From: Jonathan Link (link@fnal.gov)
Date: Wed Jul 13 2005 - 16:23:49 CDT
Greetings Alfred,
Thanks again for looking into this interesting issue. I look forward to
you following up on this problem as a Braidwwod collaborator.
Unfortunately I don't believe that your calculation is correct. As a
though experiment I considered the worst case muon (the muon that has
the largest possible path length in the shaft and still make it into our
detector. This muon enters the shaft at the top edge at the furthest
point away from the center of the detector. The ratio of the muon path
in the shaft to the total path to the detector is just proportional to
the ratio of shaft diameter to the distance from the detector to the far
wall of the shaft (proportional right triangles). Consider your rho of
3 meters and 5 meters radius case. Then this ratio is 10/35~0.3, so at
most the muon sees 30% less shielding. If we consider that all muons
see 30% less shielding then this is like going from 450 mwe to 315
mwe. This, of course, is a large overestimate because the entire shaft
subtends less that 6% of the total azimuthal angle about the detector.
Nevertheless, the muon rate for 300 mwe is only 2.7 times higher that
at 450 mwe (not 4 times) and the mean muon energy is about 63 GeV (not 44).
Your methodology seems plausible, so I assume that there must be some
bug and I encourage you continue working on this question so that we
have a ready answer when we need it, but it appears to me that this real
effect must be much smaller.
Thanks,
Jon Link
Matthew Worcester wrote:
> Hi all,
>
> I've posted a new note, "Effects of a Vertical Shaft to Muon
> Background", by Alfred Tang, currently at the Chinese University of
> Hong Kong, to the Braidwood site. The note details his modified
> Gaisser parameterization for surface muons, a different approach than
> the fit to data used by Martina and Jim's study. His more detailed
> MAND-sim talk on this work is also available at:
>
> http://neutrino.phys.ksu.edu/MAND-sim/MAND-sim%20talks/DayaBay_ksutalk.pdf
>
>
> His note also gives very interesting results from a study of the
> effect of a vertical shaft near the detector on the underground muon
> flux. Thanks again to Alfred for graciously sending such a nice
> writeup. If you have any questions on the note, please include him on
> the email.
>
> Cheers,
> Matt
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