Precision of the leptonic mixing angle <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>θ</mml:mi><mml:mn>23</mml:mn></mml:msub></mml:math> and its implications for the flavor models

Among three leptonic mixing angles, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>θ</a:mi><a:mn>23</a:mn></a:msub></a:math>, which characterizes the fractional contribution of two flavor eigenstates <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>ν</c:mi><c:mi>μ</c:mi></c:msub></c:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>ν</e:mi><e:mi>τ</e:mi></e:msub></e:math> to the third mass eigenstate <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>ν</g:mi><g:mn>3</g:mn></g:msub></g:math>, is known to be the largest but least precisely measured. The work investigates the possible reach of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>θ</i:mi><i:mn>23</i:mn></i:msub></i:math> precision with two forthcoming gigantic accelerator-based long-baseline neutrino experiments, namely, Hyper-Kamiokande (T2HK) and the Deep Underground Neutrino Experiment (DUNE), as well as a possible joint analyses of future neutrino facilities. Our simulation yields that each experiment will definitely establish the octant of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>θ</k:mi><k:mn>23</k:mn></k:msub></k:math> for all values within a <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:mn>1</m:mn><m:mi>σ</m:mi></m:mrow></m:math> parameter interval, while considering the current limitation. However, if the actual value is <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mn>0.48</o:mn><o:mo>≤</o:mo><o:msup><o:mi>sin</o:mi><o:mn>2</o:mn></o:msup><o:msub><o:mi>θ</o:mi><o:mn>23</o:mn></o:msub><o:mo>≤</o:mo><o:mn>0.54</o:mn></o:math>, it becomes challenging for these two experiments to reject the maximal (<q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>θ</q:mi><q:mn>23</q:mn></q:msub><q:mo>=</q:mo><q:mi>π</q:mi><q:mo>/</q:mo><q:mn>4</q:mn></q:math>) hypothesis and conclude its octant. This octant-blind region can be further explored with the proposed facilities European Spallation Source Neutrino Super Beam and Neutrino Factory. The accurate determination of the mixing angle <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msub><s:mi>θ</s:mi><s:mn>23</s:mn></s:msub></s:math>, as well as the accuracy of <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msub><u:mi>δ</u:mi><u:mrow><u:mi>C</u:mi><u:mi>P</u:mi></u:mrow></u:msub></u:math>, is crucial for examining a certain category of discrete non-Abelian leptonic flavor models. Specifically, if <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>C</w:mi><w:mi>P</w:mi></w:math> is conserved in the leptonic sector, the combined analysis of T2HK and DUNE will rule out the majority of these models. However, if the <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> is maximally violated, a higher precision of <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:msub><ab:mi>δ</ab:mi><ab:mrow><ab:mi>C</ab:mi><ab:mi>P</ab:mi></ab:mrow></ab:msub></ab:math> is necessary to test these flavor models.