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Flavor effects on leptogenesis
Steve Blanchet
Max-Planck-Institut für Physik, Munich
September 15, 2006
Neutrino Oscillation Workshop
Conca Specchiulla, Otranto, Italy, Sep. 9-16 2006
Based on: SB, P. Di Bari, hep-ph/0607330
S. Blanchet, NOW 2006, 15.09.062
Outline
Review of unflavored leptogenesis and its implications
Idea of how flavor enters leptogenesis General implications of flavor Specific example
Non-zero Majorana phases can lead to large effects
Summary and conclusions
S. Blanchet, NOW 2006, 15.09.063
Unflavored thermal leptogenesis Minimal extension of the SM
The BAU can be generated because [Fukugita, Yanagida, 86] : CP is violated in the decay of heavy neutrinos
Baryon number is violated in sphaleron processes Decays are out of equilibrium at some point, parametrized by
``decay parameter´´
CP asymmetry parameter
S. Blanchet, NOW 2006, 15.09.064
Unflavored thermal leptogenesis Notice how it is summed over the flavors
The fundamental Boltzmann equations are
Strong wash-out when Weak wash-out when
CP violation Out-of-equilibrium condition Sphalerons conserve B-L !
S. Blanchet, NOW 2006, 15.09.065
Unflavored thermal leptogenesis It is convenient to write the solution in the form
where are the final efficiency factors. The final baryon asymmetry is given by
and should be compared to the measured value [WMAP,06]
Assuming one typically has a N1-dominated scenario.
S. Blanchet, NOW 2006, 15.09.066
WEAK WASH-OUT STRONG WASH-OUT
S. Blanchet, NOW 2006, 15.09.067
From the upper bound on the CP asymmetry [Asaka et al., 01; Davidson, Ibarra, 02]
one obtains a lower bound on M1 and on the reheating
temperature independent of the initial conditions [Davidson,
Ibarra, 02; Buchmüller, Di Bari, Plümacher, 02] :
The suppression of the CP asymmetry for growing absolute neutrino mass scale leads to a stringent upper
bound [Buchmüller, Di Bari, Plümacher, 02] :
Implications of unflavored leptogenesis
S. Blanchet, NOW 2006, 15.09.068
How does flavor enter leptogenesis? Below some temperature ~109-11 GeV, the muon and
tauon charged lepton interactions
are in equilibrium. These interactions are then fast enough to ‘measure’ the
flavor of the state produced in the decay of the heavy neutrino; a 3-flavor basis is defined. [Barbieri, Creminelli, Strumia, Tetradis, 99 ; Endoh, Morozumi, Xiong, 03; Abada, Davidson, Josse-Michaux, Losada, Riotto, 06 ; Nardi, Nir, Racker, Roulet, 06]
S. Blanchet, NOW 2006, 15.09.069
Second type of effect: additional contribution to the individual CP asymmetries:
First type of effect: the rates of decay and inverse decay in each flavor are suppressed by the projectors
How does flavor enter leptogenesis? The fundamental Boltzmann equations become
Same as before!
[Nardi et al., 06]
[Nardi et al., 06]
S. Blanchet, NOW 2006, 15.09.0610
L
NO FLAVOR
Nj
Φ
ΦLe
LμLτ
S. Blanchet, NOW 2006, 15.09.0611
WITH FLAVOR (all projectors equal)
Nj
Φ
Φ
Lτ
LeLμ
S. Blanchet, NOW 2006, 15.09.0612
Possible scenarios: Alignment case [Nardi et al., 05]
Democratic (semi-democratic) case
One-flavor dominance
General implications of flavor There exists an upper bound on the individual CP
asymmetries [Abada, et al., 06] :
and
and
It does not decrease when the active neutrino mass scale increases!
potentially big effect!
like unflavored case
factor 2-3 effect
S. Blanchet, NOW 2006, 15.09.0613
General implications of flavor Lower bounds
3x109
alignment
democratic
semi-democratic
The lowest bounds independent of the initial conditions (K*) do not change!
S. Blanchet, NOW 2006, 15.09.0614
General implications of flavor At fixed K1, there is a relaxation of the lower bounds
[Abada et al., 06] . How much? Factor 2-3 typically, but it depends on the projectors (could be much more!).
However, the region of independence of initial conditions shrinks when the flavor effects increase (small projector, i.e. one-flavor dominance)
S. Blanchet, NOW 2006, 15.09.0615
Specific example Let us now study a specific case, , using the
known information about the PMNS mixing matrix. For a fully hierarchical light neutrino spectrum
one obtains a semi-democratic situation where
For a real UPMNS and purely imaginary
Semi-democratic
S. Blanchet, NOW 2006, 15.09.0616
Specific example: Majorana phase effects With
~ Semi-democratic
One-flavor dominance
With
S. Blanchet, NOW 2006, 15.09.0617
Summary of
with purely imaginary
Specific example: Majorana phase effects
Case of real
cf. talk by Petcov this morning
S. Blanchet, NOW 2006, 15.09.0618
Summary and conclusions Flavor effects can be important, but when they are, the
region of the parameter space where leptogenesis does not depend on the initial conditions shrinks.
The lower bounds on M1 and Treh in the strong wash-out are not relaxed, but the bounds at fixed K are. The upper limit on m1 seems to disappear when M1<1012 GeV.
Quantitatively, flavor effects yield O(1) modification of the usual results, except either when there is one-flavor dominance or when the total CP asymmetry vanishes. In both cases, Majorana phases play an important role.
The one-flavor dominance seems to occur mainly when light neutrinos are quasi-degenerate.
In conclusion, leptogenesis provides another phenomenology where Majorana phases matter.