<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>L</mml:mi><mml:mi>μ</mml:mi></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mi>τ</mml:mi></mml:msub></mml:math> solution to the IceCube ultrahig

In this work we analyze the scenario where a MeV scale <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>L</a:mi><a:mi>μ</a:mi></a:msub><a:mo>−</a:mo><a:msub><a:mi>L</a:mi><a:mi>τ</a:mi></a:msub></a:math> gauge boson can explain the deficit in the diffuse ultrahigh-energy (UHE) astrophysical neutrino spectrum observed in IceCube, as well as the discrepancy between experimental and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mi>e</c:mi><c:mo>+</c:mo></c:msup><c:msup><c:mi>e</c:mi><c:mo>−</c:mo></c:msup></c:math> scattering data-driven Standard Model calculations of the muon anomalous magnetic moment. We map the parameter space of the model where the elastic resonant s-channel scattering of UHE neutrinos with the cosmic neutrino background, mediated by the new <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msup><e:mi>Z</e:mi><e:mo>′</e:mo></e:msup></e:math>, can improve the description of the observed cascade and track spectra over the no-scattering hypothesis. Comparing to recent NA64-<g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>μ</g:mi></g:math> results, we find that some part of the parameter space remains unexplored, but at a data volume of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msup><i:mn>10</i:mn><i:mn>11</i:mn></i:msup></i:math> muons on target NA64-<k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>μ</k:mi></k:math> will completely probe this region. Published by the American Physical Society 2024