Investigating Lorentz invariance violation effects on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math> violation and mass hierarchy sensitivity at DUNE

One of the current goals of neutrino experiments is to precisely determine standard unknown oscillation parameters such as the leptonic <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>C</a:mi><a:mi>P</a:mi></a:math> phase and mass hierarchy. Lorentz invariance violation represents a potential physics factor that could influence the experiment’s ability to achieve these precise determinations. This study investigates the influence of Lorentz invariance violation on oscillation dynamics, particularly through nonisotropic <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>C</c:mi><c:mi>P</c:mi><c:mi>T</c:mi></c:math>-violating (<e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msubsup><e:mi>a</e:mi><e:mrow><e:mi>e</e:mi><e:mi>μ</e:mi></e:mrow><e:mi>X</e:mi></e:msubsup></e:math>, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msubsup><g:mi>a</g:mi><g:mrow><g:mi>e</g:mi><g:mi>τ</g:mi></g:mrow><g:mi>X</g:mi></g:msubsup></g:math>, <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msubsup><i:mi>a</i:mi><i:mrow><i:mi>μ</i:mi><i:mi>τ</i:mi></i:mrow><i:mi>X</i:mi></i:msubsup></i:math>) and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>C</k:mi><k:mi>P</k:mi><k:mi>T</k:mi></k:math>-conserving (<m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msubsup><m:mi>c</m:mi><m:mrow><m:mi>e</m:mi><m:mi>μ</m:mi></m:mrow><m:mrow><m:mi>X</m:mi><m:mi>Y</m:mi></m:mrow></m:msubsup></m:math>, <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msubsup><o:mi>c</o:mi><o:mrow><o:mi>e</o:mi><o:mi>τ</o:mi></o:mrow><o:mrow><o:mi>X</o:mi><o:mi>Y</o:mi></o:mrow></o:msubsup></o:math>, <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msubsup><q:mi>c</q:mi><q:mrow><q:mi>μ</q:mi><q:mi>τ</q:mi></q:mrow><q:mrow><q:mi>X</q:mi><q:mi>Y</q:mi></q:mrow></q:msubsup></q:math>) parameters within the Deep Underground Neutrino Experiment. We analyze the impact of these parameters on the mass hierarchy (MH) and Dirac <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>C</s:mi><s:mi>P</s:mi></s:math> phase sensitivity measurements. Our findings indicate that while MH sensitivity remains relatively unaffected, only the presence of <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msubsup><u:mi>c</u:mi><u:mrow><u:mi>μ</u:mi><u:mi>τ</u:mi></u:mrow><u:mrow><u:mi>X</u:mi><u:mi>Y</u:mi></u:mrow></u:msubsup></u:math> significantly deteriorates MH sensitivity, albeit remaining above the <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mn>5</w:mn><w:mi>σ</w:mi></w:math> threshold. Additionally, we observe a substantial compromise in <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>C</y:mi><y:mi>P</y:mi></y:math> sensitivity due to the <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:msubsup><ab:mi>c</ab:mi><ab:mrow><ab:mi>e</ab:mi><ab:mi>μ</ab:mi></ab:mrow><ab:mrow><ab:mi>X</ab:mi><ab:mi>Y</ab:mi></ab:mrow></ab:msubsup></ab:math> and <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msubsup><cb:mi>c</cb:mi><cb:mrow><cb:mi>e</cb:mi><cb:mi>τ</cb:mi></cb:mrow><cb:mrow><cb:mi>X</cb:mi><cb:mi>Y</cb:mi></cb:mrow></cb:msubsup></cb:math> parameters. Published by the American Physical Society 2024