Relic neutrino background from cosmic-ray reservoirs

We compute the flux of relic neutrino background (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi mathvariant="normal">R</a:mi><a:mi>ν</a:mi><a:mi mathvariant="normal">B</a:mi></a:mrow></a:math>) up-scattered by ultrahigh-energy (UHE) cosmic rays (CRs) in clusters that act as CR-reservoirs. The long trapping times of UHECRs make this flux larger than that of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mi mathvariant="normal">R</e:mi><e:mi>ν</e:mi><e:mi mathvariant="normal">B</e:mi></e:mrow></e:math> up-scattered by UHECRs on their way to Earth, which we also compute. We find that IceCube excludes <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mi mathvariant="normal">R</i:mi><i:mi>ν</i:mi><i:mi mathvariant="normal">B</i:mi></i:mrow></i:math> weighted overdensities larger than <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msup><m:mn>10</m:mn><m:mn>10</m:mn></m:msup></m:math> in clusters, and that PUEO, RNO-G, GRAND, and IceCube-Gen2 will test values down to <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msup><o:mn>10</o:mn><o:mn>8</o:mn></o:msup></o:math>. Our treatment incorporates the momentum transfer dependence of the neutrino-nucleus cross section, deep inelastic scattering, a mixed UHECR composition, and flavor information on the up-scattered <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mrow><q:mi mathvariant="normal">R</q:mi><q:mi>ν</q:mi><q:mi mathvariant="normal">B</q:mi></q:mrow></q:math> fluxes for both cases of neutrino mass spectrum with normal and inverted ordering, providing new handles to possibly disentangle the up-scattered <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mrow><u:mi mathvariant="normal">R</u:mi><u:mi>ν</u:mi><u:mi mathvariant="normal">B</u:mi></u:mrow></u:math> from cosmogenic neutrinos.