Mass ordering sum rule for the neutrino disappearance channels in T2K, NOvA, and JUNO

We revisit, reformulate, and extend a method for determining the neutrino mass ordering by using precision measurements of the atmospheric <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="normal">Δ</a:mi><a:msup><a:mi>m</a:mi><a:mn>2</a:mn></a:msup><a:mtext> </a:mtext><a:mtext> </a:mtext><a:mi mathvariant="normal">s</a:mi></a:math> in both electron and muon neutrino disappearance channels, first proposed by the authors in 2005 [H. Nunokawa , ]. The mass ordering is a very important outstanding question for our understanding of the elusive neutrino and determination of the mass ordering has consequences to particle physics, nuclear physics, and cosmology. The JUNO reactor experiment will start data taking this year, and the precision of the atmospheric <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi mathvariant="normal">Δ</e:mi><e:msup><e:mi>m</e:mi><e:mn>2</e:mn></e:msup><e:mtext> </e:mtext><e:mtext> </e:mtext><e:mi mathvariant="normal">s</e:mi></e:math> from electron antineutrino measurements will improve by a factor of 3 from Daya Bay’s 2.4% to 0.8% within a year. This measurement, when combined with the atmospheric <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi mathvariant="normal">Δ</i:mi><i:msup><i:mi>m</i:mi><i:mn>2</i:mn></i:msup></i:math>’s measurements from T2K and NOvA for muon neutrino disappearance, will contribute substantially to the <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi mathvariant="normal">Δ</l:mi><l:msup><l:mi>χ</l:mi><l:mn>2</l:mn></l:msup></l:math> between the two remaining neutrino mass orderings. In this paper we derive for the first time a mass ordering sum rule that can be used to address the possibility that JUNO’s atmospheric <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi mathvariant="normal">Δ</o:mi><o:msup><o:mi>m</o:mi><o:mn>2</o:mn></o:msup></o:math>’s measurement, when combined with other experiments in particular T2K and NOvA, can determine the neutrino mass ordering at the <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mrow><r:mn>3</r:mn><r:mi>σ</r:mi></r:mrow></r:math> confidence level within one year of operation. For a confidence level of <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mrow><t:mn>5</t:mn><t:mi>σ</t:mi></t:mrow></t:math> in a single experiment, we will have to wait until the middle of the next decade when the DUNE experiment is operating.