The neutrino flux from NuMI is simulated using the Flugg [125, 126, 127] package to incorporate a GEANT4 [128] geometry into a Fluka [129, 130] simulation of the hadronic production, decay, and transport processes.6 The technical details are described in Appendix F. The flux simulation is primarily a simulation of the secondary meson beam. It starts with 120 GeV Main Injector protons incident on a graphite target and simulates the production of the secondary mesons and their transport through the horn focusing fields and into the decay pipe, as well as any further downstream interactions. Whenever a particle would decay to produce a neutrino, the properties of the parent are recorded to disk. Then, from that information (position and momentum), the probability of that parent’s daughter neutrino reaching one of the detectors, as well as what energy that neutrino would have, can be calculated (these calculations are detailed in Appendix A). Effectively, every neutrino produced is forced to go to the detectors, but with a weight that accounts for its probability of actually doing so, saving significant processing time. This weighted neutrino flux serves as the input to the MINOS detector simulation described in Section 3.5.
The beam simulation uses importance sampling and weighting to reduce the number of low energy particles that need to be simulated. Naturally, the simulation produces many more low energy mesons than high energy ones, which can make it difficult to accumulate enough statistics at higher energies. Relative to the energy distribution of the experiment, the higher energies are under- represented in the beam simulation out of the box. A 1 GeV tracking threshold is included since those mesons will produce approximately 500 MeV neutrinos, which is the lowest energy neutrino
6I wrote the Flugg beam simulation and produced all the flux Monte Carlo now in use in the MINOS experiment.
Energy (GeV)
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Geant3 Flux MC Flugg Flux MC Data
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Figure 3.12: The ratio of the Near Detector spectrum with helium in the decay pipe to the spectrum with an evacuated decay pipe for neutrinos (left) and antineutrinos (right). The black line represents the older GNuMI simulation, the red line represents the newer Flugg simulation, and the blue points represent the data. As shown, the Flugg-based simulation is significantly better at reproducing the effects of helium seen in the data.
the MINOS detectors are sensitive to, but even then there are still too many low energy particles.
In order to speed up the simulation and reduce the space required on disk, pions below 30 GeV are importance sampled and weighted: a fraction of the events are thrown away, but the remaining events are given a weight larger than one so that the total weighted flux remains unchanged. This technique distributes the processing time and statistics more evenly across all energies even though many fewer high energy particles are produced. The weightW is calculated as,
W =Wparent30 GeV
|Ptotal| (3.2)
whereWparent is the importance weight of the particle’s parent (initial protons start with weight 1) and|Ptotal|is the total momentum of the particle. Weights can never be below 1 and are capped at 100 to prevent a single event from being too important.
The previous beam simulation, called GNuMI, was also part-GEANT and part-Fluka. It simu- lated the interaction of the primary protons with the target entirely in Fluka and then simulated the transport of the particles leaving the target in GEANT3. GEANT3 uses GFluka, an older less reliable version of the Fluka hadronic interaction model, to model the interactions outside the target. This two-part simulation worked well as long as interactions outside the the target were not important, but that changed when the decay pipe was filled with helium. GFluka significantly overestimated the amount of high energy neutrino production from interactions with the helium.
This mis-modeling was particularly troublesome because parents produced in the decay pipe tend to decay very close to the Near Detector, meaning they have large Near-to-Far spectral differences (see Section 5.3). The Flugg simulation, which uses the up-to-date Fluka interaction models both in the target and throughout the beamline, does a much better job of predicting the amount of production
56 3.4 MINOS Data The MINOS Experiment59
LE pME pHE
Figure 3.13: Near Detector spectra of νµ CC events in the data compared to the predic- tions from the original simulation and from the tuned simulation, in the low-energy (LE), pseudo-medium energy (pME) and pseudo-high energy (pHE) beam configurations. The corresponding data to MC ratios are shown in the bottom panels, before and after tuning.
In all cases the tuned simulation agrees very well with the data.
Simulation of the Neutrino Interactions
Neutrino interactions are modeled with the NEUGEN program [98, 99]. NEUGEN simulates both quasi-elastic and inelastic neutrino scattering in the range of 100 MeV to 100 GeV, and was developed mostly by MINOS collaborators. NEUGEN was first used in the Soudan 2 experiment.
Of particular interest to this thesis is the simulation of hadronic showers, which con- stitute the main background to the νe CC appearance analysis. Hadronization in NEU- GEN is handled by the AGKY model [100]. AGKY uses the PYTHIA/JETSET [101]
model to simulate hadronic showers at high hadronic invariant masses W but incorpo- rates a phenomenological description of low invariant mass hadronization. The reason for this is that the PYTHIA/JETSET model deteriorates near the pion production thresh- old. The phenomenological model implemented in AGKY is based on Koba-Nielsen-Olesen (KNO) scaling [102], although it incorporates several improvements. The transition from the KNO-based model to the PYTHIA/JETSET model takes place gradually at an inter- Figure 3.13: The Near Detectorνµspectrum, in data (black), raw simulation (blue), and flux-tuned simula- tion (red), in three different beam configurations. The flux tuning significantly improves the data-simulation agreement in all beam configurations.
from helium interactions, as can be seen in Figure 3.12.
Even with the best available hadronic interaction models, there is still significant uncertainty in simulating the flux, which is reflected in data-simulation discrepancies at the Near Detector. While data-simulation agreement at the Near Detector is not required for the oscillation measurement, the data is much easier to analyze if the flux simulation can be tuned to better describe the observed spectrum. The flux is warped as a function of the properties of the neutrino parents as they leave the target. The warping is determined using a simultaneous fit to multiple beam configurations including standard low energy, horn off (i.e. no focusing), pseudo-medium energy, pseudo-high energy, and runs with varying horn currents at those target positions. Running in these different modes allows the Near Detector data to sample different regions of the pT −pZ space, allowing for a better tuning to the underlying hadron production. Both neutrino and antineutrino samples are used, but the antineutrino sample, coming from unfocused neck-to-neck parents, changes little between configurations. So, to better constrain antineutrino production, the pion charge ratio is constrained to the measurement at NA49 [124]. Data-simulation discrepancies as large as 30% in the high-energy tail are brought into good agreement, as can be seen in the focused neutrino spectra in Figure 3.13 and in the unfocused antineutrino spectrum in Figure 3.14. Even so, the flux tuning has been shown to have little impact on the final oscillation analysis since the uncertainties in the flux cancel in the Near-to-Far extrapolation.
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Figure 3.14: The Near Detector ¯νµ spectrum, in data (black), raw simulation (blue), and flux-tuned sim- ulation (red). The flux tuning, constrained by the NA49 pion charge ratio, significantly improves the data-simulation.