Neutrino masses and l - PowerPoint Presentation

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Neutrino masses and lepton asymmetry in the 3-3-1 model with right-handed neutrinos

N. T. ThuyYonsei UniversityJindo Workshop, Sep 20~23, 2012

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OutlineI. IntroductionII. A review of the modelIII. Higgs sextet and neutrino massesIV. Lepton asymmetryV. Summary

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I. IntroductionTraditionally, the 3-3-1 model with right-handed neutrinos works with the three Higgs triplets. At the tree level the neutrino mass spectrum is degenerated with the mass

0, -m, m. -> This spectrum is not realistic. By introducing an addition Higg sextet, the neutrino mass problem can be solved.

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All cosmological models agree that the Universe started with the same amount of baryon and anti-baryon. However from Big-Bang Nucleosynthesis (BBN) and WMAP

, where are the number densities of baryons and antibaryons. ->The baryon asymmetry must be generated

dynamically

.

Sakharov: requires

Baryon

number violation

C and CP violation

Out of equilibrium dynamicsConsider The in the quark mixing matrix, leads to much too small a asymmetry -> We study lepton asymmetry.

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II. A review of the model The particle content in this model is given as follow:

where a= 1, 2, 3 and = 2, 3 are generation indices. The electric charges of U (D) are the same as of u (d).

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The three Higgs with VEVs are introduced:6Slide7

The Yukawa interactions can be written in the most general form as follows where the subscripts LNC and LNV, respectively indicate to the lepton number conserving and lepton number violating ones.

where a, b, and c stand for SU(3)­L indices. 7Slide8

where

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The gauge group

is broken via two steps: The VEV w is responsible for the first step of symmetry breaking giving mass for the exotic quarks, while the second

step

is due to

u

and

v

giving

mass for the usual quarks and all ordinary leptons. Therefore, they have to satisfy the constraints:

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III. Higgs sextet and neutrino masses The Lagrangian for the tree-level neutrino masses is obtained as where

The tree-level spectrum consists of only Dirac neutrinos with one particle massless and two others degenerate in mass: 0, -m, m.

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The sextet Higgs is introduced to solve neutrino masses problem, defined by

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Impose that the active neutrinos gain mass via a type II seesaw:It turns out that the neutrino masses in this model naturally small because of suppression of a large scale and a small constrained from the -parameter, where The sterile neutrinos have large masses in the scale:Taking we get

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IV. Lepton asymmetryThere must have the non conservation of the lepton number. Any lepton asymmetry generated by A would be neutralized by the decays of A*, unless

CP conservation is also violated and the decays are out of thermal equilibrium in the universe. 13Slide14

The most general potential for the three Higgs triplets and

sextet which are invariant under the is given asV=+

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Under the discrete symmetry the potential can be written as following:

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The constraints of the parameters can be calculated from the minimum condition of the potential. We get

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We assume that there is no hierarchy between the couplings of Higgs sextet with Higgs triplets, . On the other hand, S gives mass to right handed neutrinos, so the Higgs sextet is much heavier than the three Higgs

triplets. => We can ignore the mixing of Higgs sextet with Higgs triplets.

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The relevant Lagrangian is If we assign the lepton number L=0 to the sextet

S, the Yukawa couplings explicitly break L.

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We consider neutrinos as Majorana particles19Slide20

The heavy particles in this model are N and S.At tree-level,Contributions to the CP violation is due to the interference between the tree-level and the one-loop diagrams.The asymmetry can be generated through the decays

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Example of Feynman diagrams

In general, the CP asymmetry is given by21Slide22

What are we going to do?We are going to calculate the asymmetry of all possible channels of N and S.Whether the decay of N or S is important for the asymmetry. We can calculate the baryon asymmetry after we get the lepton asymmetry.Another idea: can be consider as inflaton with the potential All the above works can be considered

in the economical 331 model.22Slide23

This idea is from Chia-Min Lin: Phy. Lett B 659 (2011)23Slide24

V. SummaryNeutrino masses problem has been solved by introducing one sextet S in 3-3-1 model with right handed neutrinos. In our model, Majorana neutrinos

gain mass via like-type II seesaw. The asymmetry can be generated through the decays of N and S. Work is in process24Slide25

Thanks for Your Attentions!25