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Degenerate minimal seesaw and leptogenesis
Nuclear Physics B (Proc. Suppl.) 143 (2005) 525 www.elsevierphysics.com
Degenerate minimal seesaw and leptogenesis Krzysztof Turzy´ nski
a∗
a
Institute of Theoretical Physics, Warsaw University ul. Ho˙za 69, 00-681 Warsaw, Poland We analyze the most general version of the supersymmetric minimal seesaw model with only two right-chiral neutrinos which are degenerate in masses at the scale of the Grand Unification and show that it can lead to successful thermal leptogenesis.
The minimal version of the see-saw mechanism can be obtained by adding two very rightchiral neutrinos N1 and N2 to the spectrum of the Standard Model. The CP violating decays of these particles can produce lepton asymmetry, which is subsequently transformed into baryon asymmetry via sphaleron transitions. However, within the minimal see-saw mechanism one needs > the reheating temperature after inflation TRH ∼ 11 2 × 10 GeV in order to generate sufficient lepton asymmetry in the decays of the lightest rightchiral neutrino. In mSUGRA models, this is in< 107 GeV alcompatible with the bound TRH ∼ lowing to solve the gravitino problem. However, if MN1 = MN2 = M at the GUT scale, the radiatively generated small mass splitting enhances the CP asymmetries. Carefully studying the renormalization effects of the neutrino Yukawa couplings Yν in this case, we show that Yν can be parametrized solely by M , the low energy neutrino parameters, i.e., the neutrino masses, mixing angles and CP phases, and one additional real parameter β. We find that the enhancement of the CP asymmetries 1 and 2 in the decays of N1 and N2 due to small mass splitting is partly compensated by other RG effects in the running of Yν . In spite of this compensation, the CP asymmetries can be large enough ∗ presently participating in the Marie Curie Doctoral Training Programme at the ECT*, strada delle Tabarelle, 286, I-38050 Villazzano (Trento), Italy; the work was partly supported by the Polish State Committee for Scientific Research grants 2 P03B 129 24 for years 2003-05 and 1 P03D 014 26 for years 2004-06
0920-5632/$ – see front matter © 2005 Published by Elsevier B.V. doi:10.1016/j.nuclphysbps.2005.01.190
Figure 1. CP asymmetries 1 and 2 as functions of β for normal and inverse hierarchy of neutrino masses. Dashed, solid and dotted lines correspond to M = 1013 , 1011 , 107 GeV, respectively. Thick lines correspond to numerical integration of the full RG equations and thin lines to the approximate analytic formulae [1].
for successful thermal leptogenesis, as shown in Fig. 1. Moreover, they depend very weakly on the right-chiral neutrino masses and the resulting leptogenesis can be successful for very low reheating temperature, thereby allowing to overcome the gravitino problem [1]. REFERENCES 1. K. Turzynski, Phys. Lett. B 589 (2004) 135, [arXiv:hep-ph/040129] and references therein
Degenerate minimal seesaw and leptogenesis Krzysztof Turzy´ nski
a∗
a
Institute of Theoretical Physics, Warsaw University ul. Ho˙za 69, 00-681 Warsaw, Poland We analyze the most general version of the supersymmetric minimal seesaw model with only two right-chiral neutrinos which are degenerate in masses at the scale of the Grand Unification and show that it can lead to successful thermal leptogenesis.
The minimal version of the see-saw mechanism can be obtained by adding two very rightchiral neutrinos N1 and N2 to the spectrum of the Standard Model. The CP violating decays of these particles can produce lepton asymmetry, which is subsequently transformed into baryon asymmetry via sphaleron transitions. However, within the minimal see-saw mechanism one needs > the reheating temperature after inflation TRH ∼ 11 2 × 10 GeV in order to generate sufficient lepton asymmetry in the decays of the lightest rightchiral neutrino. In mSUGRA models, this is in< 107 GeV alcompatible with the bound TRH ∼ lowing to solve the gravitino problem. However, if MN1 = MN2 = M at the GUT scale, the radiatively generated small mass splitting enhances the CP asymmetries. Carefully studying the renormalization effects of the neutrino Yukawa couplings Yν in this case, we show that Yν can be parametrized solely by M , the low energy neutrino parameters, i.e., the neutrino masses, mixing angles and CP phases, and one additional real parameter β. We find that the enhancement of the CP asymmetries 1 and 2 in the decays of N1 and N2 due to small mass splitting is partly compensated by other RG effects in the running of Yν . In spite of this compensation, the CP asymmetries can be large enough ∗ presently participating in the Marie Curie Doctoral Training Programme at the ECT*, strada delle Tabarelle, 286, I-38050 Villazzano (Trento), Italy; the work was partly supported by the Polish State Committee for Scientific Research grants 2 P03B 129 24 for years 2003-05 and 1 P03D 014 26 for years 2004-06
0920-5632/$ – see front matter © 2005 Published by Elsevier B.V. doi:10.1016/j.nuclphysbps.2005.01.190
Figure 1. CP asymmetries 1 and 2 as functions of β for normal and inverse hierarchy of neutrino masses. Dashed, solid and dotted lines correspond to M = 1013 , 1011 , 107 GeV, respectively. Thick lines correspond to numerical integration of the full RG equations and thin lines to the approximate analytic formulae [1].
for successful thermal leptogenesis, as shown in Fig. 1. Moreover, they depend very weakly on the right-chiral neutrino masses and the resulting leptogenesis can be successful for very low reheating temperature, thereby allowing to overcome the gravitino problem [1]. REFERENCES 1. K. Turzynski, Phys. Lett. B 589 (2004) 135, [arXiv:hep-ph/040129] and references therein