Dark-matter-enhanced probe of relic neutrino clustering

We propose heavy decaying dark matter (DM) as a new probe of the cosmic neutrino background ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi mathvariant="normal">C</a:mi> <a:mi>ν</a:mi> <a:mi mathvariant="normal">B</a:mi> </a:mrow> </a:math> ). Heavy DM, with mass <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mo>≳</e:mo> <e:msup> <e:mn>10</e:mn> <e:mn>9</e:mn> </e:msup> <e:mtext> </e:mtext> <e:mtext> </e:mtext> <e:mi>GeV</e:mi> </e:math> , decaying into neutrinos can be a new source of ultrahigh-energy (UHE) neutrinos. Including this contribution along with the measured astrophysical and predicted cosmogenic neutrino fluxes, we study the scattering of UHE neutrinos with the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mrow> <g:mi mathvariant="normal">C</g:mi> <g:mi>ν</g:mi> <g:mi mathvariant="normal">B</g:mi> </g:mrow> </g:math> via standard weak interactions mediated by the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>Z</k:mi> </k:math> boson. We solve the complete neutrino transport equation, taking into account both absorption and reinjection effects, to calculate the expected spectrum of UHE neutrino flux at future neutrino telescopes, such as the IceCube-Gen2 radio. We argue that such observations can be used to probe the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mrow> <m:mi mathvariant="normal">C</m:mi> <m:mi>ν</m:mi> <m:mi mathvariant="normal">B</m:mi> </m:mrow> </m:math> properties and, in particular, local <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mrow> <q:mi mathvariant="normal">C</q:mi> <q:mi>ν</q:mi> <q:mi mathvariant="normal">B</q:mi> </q:mrow> </q:math> clustering. We find that, depending on the absolute neutrino mass and the DM mass and lifetime, a local <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mrow> <u:mi mathvariant="normal">C</u:mi> <u:mi>ν</u:mi> <u:mi mathvariant="normal">B</u:mi> </u:mrow> </u:math> overdensity <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mo>≳</y:mo> <y:msup> <y:mn>10</y:mn> <y:mn>6</y:mn> </y:msup> </y:math> can be probed at the IceCube-Gen2 radio within ten years of data taking.