Constraining Muon Internal Bremsstrahlung as a Contribution to the MiniBooNE Low Energy Excess
Using a cleanly tagged data sample of charged current events, it is demonstrated that the rate at which such events are mis-identified as ’s is accurately simulated in the MiniBooNE analysis. Such mis-identification, which could arise from muon internal bremsstrahlung, is decisively ruled out as a source of the low energy electron-like events reported in the MiniBooNE search for oscillations. This refutes the conclusions of a recent paper which postulates that hard bremsstrahlung could form a substantial background to the MiniBooNE sample.
The MiniBooNE Collaboration has reported the results of a search for oscillations at eV. In this search, no significant excess of events was observed above background for reconstructed neutrino energies above 475 MeV, but excess events were reported between 300 and 475 MeV . The data are not consistent with two-neutrino oscillations and the source of the excess is, at present, undetermined.
A recent paper  suggests that the source of the low energy excess is muon internal bremsstrahlung associated with the charged current quasi-elastic (CCQE) interaction, , as depicted in Fig 1. The issue of bremsstrahlung of muon neutrino CCQE events was raised in an earlier paper  and brought to MiniBooNE’s attention in the course of the oscillation analysis , prompting the study presented here.
Reference  asserts that events can be mis-classified as CCQE signal events if the final state muon is below erenkov threshold, since the radiated photon may imitate a final state electron. Even when the muon escapes direct detection, however, its presence may be revealed by the Michel electron from the muon decay. Making use of this Michel electron tag, the present paper demonstrates that the misidentification of events caused by muon internal bremsstrahlung cannot be the source of the observed low energy excess and is not a significant background to the MiniBooNE oscillation search. Rather than relying on Monte Carlo simulation of this process, data are used to directly constrain the contribution of the muon bremsstrahlung diagram. The study was conducted prior to the unblinding of the data for the oscillation analysis and the results were incorporated into the estimated backgrounds at that time. Because the study showed that the background to the oscillation analysis from muon internal bremsstrahlung was extremely small, it was deemed unnecessary to add such internal radiative effects to the simulation. The analysis makes use of an event sample in which the presence of a muon is tagged strictly by the presence of the Michel electron from the decay of the muon:
The MiniBooNE detector and trigger  are particularly well suited for such identification. The MiniBooNE trigger creates a 19.2 s time window surrounding the 1.6 s beam spill. When events are reconstructed, periods of time in which light is produced in the tank are identified as “subevents”. Subevents are separated by looking for gaps between PMT hit times larger than 10 ns, and are typically 100 ns in length.
In 82% of the cases where a muon is contained in the detector, a second subevent from the Michel electron is produced. The 18% without a second subevent splits into 8% that result from capture in oil (this rate has been separately measured ), 2% where simulation predicts the Michel electron creates too few PMT hits to be clearly seen (10 hit PMTs), and 8% where the muon decays sufficiently quickly that the decay cannot be time-resolved from the initial interaction.
To study the rate at which charged current interactions are mis-identified as ’s, events with two subevents are first selected. The two subevents must be separated by at least 1500 ns to avoid any instrumental effects causing the second subevent. No cuts are placed on the first subevent, but the second subevent must have fewer than 6 veto hits to ensure containment and reject cosmic muons and fewer than 200 main tank hits to ensure an energy consistent with a Michel electron. Having created, in this way, a sample of events tagged as being from a charged current interaction, the second subevent and its hits are discarded. The full set of selection cuts, identical to those used in the oscillation result, are then applied to this artificial one subevent sample. The resulting sample is a direct, in situ measurement of the bulk of the charged current contribution to the background in the sample, including that from muon internal bremsstrahlung. The only charged current background component this measurement misses is that due to muon decay so rapid that the Michel electron cannot be time separated from the parent muon. This background is constrained and checked in other ways.
The selection cuts  include precuts to isolate a clean neutrino event sample: the event must have just one subevent within the 1.6 s beam window and have fewer than 6 veto hits to remove incoming cosmic rays and exiting muons from neutrino events in the detector. Each event must also have more than 200 tank hits to reject Michel electrons from stopped cosmic rays which can enter the tank prior to the trigger window and therefore avoid the veto.
After the precuts, the same “track-based” algorithm used in the oscillation analysis  reconstructs the vertex position, angle, energy, and time of the event, assuming the light comes from an extended, straight line source. The vertex and projected track endpoint must lie within the fiducial volume of the detector and the visible energy in the tank must be MeV.
Events are identified as CCQE based on likelihoods which are built from phototube charge and time probability distribution functions. For each event, using a single-track hypothesis, the likelihood is calculated that it is an electron () or a muon (). The event is then reconstructed under a two track hypothesis, where the invariant mass is forced to be 135 MeV, and a likelihood () is formed. Finally, the event is reconstructed by finding the best two track fit allowing the invariant mass to float. This yields a best-fit mass (). Visible energy-dependent cuts on , and are then applied to isolate a CCQE signal sample. The neutrino energy is then determined using the reconstructed lepton energy and direction and assuming the interaction is CCQE.
Fig. 2 shows the spectrum of the originally-published candidate sample subject to this selection . The excess of events between 300 and 475 MeV is clearly visible. Fig. 3 shows the results of the same cuts applied to the tagged data sample. In this case, the normalization has been adjusted to correct for the Monte Carlo determined rates of one subevent and two subevent charged current interactions and for the requirement that the two subevents be separated by more than 1500 ns. Fig. 3 is therefore a direct prediction and measurement of the charged current contribution to Fig. 2. The Monte Carlo prediction for the rate at which these processes pass the selection agrees well with the data. Furthermore, the abscissa of these two figures shows that charged current processes account for only a tiny fraction of the background in Fig. 2. Muon internal bremsstrahlung (or any charged current process that can lead to muon decay at rest) therefore cannot be the source of the low energy data excess.
Muon bremsstrahlung events should be efficiently rejected by the selection. Muon tracks are considerably longer than electron tracks for the same visible energy in the MiniBooNE detector. For events where the muon energy lies above erenkov threshold, the additional track length leads to a significantly different charge and hit structure, particularly in the center of the erenkov ring. One would therefore expect the presence of the muon to pull the charge and time likelihoods of the events away from an “electron-like” hypothesis.
In this paper, charged current events are identified through the presence of a Michel electron and then subjected to the MiniBooNE oscillation analysis cuts. The rate of misidentification of these events as ’s is accurately modeled by the Monte Carlo and is not the source of the low energy excess in MiniBooNE.
It should be noted that this study says nothing about the total rate of muon internal bremsstrahlung in MiniBooNE, just the rate at which this process occurs in the sample. It may be possible to relax or adjust the selection cuts to make a measurement of muon internal bremsstrahlung at some time in the future.
Acknowledgements.We acknowledge the support of Fermilab, the Department of Energy, and the National Science Foundation in the construction, operation, and data analysis of the MiniBooNE experiment.
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