observational astronomy - Cosmic rays and neutrinos

I'm reading Gaggero's Cosmic Ray Diffusion in the Galaxy and Diffuse Gamma Emission and he makes the claim,

...the definitive proof of [Cosmic Ray proton acceleration in supernova remnants] would be the observation of neutrino emission by existing or forthcoming experiments such as IceCube or NEMO.

The existence of neutrinos stems from relativistic protons colliding with ambient protons. Neutral pions are the primary decay mode for $pp$ collisions, but charged pions can also be made alongside the neutrinos.

My question is then would the non-detection of neutrinos be a statistic issue or would it suggest Supernova Remnants do not accelerate protons?

Answer

It is more likely that the non-detection would be associated with statistics than SNR's not accelerating protons. Fermi-LAT has already shown that $\gamma$-ray emissions from 4 galactic supernova remnants (with molecular clouds nearby them) are coming from proton-proton collisions leading to neutral pions ($pp\to pp\pi^0$, $\pi^0\to2\gamma$):

(source, arxiv link)

From Halzen et al (2008),

Sources producing such hard spectra extending up to 100 TeV and more are required to explain the existence of the 'knee' in the cosmic-ray spectrum around 3 PeV, with young supernova remnants being the best candidates. However, their observation is difficult as these high-energy photons are produced inside the accelerator only within the first few hundred years.
...
Assuming an $E^{-2}$ spectrum with a cut-off at 300 TeV (consistent with a proton cut-off at the 'knee') we demonstrate that IceCube will be able to see these sources after several years of observation.

The one year result of the IceCube Neutrino Observatory (with 40 strings) shows a 90% confidence level of no point sources of neutrinos at the PeV energy range. With the extra 46 strings of the complete observatory, it is expected that point sources of neutrinos can be discovered.

The fluxes at TeV energies of $\gamma$-ray sources is around $10^{-12}$ 1/TeV/cm$^2$/s, which is near the sensitivity level of the full 86 string IceCube observatory. Aartsen et al (2014), using data obtained from 2008 through 2011, state

IceCube recently found evidence for a diffuse flux of high-energy astrophysical neutrinos, observing a 5.7$\sigma$ excess of events between $\sim$50 TeV and 2 PeV deposited within the detector. The 37 observed events are consistent with an $E^{-2.3}$ neutrino flux at the level of $1.5\times10^{-11}$ 1/TeV/cm$^{2}$/s/sr (normalized at 100 TeV), with a neutrino flavor ratio of 1:1:1. While these events have established unequivocally that astrophysical neutrinos exist, their sources have not yet been identified. One challenge is that only $\sim$20% of the events in that sample are associated with a high-energy muon which lieaves a visible track in the detector. The remaining events without a track have a poor angular resolution of $\sim$15$^\circ$.

From a live-time of 1373 days, that amounts to less than 10 events per year. Added to that, the lack of identifying the origin of these sources, the issue is more aligned with statistics than eliminating the hadronic SNR acceleration paradigm.