I'm not sure I'll be around when this is resolved :-)
The formula would be |Ue1|^2 m1 + |Ue2|^2 m2 + |Ue3|^2 m3, where Ue1,
Ue2, and Ue3 are the coefficients for the electron neutrino (elements of
the so-called PMNS mixing matrix). Absolute square is used since these
could be complex numbers.
My recommendation would be to get some feedback from people who have a
stake in the claim, to see if there are strong feelings regarding what
interpretation to use. The gray areas -- where one interpretation says
"Yes" and the other "No"-- would be 1) for the normal hierarchy, when
the lightest mass is between about 0.004 and 0.01 eV, and 2) for the
inverted hierarchy, when the lightest mass is less than 0.01 eV.
One further note: squared coefficients are used above since those
represent probabilities of being in a certain state.
On 1/2/18 11:09 AM, Jim Gillogly wrote:
> Kerry (and fx-discuss) -
> Thanks for the explanation of the state of knowledge on the Neut
> claim. It was news to me. Your identification of ambiguity in the
> claim statement means that once the data is in, investors on the
> losing side would have a reasonable basis for dissatisfaction. From
> what I've read (and I'm *not* a researcher in the area) it will likely
> be some time before a reasonable confidence level of the measurements
> is reached, so that should give time for the investors to adjust their
> holdings based on this uncertainty.
> In the meantime, I would be happy to step aside as the judge in favor
> of someone like you who really knows the field and the outcome
> options, and who has no stake in Neut. I'm also mostly inactive. If
> that's not an option, then yes, I would like to see the formula you'd
> propose for calculating option 2).
> On Tue, Jan 2, 2018 at 8:41 AM, Kerry Whisnant <firstname.lastname@example.org
> <mailto:email@example.com>> wrote:
> Yes, the long description is the relevant criterion for judging.
> As a researcher in this area, a few comments:
> First, it is generally accepted now that neutrinos have mass.
> Although the measurements are indirect, there are many different
> experiments that indicate this. While there are some alternative
> explanations for some of the data, only nonzero neutrino mass can
> explain the data in its totality.
> Second, strictly speaking the electron neutrino does not have a
> unique mass. The weak eigenstates -- electron, muon, and tau
> neutrinos, which couple to the electron, muon and tau charged
> leptons, respectively -- are linear combinations of the so-called
> mass eigenstates (which do have a specific mass). So the statement
> of the claim is not well-defined -- the electron neutrino does not
> have a unique mass, but the neutrinos states that do have a unique
> mass are not purely electron neutrino.
> I see two primary ways to go here: 1) you could say that the
> spirit of the claim is that the lightest neutrino mass eigenstate
> must be 0.01 eV or greater, and use that as the criterion, or 2)
> if you want to assign a mass to the electron neutrino, you could
> take the weighted average using the squared coefficients of the
> linear combination for the electron neutrino as weights. Since the
> claim specifically mentions the electron neutrino, I would lean
> toward the latter interpretation (I can provide the formula if you
> want to go this route). But if some people entered this claim
> thinking it referred to the lightest neutrino, there could be some
> controversy. Given the current state of the data, these two
> interpretations could very well give different answers.
> We currently don't know if the electron neutrino couples more
> strongly to the lightest or heaviest neutrino mass eigenstate. If
> interpretation 2) above is taken, and it is shown that the
> electron couples more strongly to the heaviest mass neutrino
> (which has mass > 0.05 eV) -- a situation called an inverted
> hierarchy -- then the claim could be judged true without actually
> knowing the precise neutrino masses. If it is shown that the
> electron neutrino couples more strongly to the lightest mass
> eigenstate -- called a normal hierarchy -- it will be much harder
> to reach a conclusion on the claim (you would have to show that
> the lightest mass was at least 0.004 eV).
> A final comment: no measurement in physics is ever precise --
> there are always experimental uncertainties. In our field we
> usually require a 5-sigma effect before we consider a claim to be
> proven. So it might be a good idea to require something like a
> 5-sigma confidence level before the claim is finally judged.
> Kerry Whisnant
> P.S. I am basically an inactive player in FX who still receives
> these emails, and have no stake in this claim.
> On 12/31/17 4:47 PM, Jim Gillogly wrote:
>> I changed the judge's statement for the Neut claim to reflect my
>> response to the query below. As always, please send pointers to
>> relevant research that I should take into account.
>> > I'm writing to inquire about the adjudication of the ideosphere claim
>> "Neutrino Mass > 0."
>> > In 2015, the Nobel Prize in Physics was awarded to Takaaki
>> Kajita and Arthur B. McDonald "for the discovery of neutrino
>> oscillations, which shows that neutrinos have mass."
>> > Is this enough to settle the claim?
>> Jim Gillogly
> Kerry Whisnant
> Physics & Astronomy
> Iowa State University
> Jim Gillogly
Physics & Astronomy
Iowa State University