05
• Democratic case
• One-flavor dominance SB, Di Bari, 06

and
like unflavored case
factor 2 effect
and
potentially big effect!
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From unflavored to fully-flavored lep.

• The old unflavored leptogenesis and the new
  fully-flavored one rely both on classical
  Boltzmann equations. One expects, however, that
  in the transition regime a more correct quantum
  kinetic treatment (density matrix) should be used
  Abada et al., 06.

• Such a density-matrix equation should contain the
  two asymptotic limits we know unflavored and
  fully flavored.

Q Under which condition does one expect to
recover one or the other?
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From unflavored to fully-flavored lep.

• Precession formula Stodolsky, 87

t (z)
?t
Refractive index
Damping rate
When the lepton state is (on average or
effectively) fully projected on the z-axis, the
fully-flavored Boltzmann equations can be used.
1
L1
1
2
y
2
When the lepton state remains in its original
direction (L1), then the unflavored Boltzmann
equations can be used.
x
eµ
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Condition of validity for each picture

• For the unflavored picture to hold, one needs
  that the lepton Yukawa interactions are slower
  than the inverse-decay washout at the time when
  the asymmetry is produced in the unflavored case
  Barbieri et al., 99.

• For the fully-flavored picture to hold, one needs
  that the lepton Yukawa interactions are faster
  than the inverse-decay washout at the time when
  the asymmetry is produced in the fully-flavored
  case SB, Di Bari, Raffelt, 06.

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Condition of validity for each picture

• The important point here is that the asymmetry in
  the fully-flavored regime is produced before,
  i.e. , and at this z, the inverse-decay
  rate can be much larger than H.

• Assuming an extreme one-flavor dominance, the
  fully-flavored regime is valid for

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Condition of validity for each picture
SB, Di Bari, Raffelt, 06
Full density matrix calculation required

• For a quasi-degenerate light neutrino spectrum,
  So what about the upper bound on m1?

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Upper bound on m1?
Well-known bound 0.12 eV
Theoretical
Density matrix
uncertainty
Real example
Bound 2 eV
Bound 0.1 eV
Academic lower bound (never saturated!)
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Bounds in fully-flavored lep.

• Let us take

PMNS phases off
Big effects when a one-flavor dominance is
achieved!
Low-energy phases play an important role to
achieve it!
Red
Green
Blue
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Bounds in fully-flavored lep.

• Let us take again

With the condition of validity that we found
The cut in the parameter space is striking! There
is no allowed value above 0.2 eV.
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Bounds in fully-flavored lep.

• For a general matrix and m10

The lowest bounds are not modified by flavor
effects! SB, Di Bari, 06
At large K1, the relaxation can be in general
more than a factor 2, even for m10!
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CP violation and leptogenesis

• The see-saw has many new parameters (18!)
  compared to the Standard Model, among which 6 are
  CP-violating phases.

• A useful parametrization is given by
  Casas,Ibarra, 01

3 high-energy (unmeasurable) phases
3 low-energy (measurable) phases 2 Majorana
phases and 1 Dirac phase

• The matrix can be parametrized by three
  complex rotations

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CP violation and leptogenesis

• Very interestingly, in fully-flavored
  leptogenesis, the CP phases in the PMNS matrix
  can be uniquely responsible for the generation of
  the BAU!

SB, Di Bari, 06 Pascoli, Petcov, Riotto, 06
Branco, Gonzalez Felipe, Joaquim, 06

• Pictorially, the two sources of CP violation can
  be seen as follows

eµ
t

eµ
t
22
-leptogenesis Anisimov, SB, Di Bari,
arXiv0707.3024

• Assume from now on that only the Dirac phase
  is turned on. This is a minimal condition on the
  necessary CP violation for successful
  leptogenesis because this phase appears only in
  combination with the small µ13 angle (lt0.2 at 3¾).

• In the hierarchical limit it is
  possible to explain the BAU only with this source
  of CP violation Pascoli, Petcov, Riotto, 06

Example
Problem it is quite constrained and in the weak
wash-out!
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-leptogenesis in the DL

• In the degenerate limit (DL),
  , the CP asymmetry can be enhanced Covi,
  Roulet, Vissani, 96 ,

until one hits a resonance Pilaftsis, 99 (RL)
when

• Note that in the DL, contrary to the HL, all
  three RH neutrinos contribute to the asymmetry
  and the wash-out from each of them must be taken
  into account

? strong wash-out
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-leptogenesis in the RL

• In the RL, the final asymmetry is essentially
  independent of the RH neutrino mass ? TeV scale
  possible! Pilaftsis, 99

• We found a nice link between low-energy
  parameters (µ13, mass hierarchy, absolute
  neutrino mass scale, Dirac phase) and the BAU.
  Anisimov, SB, Di Bari, 07

Allowed regions
(Far) future sensitivity
Theoretical uncertainty
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Conclusions

• Thermal leptogenesis is an attractive way to
  explain the BAU.

• Flavor effects can modify dramatically the
  predictions from leptogenesis. However, the lower
  bound on M1 is unchanged and a density-matrix
  equation should be needed for a significant
  region of the parameter space (upper bound on m1).

• Interestingly, flavor effects impose a
  description of leptogenesis where low-energy
  phases play an important role.

• In particular, it is possible to explain the BAU
  only with the Dirac phase as a source of CP
  violation. The situation is especially favorable
  in the DL.