Cosmic horizon of neutrinos

The persistent discrepancy between the experimental measurement and the Standard Model (SM) prediction of the muon’s anomalous magnetic moment <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mo stretchy="false">(</a:mo> <a:mi>g</a:mi> <a:mo>−</a:mo> <a:mn>2</a:mn> <a:msub> <a:mrow> <a:mo stretchy="false">)</a:mo> </a:mrow> <a:mrow> <a:mi>μ</a:mi> </a:mrow> </a:msub> </a:mrow> </a:math> remains one of the most intriguing hints of physics beyond the SM. A well-motivated explanation involves a light <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> gauge boson associated with a broken <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>U</g:mi> <g:mo stretchy="false">(</g:mo> <g:mn>1</g:mn> <g:msub> <g:mo stretchy="false">)</g:mo> <g:mrow> <g:msub> <g:mi>L</g:mi> <g:mi>μ</g:mi> </g:msub> <g:mo>−</g:mo> <g:msub> <g:mi>L</g:mi> <g:mi>τ</g:mi> </g:msub> </g:mrow> </g:msub> </g:math> symmetry. Such a boson not only resolves the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mo stretchy="false">(</k:mo> <k:mi>g</k:mi> <k:mo>−</k:mo> <k:mn>2</k:mn> <k:msub> <k:mo stretchy="false">)</k:mo> <k:mi>μ</k:mi> </k:msub> </k:math> anomaly, but also induces resonant interactions between high-energy cosmic neutrinos and the cosmic neutrino background ( <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mrow> <o:mi mathvariant="normal">C</o:mi> <o:mi>ν</o:mi> <o:mi mathvariant="normal">B</o:mi> </o:mrow> </o:math> ), potentially shaping the observable neutrino flux at Earth. In this work, we explore the implications of such interactions for the cosmic propagation of high-energy neutrinos. We compute the optical depth for neutrino attenuation via <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:msup> <s:mi>Z</s:mi> <s:mo>′</s:mo> </s:msup> </s:math> -mediated scattering, accounting for neutrino masses, hierarchies, and thermal distributions. We delineate the regions in <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mo stretchy="false">(</u:mo> <u:msub> <u:mi>m</u:mi> <u:msup> <u:mi>Z</u:mi> <u:mo>′</u:mo> </u:msup> </u:msub> <u:mo>,</u:mo> <u:msub> <u:mi>m</u:mi> <u:mi>ν</u:mi> </u:msub> <u:mo stretchy="false">)</u:mo> </u:math> space where the optical depth exceeds unity, defining a “neutrino cosmic horizon” beyond which high-energy neutrinos are significantly attenuated. We confront these results with the parameter space required to simultaneously explain the muon <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mi>g</y:mi> <y:mo>−</y:mo> <y:mn>2</y:mn> </y:math> anomaly and ease the Hubble tension via an additional contribution to the effective number of relativistic degrees of freedom, <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:mi mathvariant="normal">Δ</ab:mi> <ab:msub> <ab:mi>N</ab:mi> <ab:mi>eff</ab:mi> </ab:msub> <ab:mo>≃</ab:mo> <ab:mn>0.2</ab:mn> <ab:mi>–</ab:mi> <ab:mn>0.5</ab:mn> </ab:math> . Our analysis reveals a consistent region in parameter space where all three phenomena [ <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"> <db:mo stretchy="false">(</db:mo> <db:mi>g</db:mi> <db:mo>−</db:mo> <db:mn>2</db:mn> <db:msub> <db:mo stretchy="false">)</db:mo> <db:mi>μ</db:mi> </db:msub> </db:math> , <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"> <hb:msub> <hb:mi>N</hb:mi> <hb:mi>eff</hb:mi> </hb:msub> </hb:math> , and high-energy neutrino attenuation] can be explained by the same light mediator. These findings motivate future searches for spectral features in IceCube and its next-generation successors as indirect probes of new physics in the neutrino sector.