Sensitivity of DUNE in the presence of off-diagonal scalar NSI parameters

Scalar nonstandard interactions (SNSI) present an exciting pathway for probing potential new physics that extends beyond the Standard Model (BSM). The scalar coupling of neutrinos with matter can appear as a subdominant effect that can impact the neutrino oscillation probabilities. The uniqueness of these interactions lies in their direct effect on the neutrino mass matrix, which makes oscillations sensitive to the absolute neutrino mass. The impact of SNSI scales linearly with matter density, which motivates its exploration in the long-baseline sector. The presence of SNSI can influence the key measurements in the field of neutrino physics, including the determination of 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 (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>δ</c:mi><c:mrow><c:mi>C</c:mi><c:mi>P</c:mi></c:mrow></c:msub></c:math>), neutrino mass ordering, and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>θ</e:mi><e:mn>23</e:mn></e:msub></e:math> octant. The precise determination of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>δ</g:mi><g:mrow><g:mi>C</g:mi><g:mi>P</g:mi></g:mrow></g:msub></g:math> is one of the major goals of the Deep Underground Neutrino Experiment (DUNE), which is an upcoming long-baseline experiment. A better understanding of the impact of SNSI on <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>C</i:mi><i:mi>P</i:mi></i:math> measurement sensitivities is crucial for accurate interpretation of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>δ</k:mi><k:mrow><k:mi>C</k:mi><k:mi>P</k:mi></k:mrow></k:msub></k:math> phase. We have analytically explored the dependence of probabilities on the absolute <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>ν</m:mi></m:math> masses and fundamental mixing parameters in the presence of SNSI. We observe that the presence of off-diagonal SNSI elements <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mo stretchy="false">|</o:mo><o:msub><o:mi>η</o:mi><o:mrow><o:mi>α</o:mi><o:mi>β</o:mi></o:mrow></o:msub><o:mo stretchy="false">|</o:mo></o:math> and their associated phases <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msub><s:mi>ϕ</s:mi><s:mrow><s:mi>α</s:mi><s:mi>β</s:mi></s:mrow></s:msub></s:math> can significantly affect the <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>C</u:mi><u:mi>P</u:mi></u:math>-measurement sensitivities at DUNE. We note that <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>-violation sensitivities also depend on the absolute neutrino masses. We look for constraining the off-diagonal parameters for different lightest neutrino masses. We observe that <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mo stretchy="false">|</y:mo><y:msub><y:mi>η</y:mi><y:mrow><y:mi>α</y:mi><y:mi>β</y:mi></y:mrow></y:msub><y:mo stretchy="false">|</y:mo></y:math> is more tightly constrained if the neutrino mass is higher. We also explore their correlation with <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msub><cb:mi>δ</cb:mi><cb:mrow><cb:mi>C</cb:mi><cb:mi>P</cb:mi></cb:mrow></cb:msub></cb:math>, investigating potential degeneracies that can arise due to SNSI phases (<eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:msub><eb:mi>ϕ</eb:mi><eb:mrow><eb:mi>α</eb:mi><eb:mi>β</eb:mi></eb:mrow></eb:msub></eb:math>). We also perform a correlation study among different SNSI elements.