Previously, the strongest (statistically) IceCube astrophysical neutrino analysis used four years of contained event data. The significance of the result (compared to the null hypothesis of no astrophysical neutrinos) was 6.5 sigma (standard deviations), which is very strong, and well above the 5-sigma threshold widely used in particle physics as needed to claim a discovery. Based on raw numbers, the probability of getting a 5 sigma result is tiny - about 1 in 3.5 million. But, there are two things to keep in mind. First, with modern computers, it is easy to do a lot of experiments by changing parameters. One 'good' example is to consider the number of different places in the sky we could look for a signal. This large number must be considered when we search for point source searches. A more problematic example is to change analysis parameters to try to make the signal larger. We try very hard to avoid this - it is one reason that we use blind analysis where possible - but it can sometimes be hard to avoid unconscious bias. I had previously discussed an earlier analysis - almost identical, but with only 3 years of data.

The second thing to remember is that this was a single result, based on a single analysis. We were very very careful before making the contained event analysis public, but still, discoveries need confirmation. Unfortunately, IceCube is the only experiment large enough to study these neutrinos. So, we developed a complementary analysis that studies through-going muons from neutrino interactions outside the detector. The original version (alternate link to freely available version) of this analysis used 2 years of data, and found an excess, consistent with the contained event analysis, with a statistical significance of 3.7 sigma.

Now, we have released a new analysis, using 6 years of data. It finds an astrophysical flux, with a significance of 5.6 sigma - enough for a discovery on its own. The spectrum is shown at the top of this post. This data also allows us to say more about the characteristics of the astrophysical neutrinos. The measured spectral index (the 'gamma' in dN/dE_nu = A * (E_nu/1 TeV)^gamma is measured to be 2.13 +/- 0.13. This is in some tension with the findings from the contained event analysis, which find gamma much closer to 2.5. This tension could be from statistical fluctuations (it is about a 2 sigma difference, so not too improbable), or it could have something to do with the different event samples. This plot shows the tension, with the different enclosed regions showing the range of astrophysical neutrino spectral index (gamma, x axis) with the corresponding signal strength (flux, y axis). The solid red curve is from the current analysis, while the blue curve shows the combined result from previous studies. If the two measurements were in good agreement, the curves should meet. But, they don't; besides statistics, there are several possible explanations.

The through-going neutrino analysis samples, on average, more energetic neutrinos than the contained event study, so one simple explanation might be that a power law neutrino energy spectrum, like dN/dE_nu = A * (E_nu/1 TeV)^n is too simple a model. The spectral index gamma might change with energy. There is no reason to expect a single power law. Alternately, there could be some difference between the muon-neutrino sample (through-going events) and showers from a mixture of all three flavors; the latter is not expected, but statistical fluctuations, or a more complex energy spectrum seem like the most likely possibilities.

The fact that two different analyses get the same answer is very encouraging. There is, by both design and result, zero overlap between the two events samples. Further, the systematic uncertainties for the two analyses are very different, so the analyses are almost completely independent. So, for anyone who was waiting for this signal to go away, it looks increasingly unlikely.\

I should mention that this is the analysis that first found the 2.2 PeV neutrino that I have previously discussed here and here. So, if you were waiting for a more detailed publication, this new paper is it.