Implications of the DLMA Solution of <i>θ</i><sub>12</sub> for IceCube Data Using Different Astrophysical Sources
In this paper, we study the implications of the Dark Large Mixing Angle (DLMA) solutions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>12</mn></msub></se...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-08-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/9/9/380 |
| _version_ | 1797576506076037120 |
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| author | Monojit Ghosh Srubabati Goswami Supriya Pan Bartol Pavlović |
| author_facet | Monojit Ghosh Srubabati Goswami Supriya Pan Bartol Pavlović |
| author_sort | Monojit Ghosh |
| collection | DOAJ |
| description | In this paper, we study the implications of the Dark Large Mixing Angle (DLMA) solutions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>12</mn></msub></semantics></math></inline-formula> in the context of the IceCube data. We study the consequences in the measurement of the neutrino oscillation parameters, namely the octant of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>23</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>δ</mi><mi>CP</mi></msub></semantics></math></inline-formula> in light of both Large Mixing Angle (LMA) and DLMA solutions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>12</mn></msub></semantics></math></inline-formula>. We find that it will be impossible for IceCube to determine the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>δ</mi><mi>CP</mi></msub></semantics></math></inline-formula> and the true nature of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>12</mn></msub></semantics></math></inline-formula>, i.e., LMA or DLMA, at the same time. This is because of the existence of an intrinsic degeneracy at the Hamiltonian level between these parameters. Apart from that, we also identify a new degeneracy between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>23</mn></msub></semantics></math></inline-formula> and two solutions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>12</mn></msub></semantics></math></inline-formula> for a fixed value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>δ</mi><mi>CP</mi></msub></semantics></math></inline-formula>. We perform a chi-square fit using three different astrophysical sources, i.e., <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula> source, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> source, and <i>n</i> source, to find that both <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula> source and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> source are allowed within <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mi>σ</mi></mrow></semantics></math></inline-formula>, whereas the <i>n</i> source is excluded at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>σ</mi></mrow></semantics></math></inline-formula>. It is difficult to make any conclusion regarding the measurement of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>23</mn></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>δ</mi><mi>CP</mi></msub></semantics></math></inline-formula> for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula> source. However, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> (<i>n</i>) source prefers the higher (lower) octant of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>23</mn></msub></semantics></math></inline-formula> for both LMA and DLMA solution of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>12</mn></msub></semantics></math></inline-formula>. The best-fit value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>δ</mi><mi>CP</mi></msub></semantics></math></inline-formula> is around <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>180</mn><mo>∘</mo></msup></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mn>0</mn><mo>∘</mo></msup><mo>/</mo><msup><mn>360</mn><mo>∘</mo></msup></mrow></semantics></math></inline-formula>) for the LMA (DLMA) solution of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>12</mn></msub></semantics></math></inline-formula>, whereas for the DLMA (LMA) solution of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>12</mn></msub></semantics></math></inline-formula>, the best-fit value is around <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mn>0</mn><mo>∘</mo></msup><mo>/</mo><msup><mn>360</mn><mo>∘</mo></msup></mrow></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>180</mn><mo>∘</mo></msup></semantics></math></inline-formula>) for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> (<i>n</i>) source. If we assume the current best-fit values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>23</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>δ</mi><mi>CP</mi></msub></semantics></math></inline-formula> to be true, then the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> sources prefer the LMA solution of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>12</mn></msub></semantics></math></inline-formula>, whereas the <i>n</i> source prefers the DLMA solution of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>12</mn></msub></semantics></math></inline-formula>. |
| first_indexed | 2024-03-10T21:54:00Z |
| format | Article |
| id | doaj.art-ce64d9f8d4514e8abf5d2a5f95c77bbb |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-10T21:54:00Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-ce64d9f8d4514e8abf5d2a5f95c77bbb2023-11-19T13:17:11ZengMDPI AGUniverse2218-19972023-08-019938010.3390/universe9090380Implications of the DLMA Solution of <i>θ</i><sub>12</sub> for IceCube Data Using Different Astrophysical SourcesMonojit Ghosh0Srubabati Goswami1Supriya Pan2Bartol Pavlović3Center of Excellence for Advanced Materials and Sensing Devices, Ruder Bošković Institute, 10000 Zagreb, CroatiaPhysical Research Laboratory, Ahmedabad 380009, Gujarat, IndiaPhysical Research Laboratory, Ahmedabad 380009, Gujarat, IndiaDepartment of Physics, Faculty of Science, University of Zagreb, 10000 Zagreb, CroatiaIn this paper, we study the implications of the Dark Large Mixing Angle (DLMA) solutions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>12</mn></msub></semantics></math></inline-formula> in the context of the IceCube data. We study the consequences in the measurement of the neutrino oscillation parameters, namely the octant of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>23</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>δ</mi><mi>CP</mi></msub></semantics></math></inline-formula> in light of both Large Mixing Angle (LMA) and DLMA solutions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>12</mn></msub></semantics></math></inline-formula>. We find that it will be impossible for IceCube to determine the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>δ</mi><mi>CP</mi></msub></semantics></math></inline-formula> and the true nature of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>12</mn></msub></semantics></math></inline-formula>, i.e., LMA or DLMA, at the same time. This is because of the existence of an intrinsic degeneracy at the Hamiltonian level between these parameters. Apart from that, we also identify a new degeneracy between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>23</mn></msub></semantics></math></inline-formula> and two solutions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>12</mn></msub></semantics></math></inline-formula> for a fixed value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>δ</mi><mi>CP</mi></msub></semantics></math></inline-formula>. We perform a chi-square fit using three different astrophysical sources, i.e., <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula> source, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> source, and <i>n</i> source, to find that both <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula> source and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> source are allowed within <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mi>σ</mi></mrow></semantics></math></inline-formula>, whereas the <i>n</i> source is excluded at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>σ</mi></mrow></semantics></math></inline-formula>. It is difficult to make any conclusion regarding the measurement of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>23</mn></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>δ</mi><mi>CP</mi></msub></semantics></math></inline-formula> for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula> source. However, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> (<i>n</i>) source prefers the higher (lower) octant of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>23</mn></msub></semantics></math></inline-formula> for both LMA and DLMA solution of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>12</mn></msub></semantics></math></inline-formula>. The best-fit value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>δ</mi><mi>CP</mi></msub></semantics></math></inline-formula> is around <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>180</mn><mo>∘</mo></msup></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mn>0</mn><mo>∘</mo></msup><mo>/</mo><msup><mn>360</mn><mo>∘</mo></msup></mrow></semantics></math></inline-formula>) for the LMA (DLMA) solution of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>12</mn></msub></semantics></math></inline-formula>, whereas for the DLMA (LMA) solution of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>12</mn></msub></semantics></math></inline-formula>, the best-fit value is around <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mn>0</mn><mo>∘</mo></msup><mo>/</mo><msup><mn>360</mn><mo>∘</mo></msup></mrow></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>180</mn><mo>∘</mo></msup></semantics></math></inline-formula>) for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> (<i>n</i>) source. If we assume the current best-fit values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>23</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>δ</mi><mi>CP</mi></msub></semantics></math></inline-formula> to be true, then the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> sources prefer the LMA solution of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>12</mn></msub></semantics></math></inline-formula>, whereas the <i>n</i> source prefers the DLMA solution of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>θ</mi><mn>12</mn></msub></semantics></math></inline-formula>.https://www.mdpi.com/2218-1997/9/9/380neutrino oscillationastrophysical neutrinosIceCube experiment |
| spellingShingle | Monojit Ghosh Srubabati Goswami Supriya Pan Bartol Pavlović Implications of the DLMA Solution of <i>θ</i><sub>12</sub> for IceCube Data Using Different Astrophysical Sources Universe neutrino oscillation astrophysical neutrinos IceCube experiment |
| title | Implications of the DLMA Solution of <i>θ</i><sub>12</sub> for IceCube Data Using Different Astrophysical Sources |
| title_full | Implications of the DLMA Solution of <i>θ</i><sub>12</sub> for IceCube Data Using Different Astrophysical Sources |
| title_fullStr | Implications of the DLMA Solution of <i>θ</i><sub>12</sub> for IceCube Data Using Different Astrophysical Sources |
| title_full_unstemmed | Implications of the DLMA Solution of <i>θ</i><sub>12</sub> for IceCube Data Using Different Astrophysical Sources |
| title_short | Implications of the DLMA Solution of <i>θ</i><sub>12</sub> for IceCube Data Using Different Astrophysical Sources |
| title_sort | implications of the dlma solution of i θ i sub 12 sub for icecube data using different astrophysical sources |
| topic | neutrino oscillation astrophysical neutrinos IceCube experiment |
| url | https://www.mdpi.com/2218-1997/9/9/380 |
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