Type: Article
Publication Date: 2023-02-03
Citations: 2
DOI: https://doi.org/10.1007/jhep02(2023)044
A bstract We analytically calculate the neutrino conversion probability P μe in the presence of sterile neutrinos, with exact dependence on $$ \Delta {m}_{41}^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>∆</mml:mtext> <mml:msubsup> <mml:mi>m</mml:mi> <mml:mn>41</mml:mn> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> and with matter effects explicitly included. Using perturbative expansion in small parameters, the terms involving the small mixing angles θ 24 and θ 34 can be separated out, with θ 34 dependence only arising due to matter effects. We express P μe in terms of the quantities of the form sin( x ) /x , which helps in elucidating its dependence on matter effects and a wide range of $$ \Delta {m}_{41}^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>∆</mml:mtext> <mml:msubsup> <mml:mi>m</mml:mi> <mml:mn>41</mml:mn> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> values. Our analytic expressions allow us to predict the effects of the sign of $$ \Delta {m}_{41}^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>∆</mml:mtext> <mml:msubsup> <mml:mi>m</mml:mi> <mml:mn>41</mml:mn> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> at a long baseline experiment like DUNE. We numerically calculate the sensitivity of DUNE to the sterile mass ordering and find that this sensitivity can be significant in the range $$ \mid \Delta {m}_{41}^2\mid \sim \left({10}^{-4}-{10}^{-2}\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>∣</mml:mo> <mml:mi>Δ</mml:mi> <mml:msubsup> <mml:mi>m</mml:mi> <mml:mn>41</mml:mn> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>∣</mml:mo> <mml:mo>∼</mml:mo> <mml:mfenced> <mml:mrow> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> <mml:mo>−</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:mfenced> </mml:math> eV 2 , for either mass ordering of active neutrinos. The dependence of this sensitivity on the value of $$ \Delta {m}_{41}^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>∆</mml:mtext> <mml:msubsup> <mml:mi>m</mml:mi> <mml:mn>41</mml:mn> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> for all mass ordering combinations can be explained by investigating the resonance-like terms appearing due to the interplay between the sterile sector and matter effects.
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