Upper limits on the cosmic neutrino background from cosmic rays

Extragalactic and galactic cosmic rays scatter with the cosmic neutrino background during propagation to Earth, yielding a flux of relic neutrinos boosted to larger energies. If an overdensity of relic neutrinos is present in galaxies, and neutrinos are massive enough, this flux might be detectable by high-energy neutrino experiments. For a lightest neutrino of mass <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>m</a:mi><a:mi>ν</a:mi></a:msub><a:mo>∼</a:mo><a:mn>0.1</a:mn><a:mtext> </a:mtext><a:mtext> </a:mtext><a:mi>eV</a:mi></a:math>, we find an upper limit on the local relic neutrino overdensity of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mo>∼</c:mo><c:msup><c:mn>10</c:mn><c:mn>13</c:mn></c:msup></c:math> and an upper limit on the relic neutrino overdensity at TXS <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mn>0506</e:mn><e:mo>+</e:mo><e:mn>056</e:mn></e:mrow></e:math> of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mo>∼</g:mo><g:msup><g:mn>10</g:mn><g:mn>10</g:mn></g:msup></g:math>. Future experiments like GRAND or IceCube-Gen2 could improve these bounds by orders of magnitude. Published by the American Physical Society 2024