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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]

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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.