I read the link...
High energy neutrinos (in the GeV range) were generated by devices on earth and observed...these neutrinos exceeded the speed of light by about c x 10^-5...
Low energy neutrinos (in the MeV range) emitted by celestial entities were also observed...these neutrinos exceeded the speed of light by about c x 10^-9 (or 10^-12)...
Summary: High energy neutrinos seem to exceed the speed of light more than low energy neutrinos...
I will then draw your attention to this quote:
"...a superluminal neutrino can be easily accommodated in a Lorentz invariance violation (LIV) model..."
There are many models that allow for an LI violation in regards to neutrinos (most of which are viable but at this point highly theoretical)...any search with "neutrino" and "lorentz invariance" will probably get you the results you want...
You will note that equation (4) represents the specific LIV model chosen by the authors...
I will also draw your attention to this quote:
"...Especially for a large ξ of the order O(10^-5), the processes π+ → µ+ +νµ and µ− → e− +νµ + ¯νe are even forbidden so that no high energy neutrinos could be produced..."
Essentially, the means by which neutrinos can be produced inherently applies a limit to the LIV parameter ξ, or the "perturbation" term....in quantum mechanics, perturbation theory is often used to develop models for "complex" systems...in perturbation theory, you start with a "simple" model and then create the "complex" model by adding "perturbations" to the simpler model...
In general, the rest of the paper uses theory and experimental data to determine the maximum size of ξ...recall that this ξ is the LIV parameter or "perturbation" constant/term used in an equation...it is not the energy of the neutrino....
Now let's look at the conclusion:
"...In such a framework, we find the neutrino production process π+ → µ+νµ becomes kinematically forbidden for Eν > 5 GeV if taking δνγ = 2.5 × 10^−5 as shown by OPERA data..."
So, the authors have argued that one specific neutrino production process (pion decay) cannot generate neutrinos with enough energy to exceed the speed of light...
I would like to point out that the OPERA experiment used a different process (π → µνµ)...a third process was also analyzed (µ → νµ + e + ¯νe)...additionally, there are references to other neutrino production processes (like "three body decay" and what not)...
As far as I can tell, this paper in no way argues against the ability of neutrinos to exceed the speed of light...what this paper does do is argue that one particular neutrino process cannot generate superluminal neutrinos...most importantly, this paper analyzes the results from other production processes, and uses them to put an experimentally determined limit on the LIV parameter ξ...
This parameter is utilized by a contending model that describes the superluminal behavior of neutrinos...in essence, this paper takes data from a bunch of experiments and places an upper limit on a "constant" used in some equation that shows how neutrinos can go faster than light...
I've never heard of this having supposedly negative mass before
First, I never said negative mass...I said imaginary mass, which would lead to a negative squared mass...
Here is one such paper that investigates this possibility, though I'm sure there are others, as the idea has been around for a while...
As you have said, experimental data has essentially proven that neutrinos oscillate between flavors.....quantum electrodynamics shows that an oscillation of this type can only occur for particles with mass...furthermore, it shows that each flavor eigenstate is a superposition of mass eigenstates and vice versa...
In this superposition, one could assign imaginary amplitudes to the mass eigenstates...so, either an imaginary mass or imaginary amplitudes associated with the mass eigenstates could lead to superluminal neutrinos...