It has been a while since I last discussed the so-called 'GZK' neutrinos, neutrinos which are produced when ultra-high energy cosmic-rays interact with cosmic microwave background (CMB) photons. As you may recall, CMBR photons were produced during the big bang; they have cooled off during the roughly 14 billion years since then. They are now mostly at microwave frequencies, with a peak at 6.6 GHz, corresponding to an average photon energy of 0.00024 electron Volt, or a temperature of 2.725 degrees Kelvin (i.e. above absolute zero). Although this is not much energy, it can be enough to excite ultra-high energy protons into a state called the Delta-plus (basically an excited proton). When the Delta-plus decays, it produces a proton and a neutral pion, or a neutron and a positively charged pion. When the positively charged pions decay, they produce a neutrino and a muon; when the muon decays, it produces two more neutrinos and an electron.
We know that ultra-high energy cosmic rays exist, and we know that CMB photons exist, so these are often considered to be a 'guaranteed' source of neutrinos. These neutrinos are the main goal of radio-detection experiments like ARIANNA, ARA and, of course, ANITA. However, there are a few caveats. If the highest energy cosmic rays are mostly iron, rather than protons, then the flux of these GZK neutrinos will be drastically reduced, below the point where these experiments can see them. Also GZK neutrinos have been produced continuously since the early universe (and are almost never absorbed), so the number of GZK neutrinos existing today depends on how many ultra-energetic cosmic-rays there were in the early universe; this is a much smaller uncertainty than due to the proton vs. iron (or something in between) question.
Until recently, all searches have been negative. The one possible exception is an anomalous event observed by the ANITA experiment, the fourth, 'anomalous' event in their recent paper. I have previously discussed ANITA; this event emerged from a reanalysis of data from their first flight. The ANITA Collaboration describes the event as consistent from a primary source that emerged from the earth; this might be from a neutrino or a long-lived tau lepton. The tau lepton could have been produced in an air shower, and travelled through the Earth, before emerging to produce this shower. The event could also be a mis-reconstructed downward-going shower. Although the event is very interesting, we do see the difficulty of trying to draw conclusions based on one event. It is also clear that the ANITA collaboration feels this difficulty; the event is one of four presented in a paper on downward-going cosmic-rays, rather than highlighted on its own.
Of course, IceCube is also looking for GZK neutrinos. Our latest search, based on 6 years of data, has recently appeared here. To cut to the chase, we didn't find any GZK neutrinos; the analysis did find two lower energy (by GZK standards) events, including the previously announced energy champ. From this non-detection, we set limits that are finally reaching the 'interesting' region. The plot below shows our upper limits as a function of energy, compared with several models.