Constraining the pseudo-Dirac nature of neutrinos using astrophysical neutrino flavor data

The three Standard Model neutrinos can have Majorana mass or strictly Dirac mass, but both scenarios are practically indistinguishable in neutrino oscillation experiments. If they are pseudo-Dirac, however, there will be new mass splittings among the pseudo-Dirac pairs, potentially leaving traces in neutrino oscillation phenomena. In this work, we use flavor ratios of astrophysical neutrinos to discriminate different possible mass spectra of pseudo-Dirac neutrinos. We show that it will be possible to impose robust bounds of order <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>δ</a:mi><a:msubsup><a:mrow><a:mi>m</a:mi></a:mrow><a:mrow><a:mn>3</a:mn></a:mrow><a:mrow><a:mn>2</a:mn></a:mrow></a:msubsup><a:mo>≲</a:mo><a:msup><a:mrow><a:mn>10</a:mn></a:mrow><a:mrow><a:mo>−</a:mo><a:mn>12</a:mn></a:mrow></a:msup><a:mtext> </a:mtext><a:mtext> </a:mtext><a:msup><a:mrow><a:mi>eV</a:mi></a:mrow><a:mrow><a:mn>2</a:mn></a:mrow></a:msup></a:mrow></a:math> on the new mass squared splitting involving the third pseudo-Dirac mass eigenstates (those with the least electron flavor composition) with the future experiment IceCube-Gen2. The derived sensitivity is robust because it only assumes an extragalactic origin for the astrophysical neutrinos and hierarchical pseudo-Dirac mass spectrum. In case the neutrino sources are known in the future, such bounds can potentially improve by up to five orders of magnitude, reaching <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>δ</c:mi><c:msubsup><c:mi>m</c:mi><c:mn>3</c:mn><c:mn>2</c:mn></c:msubsup><c:mo>≲</c:mo><c:msup><c:mn>10</c:mn><c:mrow><c:mo>−</c:mo><c:mn>17</c:mn></c:mrow></c:msup><c:mtext> </c:mtext><c:mtext> </c:mtext><c:msup><c:mi>eV</c:mi><c:mn>2</c:mn></c:msup></c:math>.