Simulation

72 The MINOS Experiment

Chapter 4

An Oscillation Analysis in Brief

All oscillation analyses in MINOS follow the same basic structure. Everything begins with a signal in the detector: light in the scintillator strips. The light is amplified by photomultiplier tubes, digitized by the front-end electronics, and becomes a single ‘hit.’ The reconstruction algorithm then groups many hits together in space and time to produce ‘tracks’ (typically muons) and ‘showers.’

Tracks and showers that share a vertex are then grouped together into a neutrino ‘event.’

There are a number of classes of beam-induced events that occur in the detectors: charged- current (CC) νµ and ¯νµ, neutral current (NC), CC νe and ¯νe (both inherent in the beam and a possible appearance signal), and CCντ and ¯ντ (only at the Far Detector).¹ Each oscillation analysis is focused on looking for changes between the event samples in the the Near and Far Detectors. The first step in any analysis, then, is to select as pure a sample as possible of the event class of interest.

Here, the signal sample is CC ¯νµ’s, whose main backgrounds are CCνµ’s and NC’s.

Once a sample has been selected (many more details on that process are given in Sections 5.1 and 6.1), the event energies are required. The energy of a CC neutrino event is estimated by summing the shower energy, measured via calorimetry, and the track energy, measured via the range the muon travels or the amount it curves in the detector (more details are given in Section 3.4). These energy measurements are collected together to form Near and Far Detector energy spectra. While closely related, these two spectra are not identical. In addition to having lower statistics because of being further away from the neutrino source, the Far Detector also has spectral differences related to a combination of the geometry of the beamline and the kinematics of the meson decays that produce the neutrinos (see Section 5.3).

The Monte Carlo simulation is used to account for these Near-to-Far differences, converting the measured Near Detector spectrum to a ‘prediction’ of what the Far Detector spectrum would look like with any arbitrary choice of oscillation parameters. This process is called extrapolation.

1All these event categories are also produced by neutrinos produced by cosmic rays in the atmosphere, but these can be effectively eliminated by selecting only events in-time with the beam ‘spill triggers,’ which account for less than 0.01% of the Far Detector live time. The average rate of atmospheric neutrino interactions is less than half that of beam neutrinos.

74 An Oscillation Analysis in Brief Since these Far Detector predictions are based on the Near Detector spectrum, cross section and flux systematics largely cancel.² Take, for example, a systematic error in the simulation’s neutrino interaction cross section; say it is high by 10%. With only one detector there would appear to be a 10% deficit of neutrinos. With two detectors, however, the simulation is only required to convert the measured Near Detector data into a Far Detector prediction. Since neutrinos interact in both detectors using the same cross section, they will both be 10% high but therelativenumber of events expected at the Far Detector for a given number of events in the Near Detector remains unchanged.

The systematic has been ‘cancelled out’ in the extrapolation process – this is the power of the two-detector design.

Since the prediction can be produced for any arbitrary set of oscillation parameters, those param- eters can be varied to find the values that best fit the data. In practice, a search is performed over the possible oscillation parameters to find the ones that maximize the likelihood of the observed data spectrum given the prediction. Then, starting from the best fit parameters, a two-dimensional confi- dence interval (contour) can be drawn showing how the data constrain the values of the parameters.

For more details, see Sections 5.6, 5.7, and 6.5.

2Given the spectral differences mentioned above, the systematics do not cancel completely, but their effects can be estimated and are small. See Sections 5.4 and 6.3.

Chapter 5

Antineutrinos in a Neutrino Beam

The first 7.2×10²⁰ POT of data was taken with the NuMI beamline running in neutrino mode as described in Section 3.1.1. However, the neutrino-mode beam has a small (approximately 7%) component of antineutrinos. Two measurements were made with the antineutrinos from the first 3.2×10²⁰ POT of running: one looking for antineutrino oscillations via disappearance, and one looking for neutrino-to-antineutrino transitions via antineutrino appearance.¹ The disappearance analysis measures the|∆m²atm|and sin²(2¯θ23) parameters from the oscillation survival probability:

P(¯νµ→ν¯µ) = 1−sin²(2¯θ23) sin²

∆m²atm

L 4E

(5.1)

Figure 5.1: Simulated Far Detector reconstructed energy spectrum showing the effect of transitions with α= 0.12 and oscillations with|∆m²_atm|= 5.65×10⁻³eV² and sin²(2¯θ₂₃) = 1. The values chosen correspond to the lowest parameter values with measurable effects at 99% CL.

1I performed the neutrino-to-antineutrino transition analysis.

76 Antineutrinos in a Neutrino Beam

pZ

0 20 40 60 80 100 120

Tp

0 0.2 0.4 0.6 0.8 1

0 100000 200000 300000 400000 500000

target at +10cm horn at 185kA

ν

µ

→ π

+

[GeV/c]

T

p

[GeV/c]

p

Z MINOS Preliminary

pZ

0 20 40 60 80 100 120

Tp

0 0.2 0.4 0.6 0.8 1

0 5000 10000 15000 20000 25000 30000 35000 40000 45000

target at +10cm horn at 185kA

ν

µ

→ π

-

[GeV/c]

T

p

[GeV/c]

p

Z MINOS Preliminary

Figure 5.2: The pT vs. pZ distribution of theπ^± parents that produce neutrinos (left) and antineutrinos (right) at the Near Detector when the beam is in low-energy neutrino-mode mode. The unfocused component has a broad range ofpZ, and hence total momentum, producing the diffuse high-energy tail.

where Lis the baseline over which the oscillations occur and E is the energy of the neutrino. The appearance analysis constrains the possibility that some fraction, α, of the neutrinos that MINOS has observed to disappear are actually transitioning to antineutrinos:

P(νµ →ν¯µ) =αsin²(2θ23) sin²

∆m²atm

L 4E

(5.2) which would be visible as an anomalous low-energy peak in the antineutrino spectrum. A simulated example of each of these signals is shown in Figure 5.1.

Antineutrinos are produced in the decays of pions produced by colliding primary protons with the graphite target.

p+ C→π⁻+ X (5.3)

π⁻ →µ⁻+ ¯νµ (5.4)

The antineutrinos in the neutrino-mode beam come primarily from low-pT pions leaving the target headed directly down the axis of the beamline and thus avoid being defocused. These “neck-to-neck”

pions, so-called since they pass directly through the necks of both horns, are unaffected by the horn magnetic fields. Without the momentum-selecting benefit of focusing, the antineutrinos are left with a broader spectrum with a higher peak energy than the neutrinos (7 GeV instead of 3 GeV). A comparison of the neutrino and antineutrino parents’pT−pZdistributions can be seen in Figure 5.2.