I compiled this page from a couple of email answers about the precision of our
muon energy loss simulation.


Version 1:

The most uncertain cross section at higher energies is photonuclear. From the
technical report on http://dima.lbl.gov/~dima/work/MUONPR/, figure 38, you can
see how different cross section predictions are. Some of the cross section
models on this plot are now considered outdated. I would probably only take the
difference between ALLM 97 and Butkevich (only valid/published up to ~10^6
GeV), and something like BB1981 or ZEUS with hard component). It seems the
range between the curves is then of the order ~8% over most of the higher
energies and less than that for lower energies. Since we use ALLM 97 by
default, we are on the lower prediction for this cross section, and I've seen a
paper on Antares where the highest curve was used (BB+hard component). Since we
are not in the middle of the range, we should probably take the full 8% as the
uncertainty (or +8%-0% or something like that).

Other cross sections are more precise. Ionization is negligible at higher
energies. Uncertainty in bremsstrahlung you can estimate from the curves in
figure 35 (forget the blue curve, it only works for electrons). In fact the PS
(green) curve is outdated as well, so the agreement between the remaining two
models is perfect. Epair cross section is also completely calculable just from
QED and is known to ~1% (i saw this number in one of the references).

Then you can see how the cross sections come together in figure 7. You see that
photonuclear cross section is never higher than the other two (brems and
epair), and is probably never higher than ~20-25% of the total. So the major
contributions are phnu (8% * 20%), epair (1% * 40%), and brems (0% * 40%),
total being 2%. This is the number I would quote I guess.

Version 2:

Computational uncertainty, i.e., precision errors of parameterizations and
integral evaluations, as well as the propagation method itself is estimated at
0.1% (with reasonable values of the vcut, ecut, and cont options).

Uncertainties of the cross sections themselves, i.e., our knowledge, or the
formulae that were coded from references are estimated at ~2-4%. The epair
formula is claimed with only a 1-2% precision, and it can be calculated almost
entirely from first principles. The ionization and bremsstrahlung losses are
probably known just as well. The worst is the photonuclear cross section. From
figure 38 (of the mmc report) comparing the most recent parameterizations of
ALLM and Butkevich I'd say an uncertainty of up to 5-10% (depending on the
energy range for which this cross section is used) is not unreasonable to be
claimed. This gets somewhat diluted as the photonuclear cross section is ~20%
of the total cross section, the main components being the better-known epair
and bremsstrahlung. At 10^20-10^30 eV all cross sections are blind
extrapolations, i would not claim anything about their precision.

How to propagate these errors:

modify the individual cross sections via the

-c[i/b/p/e/d]=[cross section modifier, 0:disable]

parameters (indices are for ionization, brems, photonuclear, epair, and decay).

You should be able to generate some sets with so modified cross sections (just
add such an option to the opts option of mmc-icetray, e.g., "-ci=1.02").