Lepton predictions and cosmological limits on neutrino mass

From: Jay R. Yablon (jyablon_at_nycap.rr.com)
Date: 02/14/05 

Date: Mon, 14 Feb 2005 20:34:54 +0000 (UTC)

In an earlier post I called attention to my having predicted a tau neutrino
mass inthe 13.5 MeV range, posted at
http://home.nycap.rr.com/jry/FermionMass.htm.

One of the board participants pointed out, correctly, that while my neutrino
results fit within the particle data, they contradict the cosmological data
which appears to set a much lower upper bound.

This has chastened me to be more careful about how I discuss the concordance
(or lack thereof) between by results and the experimental data:

I am able to use the electron masses to predict a weak mixing angle in the
range from .223 to .227. The two sides of the NuTeV anomaly place the weak
mixing angle at one end or the other of this range. The prediction I make
from the electron masses is not contradicted, nor, in light of the data
spread presently out there, is it confirmed. It adds another perspective on
how the weak mixing angle might relate to other experimental and theoretical
parameters -- in this case the electron masses -- and it does not appear to
be ruled out by what we presently know about the weak mixing angle. It adds
another data point to chew over.

Yet, this same calculation also suggests an approximate 13.5 MeV tau
neutrino mass. If the particle folks were to get the ceiling down below 10
MeV and still not have a tau neutrino mass, then I would have to understand
why my results work for the electrons but not the neutrinos and that would
present a puzzle that in all candor is a challenge. I believe such a result
might be accommodated through leptonic Cabibbo mixing in which mass that I
am expecting will show among the neutrinos gets shifted to the electrons, or
by modifying the assumptions I make about the role of Lepton number as a
mass-generating charge. Or, I might than have to accept that my work
predicts the electron mass sum to within 0.75%, and leave open the question
of where the remaining 0.75% comes from. This is because the neutrino is
relevant only to the final 0.75% of the electron masses which my results
reveal. For the first 99.25%, the neutrino is irrelevant. I would not be
the first peron looking for some "missing mass."

On the other hand, if somebody's particle experiment comes up with a tau
neutrino hit above 10 MeV, then the cosmological results would face a
challenge, and my own modest efforts would be the least of it.

What is wonderful about this sort of endeavor that in the end, it is nature
which arbitrates these discussions. Before the cautionary Email from one of
the participants, I was
almost ready to bet the farm on a 13.5 MeV tau neutrino mass because of my
excitement at being able to pin the electron masses so closely. Now, I am
more careful.

I look forward with great interest to what does (or does not) happen as the
particle folks double their accuracy in the tau neutrino search, down to 10
MeV or less.

_____________________________
Jay R. Yablon
Email: jyablon@nycap.rr.com

Relevant Pages

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