I have (finally!) finished an official analysis of the upward-going
muon result.
HIGHLIGHTS
Best-Fit point: sin^(2 theta) = 1.00
delta-m^2 = 2.51x10^-3
flux scale = 1.10 (that is, add 10% to Bartol)
Monte Carlo probability to observe a result with lower likelyhood
than data, given the best-fit point:
5.1%
Exclusion of zero-oscillation hypothesis, using nominal Bartol flux
scale of 1.00 (not best fit of 1.10): 96%.
Exclusion of maximal mixing (sin^2 2 theta = 1.00, dm^2 = 1.0): 99%.
Details have been posted in upmu97.ps in the following places:
cithep: \users\macro\nustat97.ps
vaxgs: DISK$MACRO2:[LONGLEY]nustat97.ps
But here's a synopsis:
The 5.1% number is a bit higher than what I gave in Michigan (I
think 3.6%, but don't rememebr for sure) because I have now included the
direction and bin-to-bin correlations in the likelihood, not just the plain
bin-by-bin Poisson probabilities. This was something that had been
bothering me for a long time, and Stephane gave me a good reference in
Michigan. But I spent a few weeks making sure this was a good idea before
I put it in. The fact that the probability of othe result goes up when I
include this just indicates that the "shape" of the distribution is not
really that strange, if we pick an oscillation hypothesis that splits the
middle between the first two (low) points and the next two (high) points.
The SIZE of the deviation is still a little big, however, which gives the
relatively small number.
At the MACRO meeting I asked Francesco how high the number had to
go before we would publish the contour plots. I think he said something
like, "10%... no, maybe 5%." Francesco, do you remember the conversation?
At any rate I hope I've moved the number into the "annoying" range. I
personally think the thing is still a little weak, particularly as I just
added some terms to the likelihood which bring the probability up by a
factor of order one. But I want to stress that the shape terms are
somthing I've been worried about for a long time, that they weren't simply
added to make things look better, and that the total likelyhood is _not_
just something I made up but appears in the literature. Anyway, I think we
should at least talk about the exclusion plots again.
At the Michigan meeting, Barry asked me what the conclusion of my
talk was. I said it was that there was a pretty good chance that there was
an unresolved systematic effect in the experiment. That was a little flip,
but it's essentially correct. There's just NO WAY to tell whether we have
a systematic problem or not, and we _do_ have an unusualy result. But
given that a probability of about 5%, and given that we have made a very
good attempt to track down the most obvious possible systematic effects, I
think we should, as I said, at least talk about exclusion plots.
Another way to answer Barry's question, of course, which nominally
contains the same information but is not as conservative as the answer I
first gave, is "There is a reasonable chance that nothing is wrong at all."
What does "reasonable" mean? Well, a priori it means 5.1%. But given
that we've checked out some of the likely systematic effects post hoc, at
least some of the 94.9% "systematic" phase space has gone away. How much?
There's no way to know. But I guess the number now has something like a
"lower limit" of 5.1%.
I personally lean toward putting the exclusion plots out there, but
I have absolutely not formed a final opinion and would like to talk about
it some more. Unfortunatley I don't think it should wait until the next
collaboration meeting. Any ideas?
- Nat
PS Doug for some reason I am not on the macro-upmu mailing list. Can you
add me?
Assistant Professor Nat Longley
Department of Physics and Astronomy
Swarthmore College
Swarthmore, PA 19081-1397
nlongle1@swarthmore.edu
(610) 328-8249 fax: (610) 328-7895