Modifications to NUSIM

One problem found with NUSIM was that 20% of the simulated neutrino events didn't have a muon track. The fix to this problem was to obtain a better estimate of the maximum muon range. The simulation randomly places the interaction vertex within a volume determined by their maximum range from a plane /sim 300<> meters above the detector for up-going neutrinos. If the vertex is located below the earth/ice boundary, then the muon is propagated to this interface using muprop_rock.f fortran routine. If the energy decrease to 1 GeV before reaching the interface, it is not recorded in the output. Hence, there will be neutrino information written in the f2000 output, but no muon track is recorded. These events cannot trigger in AMANDA. If the maximum muon range is larger than the actual muon range, then a fraction of muons will range out before reaching the earth/ice interface. To check this behavior in detail the muprop_rock.f code was used to calculate muon range versus initial muon energy. Figure 39 show the results of this calculation for three different intervals of muon energy. The scattered points are the range given by muprop_rock. The dashed line is the maximum muon range estimated by the previous code and the dotted line is the improved estimate. In the plot to the left, the solid line is the improved estimate. For the muon energy greater than 10 TeV, no change was observed in the range. The equations used for estimating the maximum muon range are shown in Table 12. After making the improvement, 95% of the events contain muon tracks. This increases the trigger efficiency of NUSIM. Another correction changed the density of ice from 1 g/cm³<> to 0.92 g/cm³<> throughout the code.

 

Table 12: The equations used to estimate the maximum muon range for the signal Monte Carlo simulation.

$E{\mu}<$ 1 TeV	Old estimate:	$range= E_{\mu}/0.002$
	New estimate:	$range= 4.5 \cdot 10^{5} \cdot ln (10^{-3}\cdot(E_{\mu}+1050))$
$1 TeV < E_{\mu} < 10 TeV$	Old estimate:	$range= 10^{5}(3.5+9.0(log_{10}(E_{\mu})-3.0))$
	New estimate:	$range= 10^{5}(3.5+7.5(log_{10}(E_{\mu})-3.0))$
$E_{\mu} > 10 TeV$	Same estimate:	$range= 10^{5} \cdot (12 + 6 \cdot (log_{10}(E_{\mu})-4))$

  

Figure 39: each plot the Y-axis is the muon range in meters and X-axis is muon energy in log₁₀(E/GeV). The top left plot show the muon range for initial muon energies less than 1000 GeV. The top right plot for initial muon energies between 1000 GeV and 1x10⁴ GeV and the bottom plot for muon energies above 1x10⁴ GeV. See text for description of the lines.