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Determining the Dirac CP Violation Phase and Neutrino Mass Hierarchy

Received: 22 July 2021     Accepted: 2 August 2021     Published: 12 August 2021
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Abstract

There is still a problem in neutrino physics related to the configuration of neutrino masses: Are neutrinos arranged by masses following the Standard Model as three generations of fundamental particles, Gen III>Gen II>Gen I, thus forming a structural-normal hierarchy, or deviate from that principle? The biggest obstacle that is still present is the sign of the absolute value of the difference of the square of neutrino masses. It was avoided by applying the theory of neutrino oscillation probability for each structure of the neutrino mass hierarchy. With such theoretical approach the equation of motion was derived for each structure in which Dirac CP violation phase appeared as an unknown quantity. This enables direct calculation of the explicit value for the Dirac CP violation phase. Two examples were analyzed: The first example is devoted to the normal mass ordering and the second one is devoted to the inverted mass ordering. The data used for theoretical calculations presented in this paper are obtained on the basis of the latest reassessed data by processing the results of experimental measurements. On the basis of the performed calculations, normal mass ordering is unconditionally excluded as a potential option regarding the neutrino mass ordering in nature. On the basis of the derived equation of neutrino motion, a possible numerical value of the Dirac CP violation phase and Jarlskog invariant is found.

Published in American Journal of Modern Physics (Volume 10, Issue 4)
DOI 10.11648/j.ajmp.20211004.11
Page(s) 60-70
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

Special Relativity, Leptons, Ordinary Neutrino, Neutrino Mass and Mixing, PMNS Matrix, Jarlskog Invariant, Dirac CP Phase

References
[1] K. Nakamura et al (2010), “Review of particle physics”, Journal of Physics G Nucl. Part. Phys. 37075021.
[2] M. Tanabashi et al., Particle data group, Review of particle physics, Phys. Rev. D 98, 030001 (2018).
[3] Fukuda Y. Hajokawa, T. Ichichara, E., Inove K., Ishicara K., IshinoK., et al. (Super-Kamiokande Collaboration) (1998) Evidence for oscillation of atmospheric neutrinos. Phys. Rev. Lett. 81 1562-1567.
[4] Abe, K. et al. T2K Collaboration (August 2013), Evidence of electron neutrino appearance in a muon neutrino beam, Physical Review D 88 (3) 032002 arxiv.1304.0841.
[5] Particle Data Group Collaboration, Review of particle physics, Phys. Rev. D 98 (2018) 3, 030001.
[6] M. A. Acero et al., New constraint on oscillation parameters from ve appearance and vµ disappearance in the NOvA experiment, Phys. Rev. D98, 032012 (2018).
[7] K. Abe et al. [T2K], Search for CP violation in neutrino and antineutrino oscillations by the T2K experiment with 2.2x1021 protons on target, Phys. Rev. Let. 121, 187802 (2018).
[8] C. Giganti, S. Levignac, M. Zito, Neutrino oscillations: the rise of the PMNS paradigm, arxiv: 1710.00715v2 [hep-ex] 16 Nov 2017.
[9] R. B. Patterson, Prospect measurement of the neutrino mass hierarchy, Annual Review of Nuclear and Particle Science, Volume 65, 2015/Patterson/pp. 177-192.
[10] P. F. de Salas, D. V. Forero, S. Gariazzo, P. Maetinez-Mirave, O. Mena, C. A. Termes, M. Tortola and J. W. F. Valle, 2020 global reassessment of the neutrino oscillations picture, JHEP 02 (2021) 071.
[11] P. F. de Salas, S. Garazzo, O. Mena, C. A. Ternes and M. Tortola, Neutrino mass ordering from oscillations and beyond: 2018 status and future prospects, Front. Astron. Space Sci. 09 October 2018.
[12] NuFIT 5.0 (2020).
[13] Planck 2018 results: VI. Cosmological parameters, arxiv: 1807.06209v2 [astro-ph.CO] 20 Sep 2019.
[14] S. R. Choudhury, S. Hannestad, Updated results on neutrino mass and mass hierarchy from cosmology with Planck 2018 likelihood, arxiv: 1907.12598v3, 15 Jul 2020.
[15] I. Esteban, M. C. Gonzale-Garcia, A. Hernandez-Cabezudo, M. Maltoni, T. Schwetz, Global analysis of three flavor neutrino oscillations: synergies and tensions in the determinations of θ23, δcp, and the mass ordering, J. High Energy Phys. 01 (2019) 106.
[16] I. Girardi, S. T. Petcov, A. V. Titov, Determining the Dirac CP violation phase in the neutrino mixing matrix from sum rules, Nucl. Phys. B 894 (2015) 733-768.
[17] H. Okada and M. Tanimoto, Spontaneous CP violation by modulus τ in A4 model of lepton flavours, JHEP 03 (2021) 010.
[18] J. Gehrlein and M. Spinrath, Highlight the correlation between the Dirac CP V phase and the atmospheric mixing angle to the allowed range for the neutrino mass scale, JHEP 02 (2021).
[19] G. Ghosh, Significance of Broken μ-τ Symmetry in Correlating δCP, θ13, Lightest Neutrino Mass, and Neutrinoless Double Beta Decay 0νββ., Advances in High Energy Physics, Volume 2021, Article ID 956 3917, 23 page.
[20] L. Graf, S. Jana, M. Lindner, W. Rodejohann, and Xun-jie Xu, Flavored neutrinoless double beta decay, Physical Review D 103, 055007 (2021).
[21] A. Formaggio, A. L. C. de Gouvea, R. G. H. Robertson, Direct measurements of neutrino mass, arxiv: 2102.00594v2 [nucl-exp] 11 Feb 2021.
[22] H. Georgi and C. Jarlskog, Phys. Lett. 86B, 297, (1979).
[23] C. Jarlskog, Phys. Rev. Lett. 55, 1039 (1985).
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  • APA Style

    Zoran Bozidar Todorovic. (2021). Determining the Dirac CP Violation Phase and Neutrino Mass Hierarchy. American Journal of Modern Physics, 10(4), 60-70. https://doi.org/10.11648/j.ajmp.20211004.11

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    ACS Style

    Zoran Bozidar Todorovic. Determining the Dirac CP Violation Phase and Neutrino Mass Hierarchy. Am. J. Mod. Phys. 2021, 10(4), 60-70. doi: 10.11648/j.ajmp.20211004.11

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    AMA Style

    Zoran Bozidar Todorovic. Determining the Dirac CP Violation Phase and Neutrino Mass Hierarchy. Am J Mod Phys. 2021;10(4):60-70. doi: 10.11648/j.ajmp.20211004.11

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  • @article{10.11648/j.ajmp.20211004.11,
      author = {Zoran Bozidar Todorovic},
      title = {Determining the Dirac CP Violation Phase and Neutrino Mass Hierarchy},
      journal = {American Journal of Modern Physics},
      volume = {10},
      number = {4},
      pages = {60-70},
      doi = {10.11648/j.ajmp.20211004.11},
      url = {https://doi.org/10.11648/j.ajmp.20211004.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20211004.11},
      abstract = {There is still a problem in neutrino physics related to the configuration of neutrino masses: Are neutrinos arranged by masses following the Standard Model as three generations of fundamental particles, Gen III>Gen II>Gen I, thus forming a structural-normal hierarchy, or deviate from that principle? The biggest obstacle that is still present is the sign of the absolute value of the difference of the square of neutrino masses. It was avoided by applying the theory of neutrino oscillation probability for each structure of the neutrino mass hierarchy. With such theoretical approach the equation of motion was derived for each structure in which Dirac CP violation phase appeared as an unknown quantity. This enables direct calculation of the explicit value for the Dirac CP violation phase. Two examples were analyzed: The first example is devoted to the normal mass ordering and the second one is devoted to the inverted mass ordering. The data used for theoretical calculations presented in this paper are obtained on the basis of the latest reassessed data by processing the results of experimental measurements. On the basis of the performed calculations, normal mass ordering is unconditionally excluded as a potential option regarding the neutrino mass ordering in nature. On the basis of the derived equation of neutrino motion, a possible numerical value of the Dirac CP violation phase and Jarlskog invariant is found.},
     year = {2021}
    }
    

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  • TY  - JOUR
    T1  - Determining the Dirac CP Violation Phase and Neutrino Mass Hierarchy
    AU  - Zoran Bozidar Todorovic
    Y1  - 2021/08/12
    PY  - 2021
    N1  - https://doi.org/10.11648/j.ajmp.20211004.11
    DO  - 10.11648/j.ajmp.20211004.11
    T2  - American Journal of Modern Physics
    JF  - American Journal of Modern Physics
    JO  - American Journal of Modern Physics
    SP  - 60
    EP  - 70
    PB  - Science Publishing Group
    SN  - 2326-8891
    UR  - https://doi.org/10.11648/j.ajmp.20211004.11
    AB  - There is still a problem in neutrino physics related to the configuration of neutrino masses: Are neutrinos arranged by masses following the Standard Model as three generations of fundamental particles, Gen III>Gen II>Gen I, thus forming a structural-normal hierarchy, or deviate from that principle? The biggest obstacle that is still present is the sign of the absolute value of the difference of the square of neutrino masses. It was avoided by applying the theory of neutrino oscillation probability for each structure of the neutrino mass hierarchy. With such theoretical approach the equation of motion was derived for each structure in which Dirac CP violation phase appeared as an unknown quantity. This enables direct calculation of the explicit value for the Dirac CP violation phase. Two examples were analyzed: The first example is devoted to the normal mass ordering and the second one is devoted to the inverted mass ordering. The data used for theoretical calculations presented in this paper are obtained on the basis of the latest reassessed data by processing the results of experimental measurements. On the basis of the performed calculations, normal mass ordering is unconditionally excluded as a potential option regarding the neutrino mass ordering in nature. On the basis of the derived equation of neutrino motion, a possible numerical value of the Dirac CP violation phase and Jarlskog invariant is found.
    VL  - 10
    IS  - 4
    ER  - 

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Author Information
  • Faculty of Electrical Engineering, Department of Physics, University of Belgrade, Belgrade, Serbia

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