Abstract
We perform a systematic and complete analysis of texture zeros in the lepton mass matrices and identify all viable and maximally restrictive cases of pairs (M ℓ , M D ) and (M ℓ , M L ), where M ℓ , M D and M L are the charged-lepton, Dirac neutrino and Majorana neutrino mass matrices, respectively. To this end, we perform a thorough analysis of textures which are equivalent through weak-basis permutations. Furthermore, we introduce numerical measures for the predictivity of textures and apply them to the viable and maximally restrictive texture zero models. It turns out that for Dirac neutrinos these models can at most predict the smallest neutrino mass and the CKM-type phase of the mixing matrix. For Majorana neutrinos most models can, in addition, predict the effective neutrino mass for neutrinoless double beta decay.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D.V. Forero, M. Tortola and J.W.F. Valle, Global status of neutrino oscillation parameters after Neutrino-2012, Phys. Rev. D 86 (2012) 073012 [arXiv:1205.4018] [INSPIRE].
M.C. Gonzalez-Garcia, M. Maltoni, J. Salvado and T. Schwetz, Global fit to three neutrino mixing: critical look at present precision, JHEP 12 (2012) 123 [arXiv:1209.3023] [INSPIRE].
D.V. Forero, M. Tortola and J.W.F. Valle, Neutrino oscillations refitted, arXiv:1405.7540 [INSPIRE].
G.L. Fogli et al., Global analysis of neutrino masses, mixings and phases: entering the era of leptonic CP-violation searches, Phys. Rev. D 86 (2012) 013012 [arXiv:1205.5254] [INSPIRE].
C.I. Low, Generating extremal neutrino mixing angles with Higgs family symmetries, Phys. Rev. D 70 (2004) 073013 [hep-ph/0404017] [INSPIRE].
C.I. Low, Abelian family symmetries and the simplest models that give θ 13 = 0 in the neutrino mixing matrix, Phys. Rev. D 71 (2005) 073007 [hep-ph/0501251] [INSPIRE].
H. Serôdio, Yukawa sector of Multi Higgs doublet models in the presence of Abelian symmetries, Phys. Rev. D 88 (2013) 056015 [arXiv:1307.4773] [INSPIRE].
W. Grimus, A.S. Joshipura, L. Lavoura and M. Tanimoto, Symmetry realization of texture zeros, Eur. Phys. J. C 36 (2004) 227 [hep-ph/0405016] [INSPIRE].
R.G. Felipe and H. Serôdio, Abelian realization of phenomenological two-zero neutrino textures, arXiv:1405.4263 [INSPIRE].
P.H. Frampton, S.L. Glashow and D. Marfatia, Zeroes of the neutrino mass matrix, Phys. Lett. B 536 (2002) 79 [hep-ph/0201008] [INSPIRE].
Z.-z. Xing, Texture zeros and Majorana phases of the neutrino mass matrix, Phys. Lett. B 530 (2002) 159 [hep-ph/0201151] [INSPIRE].
Z.-z. Xing, A full determination of the neutrino mass spectrum from two zero textures of the neutrino mass matrix, Phys. Lett. B 539 (2002) 85 [hep-ph/0205032] [INSPIRE].
A. Kageyama, S. Kaneko, N. Shimoyama and M. Tanimoto, Seesaw realization of the texture zeros in the neutrino mass matrix, Phys. Lett. B 538 (2002) 96 [hep-ph/0204291] [INSPIRE].
W. Grimus and L. Lavoura, On a model with two zeros in the neutrino mass matrix, J. Phys. G 31 (2005) 693 [hep-ph/0412283] [INSPIRE].
S. Dev, S. Kumar, S. Verma and S. Gupta, Phenomenological implications of a class of neutrino mass matrices, Nucl. Phys. B 784 (2007) 103 [hep-ph/0611313] [INSPIRE].
S. Dev, S. Kumar, S. Verma and S. Gupta, Phenomenology of two-texture zero neutrino mass matrices, Phys. Rev. D 76 (2007) 013002 [hep-ph/0612102] [INSPIRE].
W. Grimus and P.O. Ludl, Maximal atmospheric neutrino mixing from texture zeros and quasi-degenerate neutrino masses, Phys. Lett. B 700 (2011) 356 [arXiv:1104.4340] [INSPIRE].
P.O. Ludl, S. Morisi and E. Peinado, The reactor mixing angle and CP-violation with two texture zeros in the light of T2K, Nucl. Phys. B 857 (2012) 411 [arXiv:1109.3393] [INSPIRE].
S. Kumar, Implications of a class of neutrino mass matrices with texture zeros for non-zero θ 13, Phys. Rev. D 84 (2011) 077301 [arXiv:1108.2137] [INSPIRE].
H. Fritzsch, Z.-z. Xing and S. Zhou, Two-zero textures of the Majorana neutrino mass matrix and current experimental tests, JHEP 09 (2011) 083 [arXiv:1108.4534] [INSPIRE].
D. Meloni and G. Blankenburg, Fine-tuning and naturalness issues in the two-zero neutrino mass textures, Nucl. Phys. B 867 (2013) 749 [arXiv:1204.2706] [INSPIRE].
B. Adhikary, M. Chakraborty and A. Ghosal, Scaling ansatz, four zero Yukawa textures and large θ 13, Phys. Rev. D 86 (2012) 013015 [arXiv:1205.1355] [INSPIRE].
J. Liao, D. Marfatia and K. Whisnant, Texture and cofactor zeros of the neutrino mass matrix, arXiv:1311.2639 [INSPIRE].
B. Adhikary, A. Ghosal and P. Roy, Maximal zero textures of the inverse seesaw with broken μτ symmetry, arXiv:1311.6746 [INSPIRE].
D. Meloni, A. Meroni and E. Peinado, Two-zero Majorana textures in the light of the Planck results, Phys. Rev. D 89 (2014) 053009 [arXiv:1401.3207] [INSPIRE].
S. Dev, R.R. Gautam, L. Singh and M. Gupta, Near maximal atmospheric neutrino mixing in neutrino mass models with two texture zeros, arXiv:1405.0566 [INSPIRE].
C. Hagedorn and W. Rodejohann, Minimal mass matrices for Dirac neutrinos, JHEP 07 (2005) 034 [hep-ph/0503143] [INSPIRE].
H. Fritzsch, Weak interaction mixing in the six-quark theory, Phys. Lett. B 73 (1978) 317 [INSPIRE].
H. Fritzsch, Quark masses and flavor mixing, Nucl. Phys. B 155 (1979) 189 [INSPIRE].
H. Nishiura, K. Matsuda and T. Fukuyama, Lepton and quark mass matrices, Phys. Rev. D 60 (1999) 013006 [hep-ph/9902385] [INSPIRE].
Z.-z. Xing, Hierarchical neutrino masses and large mixing angles from the Fritzsch texture of lepton mass matrices, Phys. Lett. B 550 (2002) 178 [hep-ph/0210276] [INSPIRE].
M. Bando, S. Kaneko, M. Obara and M. Tanimoto, Can symmetric texture reproduce neutrino bilarge mixing?, Phys. Lett. B 580 (2004) 229 [hep-ph/0309310] [INSPIRE].
Z.-z. Xing and S. Zhou, Isomeric lepton mass matrices and bilarge neutrino mixing, Phys. Lett. B 593 (2004) 156 [hep-ph/0403261] [INSPIRE].
S. Zhou and Z.-z. Xing, A systematic study of neutrino mixing and CP-violation from lepton mass matrices with six texture zeros, Eur. Phys. J. C 38 (2005) 495 [hep-ph/0404188] [INSPIRE].
K. Matsuda and H. Nishiura, Can four-zero-texture mass matrix model reproduce the quark and lepton mixing angles and CP-violating phases?, Phys. Rev. D 74 (2006) 033014 [hep-ph/0606142] [INSPIRE].
M. Randhawa, G. Ahuja and M. Gupta, Implications of Fritzsch-like lepton mass matrices, Phys. Lett. B 643 (2006) 175 [hep-ph/0607074] [INSPIRE].
T. Fukuyama, K. Matsuda and H. Nishiura, Zero texture model and SO(10) GUT, Int. J. Mod. Phys. A 22 (2007) 5325 [hep-ph/0702284] [INSPIRE].
G. Ahuja, S. Kumar, M. Randhawa, M. Gupta and S. Dev, Texture 4 zero Fritzsch-like lepton mass matrices, Phys. Rev. D 76 (2007) 013006 [hep-ph/0703005] [INSPIRE].
G. Ahuja, M. Gupta, M. Randhawa and R. Verma, Texture specific mass matrices with Dirac neutrinos and their implications, Phys. Rev. D 79 (2009) 093006 [arXiv:0904.4534] [INSPIRE].
N. Mahajan, M. Randhawa, M. Gupta and P.S. Gill, Investigating texture six zero lepton mass matrices, PTEP 2013 (2013) 083B02 [arXiv:1010.5640] [INSPIRE].
X.-w. Liu and S. Zhou, Texture zeros for Dirac neutrinos and current experimental tests, Int. J. Mod. Phys. A 28 (2013) 1350040 [arXiv:1211.0472] [INSPIRE].
H. Fritzsch and S. Zhou, Neutrino mixing angles from texture zeros of the lepton mass matrices, Phys. Lett. B 718 (2013) 1457 [arXiv:1212.0411] [INSPIRE].
P. Fakay, S. Sharma, G. Ahuja and M. Gupta, Leptonic mixing angle θ 13 and ruling out of minimal texture for Dirac neutrinos, PTEP 2014 (2014) 023B03 [arXiv:1401.8121] [INSPIRE].
S. Sharma, P. Fakay, G. Ahuja and M. Gupta, Majorana neutrinos and non minimal lepton mass textures, arXiv:1402.1598 [INSPIRE].
G.C. Branco, D. Emmanuel-Costa, R. Gonzalez Felipe and H. Serodio, Weak basis transformations and texture zeros in the leptonic sector, Phys. Lett. B 670 (2009) 340 [arXiv:0711.1613] [INSPIRE].
W. Wang, Parallel lepton mass matrices with texture/cofactor zeros, arXiv:1402.6808 [INSPIRE].
M. Gupta and G. Ahuja, Flavor mixings and textures of the fermion mass matrices, Int. Jour. Mod. Phys. A, 27 (2012) 1230033 [arXiv:1302.4823] [INSPIRE].
G.C. Branco, L. Lavoura and J.P. Silva, CP Violation, Int. Ser. Monogr. Phys. 103 (1999) 1 [INSPIRE].
G.C. Branco, D. Emmanuel-Costa and R. Gonzalez Felipe, Texture zeros and weak basis transformations, Phys. Lett. B 477 (2000) 147 [hep-ph/9911418] [INSPIRE].
P.O. Ludl, Current status of constraints on the elements of the neutrino mass matrix, Acta Phys. Polon. B 44 (2013) 2339 [arXiv:1310.4455] [INSPIRE].
Particle Data Group collaboration, J. Beringer et al., Review of particle physics, Phys. Rev. D 86 (2012) 010001 [INSPIRE].
J.A. Nelder and R. Mead, A simplex method for function minimization, Comput. J. 7 (1965) 308.
B.W. Kernighan and D.M. Ritchie, The C programming language, Prentice Hall, Englewood Cliffs, U.S.A. (1988).
MATLAB ® Release 2011b, The MathWorks, Inc., Natick, Massachusetts, U.S.A. .
P.O. Ludl, Implications of finite family symmetry groups on the leptonic and scalar sector, dissertation, University of Vienna, Vienna, Austria (2012).
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1406.3546
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Ludl, P., Grimus, W. A complete survey of texture zeros in the lepton mass matrices. J. High Energ. Phys. 2014, 90 (2014). https://doi.org/10.1007/JHEP07(2014)090
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2014)090