I have been following up on my study of NEUGEN and Lipari neutrino
interaction codes. Unfortunately, when I increased my statistics the
discrepancy grew worse. Simulating 79 years of numu and numubar only
(both CC and NC) (that is, 100,000 NEUGEN events and 66,150 Lipari
events with a threshold of 0.1 GeV), my analysis has 1821 detectable
semicontained events from the Lipari sample and 2337 from NEUGEN.
Regarding the large discrepancy of low energy events generated, this
is mostly because in the NEUGEN model the CC quasielastic cross
sections are considerably higher (integrated over all energies, NEUGEN
generates about 12% more CC events than Lipari) and because in Lipari
the NC elastic cross sections are identically zero (NEUGEN generates
almost three times as many NC events as Lipari).
However, these low energy differences are irrelevant to the detectable
event discrepancy. The Lipari deficit with respect to NEUGEN
detectable events is around 20% throughout the detectable energy range
(i.e. 0.3 GeV to 30 GeV). In both models only about 2% of detectable
events are from NC events. The deficit is there for both neutrinos
and antineutrinos, on both protons and neutrons. Also, the angular
distribution of the parent neutrino of detectable events is
significantly different (Lipari is flatter). I suspect this may have
to do with different correlation of muon direction with neutrino
direction, but I have not verified this.
Regarding Daniele's excellent work on cross section uncertainties, I
am very troubled by the low chi-squares he obtains fitting
experimental data (chi-square is 4 or 5 with 17 degrees of freedom in
the high energy case). This could occur either because the
experiments overestimated their errors, or (more likely I think)
because the points at different energies share a common systematic
error.
Consider this toy problem: I have a dot on my wall at a height of 100
cm. I measure it 16 times with an inaccurate meter stick which is 1%
too long. Suppose my event-to-event measurement error is 0.01 cm, and
I somehow accurately estimate my systematic uncertainty to be 1 cm.
If I plot my 16 measurements with an error bar of 1.00005 cm (1 cm
plus 0.01 cm added in quadrature), they will cluster nicely around 99,
with a chi-square of around .0016/16. If I vary my answer by 1/4th of
an error bar (i.e. 0.25 cm) I will change chi-square to about 1. So I
would estimate the dot is at 99 +/- 0.25 cm. The real answer is 4
sigma away. The problem, of course, is that the systematic errors are
not independent. So I don't think we can use this technique to
estimate the cross sections better than the systematic errors of the
various experiments.
Bob
P.S. I'd like to remind everyone about this mailing list, which is a
good way to reach everyone in the neutrino working group and is
automatically archived to the WWW (password protected). Due to the
mail problems at Caltech, we have moved the lists to BU. (There will
probably be a general announcement about this in a day or so.) So now
the mailing list is macro-upmu@budoe.bu.edu and the archives can be
accessed through http://budoe.bu.edu/~macro at the bottom of the page
(when prompted for an account and password, use the MACRO account with
the usual password).