Neutrinoless double beta decay (NDBD) is the only experiment that could probe
the Majorana nature of the neutrino. Here we study the theoretical implications
of NDBD for models yielding tri-bimaximal lepton mixing like A4 and S4.Comment: Talk given at TAUP09, July 1-5, 2009 (Roma).The proceeding will be
  published in Journal of Physics, Conference Series (Editors: E. Coccia, L.
  Pandola, N. Fornengo, R. Aloisio

Altarelli G

Bazzocchi F

Hirsch M

Stefano Morisi

Journal of Physics Conference Series

English

arXiv

Crossref

Probing the Majorana nature of the neutrino with neutrinoless double beta decay

11th International Conference on Topics in Astroparticle and Underground Physics (TAUP 2009). Rome, ITALY, JUL 01-05, 2009Neutrino less double beta decay (0 nu beta beta) is the only experiment that could probe the Majorana nature of the neutrino. Here we study the theoretical implications of 0 nu beta beta for models yielding tri-bimaximal lepton mixing like A(4) and S-4.We thank Martin Hirsch for useful comments. This work was supported by the Spanish grant
FPA2008-00319/FPA and PROMETEO/2009/091

Morisi, Stefano

Digital.CSIC

arXiv:0910.2542v1  [hep-ph]  14 Oct 2009IFIC 09-49Probing the Majorana nature of the neutrino withneutrinoless double beta decayStefano MorisiInstitut de F´ısica Corpuscular – C.S.I.C./Universitat de Vale`nciaEdificio Institutos de Paterna, Apt 22085, E–46071 Valencia, SpainE-mail: morisi@ific.uv.esAbstract. Neutrinoless double beta decay (0νββ) is the only experiment that could probethe Majorana nature of the neutrino. Here we study the theoretical implications of 0νββ formodels yielding tri-bimaximal lepton mixing like A4 and S4.1. IntroductionNeutrinoless double beta decay (0νββ) is the only experiment that can probe the MajoranaNature of the neutrino. 0νββ is a ∆L = 2 lepton number violating decay that can occur if theneutrino is a Majorana particle. For an introduction see for instance [1]. The generic effectiveMajorana mass term can be write asLd5 =λνijΛLiφLjφ, (1)where φ is the standard model higgs doublet and Λ is an effective scale. When φ takes a vev〈φ〉 = v, the operator in eq. (1) gives the Majorana mass term mνij = λνijv2/Λ. In generalmν is an arbitrary 3 by 3 symmetric complex matrix. It has been observed [2] that neutrinodata are in very good agreement with zero a rector angle sin θ13 = 0, maximal atmosphericangle sin2 θ23 = 1/2 and large but not maximal solar angle sin2 θ12 = 1/3. A Leptonic mixingmixing matrix with such a values is called tri-bimaximal (TBM). The most generic neutrinomass matrix yielding to TBM mixing is invariant under exchanged the second family with thethird family (µ ↔ τ symmetry) and the sum of the elements each row of mν is constant, namely∑j mν1j =∑j mν2j =∑j mν3j. We call a neutrino mass matrix of such type tri-bimaximal formmass matrix.We can extend the standard model by means of a flavor symmetry Gf that yields a tri-bimaximal form mass matrix. Examples are the group of even permutation of four objects A4[3, 4] or the group of all the permutation of four objects S4 [5, 6]. We observe that A4 is thesmallest non-Abelian group with a triplet representation allowing to arrange in one multipletthe three families. For now on we focus on A4 flavor symmetry. We assume three Higgs doubletstransforming as a triplet (φ1, φ2, φ3) ∼ 3 and the lepton doublets Le, Lµ, Lτ , transforming as atriplet of A4. The most generic A4 invariant dimension five operators are given asL5d =c1Λ(Liφ)1(Ljφ)1 +c2Λ(Liφ)1′(Ljφ)1′′ +c3Λ(Liφ)3(Ljφ)3 +10-3 10-2 10-1 10010-410-310-210-1100mΝ HeVLÈmeeÈHeVLMajoranaGERDA-IICUORED m232> 0D m232< 0GERDA-Ipresent 0Ν 2ΒboundsKATRINFigure 1. Allowed range of mee as afunction of the lightest neutrino mass forA4 based model.10-3 10-2 10-1 10010-410-310-210-1100mΝ HeVLÈmeeÈHeVLMajoranaGERDA-IICUORED m232> 0D m232< 0GERDA-Ipresent 0Ν 2ΒboundsKATRINFigure 2. Allowed range of mee as afunction of the lightest neutrino mass forS4 based model.+c4Λ(LiLj)1(φφ)1 +c5Λ(LiLj)1′(φφ)1′′ +c′5Λ(LiLj)1′′(φφ)1′ +c6Λ(LiLj)3(φφ)3. (2)The resulting neutrino mass matrix is of tri-bimaximal form if and only if c5 = c′5 = 0. Such acondition can naturally be explained by adding Higgs doublets or flavons carrying extra Abeliansymmetries, see for instance [4].Differently the most generic S4 invariant dimension five operatorsL5d =λ1Λ(Liφ)1(Ljφ)1 +λ2Λ(Liφ)2(Ljφ)2 +λ3Λ(Liφ)31(Ljφ)31 +λ′3Λ(Liφ)32(Ljφ)32 ++λ4Λ(LiLj)1(φφ)1 +λ5Λ(LiLj)2(φφ)2 +λ6Λ(LiLj)31(φφ)31 , (3)give neutrino mass matrix of tri-bimaximal form. In S4 we do not need to introduce extra scalarsor add symmetries in order to have tri-bimaximal in the neutrino sector. The resulting neutrinomass matrix is diagonalized by the tri-bimaximal matrix.Now we study the theoretical implications for 0νββ in models based on the two flavor groupsA4 and S4. The allowed ranges of mee as a function of the lightest neutrino are presented inFigures (1) and (2). The two bands correspond to the normal hierarchy and the inverse hierarchywith sin2 θ12 = 1/3, sin2 θ23 = 1/2, sin2 θ13 = 0 (tri-bimaximal). We call this bands the tri-bimaximal region for 0νββ.In order to simplify the discussion and to show the difference between A4 and S4 based models,we assume c1 = c2 = c3 = 0 and λ1 = λ2 = λ3 = λ′3 = 0. This could be the case if the dimensionfive operators arise from type-II seesaw mechanism only. We have already said that A4 givestri-bimaximal mixing if c5 = c′5 = 0.If λ5 = 0 A4 and S4 are phenomenologically equivalent since the operators proportional toc4 and c6 correspond to the operators proportional to λ4 and λ6 respectively.If λ5 6= 0, then A4 and S4 are not phenomenologically equivalent. For instance the S4 allowedrange for mee is the full tri-bimaximal region. When λ4 = 0 the allowed mee ranges for A4 andS4 are given respectively in Figures (1) and (2).In particular, in Figure (1) we see that A4 is compatible only with normal hierarchy. The A4case has a lower bound with mee > 3 · 10−3, see [7]. In Figure (2) we see that S4 is compatibleonly with inverse hierarchy.[8] and [9] have studied 0νββ implications assuming respectively type-I and inverse/linearseesaw mechanisms with A4 flavor symmetry. An effective neutrino mass model with S4 flavorsymmetry has been studied in [10]. In [11] a model with type-I seesaw with S4 flavor symmetryhas been studied.Note that for values of the lightest mass bigger than 10−1 eV, namely when neutrino arequasi degenerate, A4 and S4 allowed ranges are well separated. Therefore it could be in principlepossible to distinguish A4 from S4 in the quasi degenerate region.In case of inverse hierarchy there is a lower limit for mee. In [1] the dependence of such alimit as a function of the solar angle has been studied. However, in case of normal hierarchy ingeneral there is no lower limit. If mν1 = mee = 0 we have that the lower limit depends from thevalues of the solar and reactor angles,sin2 θ12 cos2 θ13eiα√∆m212+ sin2 θ13eiβ√∆m213= 0. (4)This equation gives a relation between the solar and the reactor angles and the allowed regionis represented in Figure (3) with the blue band. The small red region is the range allowed bythe data at 3σ and compatible with mν1 = mee = 0, namely eq. (4).0.45 0.50 0.55 0.60 0.650.180.200.220.240.260.280.30Sin Θ12SinΘ 13Figure 3. Relation between solar and reactor angles for normal hierarchy when mν1 = mee = 0.AcknowledgmentsWe thank Martin Hirsch for useful comments. This work was supported by the Spanish grantFPA2008-00319/FPA and PROMETEO/2009/091.References[1] M. Hirsch, arXiv:hep-ph/0609146.[2] P. F. Harrison, D. H. Perkins and W. G. Scott, Phys. Lett. B 530, 167 (2002) [arXiv:hep-ph/0202074].[3] K. S. Babu, E. Ma and J. W. F. Valle, Phys. Lett. B 552, 207 (2003) [arXiv:hep-ph/0206292];[4] G. Altarelli and F. Feruglio, Nucl. Phys. B 720, 64 (2005) [arXiv:hep-ph/0504165].[5] C. S. Lam, Phys. Rev. Lett. 101, 121602 (2008) [arXiv:0804.2622 [hep-ph]].[6] F. Bazzocchi and S. Morisi, arXiv:0811.0345 [hep-ph].[7] G. Altarelli, arXiv:0711.0161 [hep-ph].[8] M. Hirsch, S. Morisi and J. W. F. Valle, Phys. Rev. D 78, 093007 (2008) [arXiv:0804.1521 [hep-ph]].[9] M. Hirsch, S. Morisi and J. W. F. Valle, Phys. Lett. B 679, 454 (2009) [arXiv:0905.3056 [hep-ph]].[10] F. Bazzocchi, L. Merlo and S. Morisi, Nucl. Phys. B 816, 204 (2009) [arXiv:0901.2086 [hep-ph]].[11] F. Bazzocchi, L. Merlo and S. Morisi, Phys. Rev. D 80, 053003 (2009) [arXiv:0902.2849 [hep-ph]].

Probing the Majorana nature of the neutrino with neutrinoless double
  beta decay

Probing the Majorana nature of the neutrino with neutrinoless double beta decay

Abstract

Similar works

Full text

Available Versions

Crossref

Digital.CSIC