Consistency of perturbed tribimaximal, bimaximal and democratic mixing with neutrino mixing data

Garg, Sumit K.

doi:10.1016/j.nuclphysb.2018.04.022

Consistency of perturbed tribimaximal, bimaximal and democratic mixing with neutrino mixing data

Sumit K. Garg (Department of Physics, CMR University, Bengaluru 562149, India)

We scrutinize corrections to tribimaximal (TBM), bimaximal (BM) and democratic (DC) mixing matrices for explaining recent global fit neutrino mixing data. These corrections are parameterized in terms of small orthogonal rotations (R) with corresponding modified PMNS matrices of the forms $(R_{i j}^{l} \cdot U, U \cdot R_{i j}^{r}, U \cdot R_{i j}^{r} \cdot R_{k l}^{r}, R_{i j}^{l} \cdot R_{k l}^{l} \cdot U)$ where $R_{i j}^{l, r}$ is rotation in ij sector and U is any one of these special matrices. We showed that for perturbative schemes dictated by single rotation, only $(R_{12}^{l} \cdot U_{B M}, R_{13}^{l} \cdot U_{B M}, U_{T B M} \cdot R_{13}^{r})$ can fit the mixing data at 3σ level. However for $R_{i j}^{l} \cdot R_{k l}^{l} \cdot U$ type rotations, only $(R_{23}^{l} \cdot R_{13}^{l} \cdot U_{D C})$ is successful to fit all neutrino mixing angles within 1σ range. For $U \cdot R_{i j}^{r} \cdot R_{k l}^{r}$ perturbative scheme, only $(U_{B M} \cdot R_{12}^{r} \cdot R_{13}^{r}, U_{D C} \cdot R_{12}^{r} \cdot R_{23}^{r}, U_{T B M} \cdot R_{12}^{r} \cdot R_{13}^{r})$ are consistent at 1σ level. The remaining double rotation cases are either excluded at 3σ level or successful in producing mixing angles only at $2 σ - 3 σ$ level. We also updated our previous analysis on PMNS matrices of the form $(R_{i j} \cdot U \cdot R_{k l})$ with recent mixing data. We showed that the results modifies substantially with fitting accuracy level decreases for all of the permitted cases except $(R_{12} \cdot U_{B M} \cdot R_{13}, R_{23} \cdot U_{T B M} \cdot R_{13} and R_{13} \cdot U_{T B M} \cdot R_{13})$ in this rotation scheme.

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      "value": "We scrutinize corrections to tribimaximal (TBM), bimaximal (BM) and democratic (DC) mixing matrices for explaining recent global fit neutrino mixing data. These corrections are parameterized in terms of small orthogonal rotations (R) with corresponding modified PMNS matrices of the forms <math><mo>(</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow><mrow><mi>l</mi></mrow></msubsup><mo>\u22c5</mo><mi>U</mi><mo>,</mo><mspace width=\"0.25em\"></mspace><mi>U</mi><mo>\u22c5</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow><mrow><mi>r</mi></mrow></msubsup><mo>,</mo><mspace width=\"0.25em\"></mspace><mi>U</mi><mo>\u22c5</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow><mrow><mi>r</mi></mrow></msubsup><mo>\u22c5</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>k</mi><mi>l</mi></mrow><mrow><mi>r</mi></mrow></msubsup><mo>,</mo><mspace width=\"0.25em\"></mspace><msubsup><mrow><mi>R</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow><mrow><mi>l</mi></mrow></msubsup><mo>\u22c5</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>k</mi><mi>l</mi></mrow><mrow><mi>l</mi></mrow></msubsup><mo>\u22c5</mo><mi>U</mi><mo>)</mo></math> where <math><msubsup><mrow><mi>R</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow><mrow><mi>l</mi><mo>,</mo><mi>r</mi></mrow></msubsup></math> is rotation in ij sector and U is any one of these special matrices. We showed that for perturbative schemes dictated by single rotation, only <math><mo>(</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mn>12</mn></mrow><mrow><mi>l</mi></mrow></msubsup><mo>\u22c5</mo><msub><mrow><mi>U</mi></mrow><mrow><mi>B</mi><mi>M</mi></mrow></msub><mo>,</mo><mspace width=\"0.25em\"></mspace><msubsup><mrow><mi>R</mi></mrow><mrow><mn>13</mn></mrow><mrow><mi>l</mi></mrow></msubsup><mo>\u22c5</mo><msub><mrow><mi>U</mi></mrow><mrow><mi>B</mi><mi>M</mi></mrow></msub><mo>,</mo><mspace width=\"0.25em\"></mspace><msub><mrow><mi>U</mi></mrow><mrow><mi>T</mi><mi>B</mi><mi>M</mi></mrow></msub><mo>\u22c5</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mn>13</mn></mrow><mrow><mi>r</mi></mrow></msubsup><mo>)</mo></math> can fit the mixing data at 3\u03c3 level. However for <math><msubsup><mrow><mi>R</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow><mrow><mi>l</mi></mrow></msubsup><mo>\u22c5</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>k</mi><mi>l</mi></mrow><mrow><mi>l</mi></mrow></msubsup><mo>\u22c5</mo><mi>U</mi></math> type rotations, only <math><mo>(</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mn>23</mn></mrow><mrow><mi>l</mi></mrow></msubsup><mo>\u22c5</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mn>13</mn></mrow><mrow><mi>l</mi></mrow></msubsup><mo>\u22c5</mo><msub><mrow><mi>U</mi></mrow><mrow><mi>D</mi><mi>C</mi></mrow></msub><mo>)</mo></math> is successful to fit all neutrino mixing angles within 1\u03c3 range. For <math><mi>U</mi><mo>\u22c5</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow><mrow><mi>r</mi></mrow></msubsup><mo>\u22c5</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>k</mi><mi>l</mi></mrow><mrow><mi>r</mi></mrow></msubsup></math> perturbative scheme, only <math><mo>(</mo><msub><mrow><mi>U</mi></mrow><mrow><mi>B</mi><mi>M</mi></mrow></msub><mo>\u22c5</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mn>12</mn></mrow><mrow><mi>r</mi></mrow></msubsup><mo>\u22c5</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mn>13</mn></mrow><mrow><mi>r</mi></mrow></msubsup><mo>,</mo><mspace width=\"0.25em\"></mspace><msub><mrow><mi>U</mi></mrow><mrow><mi>D</mi><mi>C</mi></mrow></msub><mo>\u22c5</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mn>12</mn></mrow><mrow><mi>r</mi></mrow></msubsup><mo>\u22c5</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mn>23</mn></mrow><mrow><mi>r</mi></mrow></msubsup><mo>,</mo><mspace width=\"0.25em\"></mspace><msub><mrow><mi>U</mi></mrow><mrow><mi>T</mi><mi>B</mi><mi>M</mi></mrow></msub><mo>\u22c5</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mn>12</mn></mrow><mrow><mi>r</mi></mrow></msubsup><mo>\u22c5</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mn>13</mn></mrow><mrow><mi>r</mi></mrow></msubsup><mo>)</mo></math> are consistent at 1\u03c3 level. The remaining double rotation cases are either excluded at 3\u03c3 level or successful in producing mixing angles only at <math><mn>2</mn><mi>\u03c3</mi><mo>\u2212</mo><mn>3</mn><mi>\u03c3</mi></math> level. We also updated our previous analysis on PMNS matrices of the form <math><mo>(</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>\u22c5</mo><mi>U</mi><mo>\u22c5</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>k</mi><mi>l</mi></mrow></msub><mo>)</mo></math> with recent mixing data. We showed that the results modifies substantially with fitting accuracy level decreases for all of the permitted cases except <math><mo>(</mo><msub><mrow><mi>R</mi></mrow><mrow><mn>12</mn></mrow></msub><mo>\u22c5</mo><msub><mrow><mi>U</mi></mrow><mrow><mi>B</mi><mi>M</mi></mrow></msub><mo>\u22c5</mo><msub><mrow><mi>R</mi></mrow><mrow><mn>13</mn></mrow></msub><mo>,</mo><mspace width=\"0.25em\"></mspace><msub><mrow><mi>R</mi></mrow><mrow><mn>23</mn></mrow></msub><mo>\u22c5</mo><msub><mrow><mi>U</mi></mrow><mrow><mi>T</mi><mi>B</mi><mi>M</mi></mrow></msub><mo>\u22c5</mo><msub><mrow><mi>R</mi></mrow><mrow><mn>13</mn></mrow></msub><mtext> and </mtext><msub><mrow><mi>R</mi></mrow><mrow><mn>13</mn></mrow></msub><mo>\u22c5</mo><msub><mrow><mi>U</mi></mrow><mrow><mi>T</mi><mi>B</mi><mi>M</mi></mrow></msub><mo>\u22c5</mo><msub><mrow><mi>R</mi></mrow><mrow><mn>13</mn></mrow></msub><mo>)</mo></math> in this rotation scheme."
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Published on:: 25 May 2018
Publisher:: Elsevier
Published in:: Nuclear Physics B , Volume 931 C (2018)

Pages 469-505
DOI:: https://doi.org/10.1016/j.nuclphysb.2018.04.022
Copyrights:: The Author(s)
Licence:: CC-BY-3.0

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