Re: new note on muon background

From: Alfred Tang (
Date: Thu Jul 14 2005 - 05:05:35 CDT

Dear Jonathan
Thanks for the thoughtful reply. I agree that I shall check my results very
carefully before I believe them myself. To be honest, I was a bit
skeptical myself when I first looked at the outputs of my program. But I
did not see anything obviously wrong so far. I will keep checking. If
for nothing else, my paper will hopefully stir some thinking. Regarding
your thought experiment, my experience is that it is sometimes difficult
to get an intuitive feeling for muon background in the case of a complicated
geometry. It is why we need to rely on an exact Monte Carlo
calculation. Since I do not yet have a chance to digest my results, I will
not engage your thought experiment directly at the present time. I am
in the middle of a move from Hong Kong to KS these next few weeks so that
the mental digestion process may seem slower at times. By the way, there
is a typo in Eq (10) of my short paper where I left out a term but my
program is implemented correctly. So don't worry if someone catches it--it
is just a typo. I will ask Matt to replace the paper at a later point
when I have more results to show. Thanks again for your comments.
Please feel free to email me if you have further comments. I enjoy
hearing from you.

On Wed, 13 Jul 2005, Jonathan Link wrote:

> 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:
> >
> >
> >
> >
> > 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

Alfred Tang

The Chinese University of Hong Kong
Department of Physics
Shatin, New Territories
Hong Kong SAR


office phone: +852 2609-6315

Personal webpage:

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