A measurement of muon neutrino disappearance with the MINOS detectors and NuMI beam

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Summary

A measurement of muon neutrino disappearance with

• The MINOS detectors and NuMI beam Publication No. Rustem Ospanov, Ph.D. The University of Texas at Austin, 2008 Supervisor: Karol Lang MINOS is a long-baseline two-detector neutrino oscillation experiment that uses a high intensity muon neutrino beam to investigate the phenomena of neutrino oscillations.
• The neutrino beam is produced by the NuMI facility at Fermilab, Batavia, Illinois, and is observed at near and far detectors placed 734 km apart.
• The neutrino interactions in the near detector are used to measure the initial muon neutrino flux.
• The vast majority of neutrinos travel through the near detector and Earth matter without interactions.
• This thesis presents a measurement of the muon neutrino oscillation parameters in the framework of the two-neutrino oscillation hypothesis.

1.1 A brief history of neutrinos

• In 1914, James Chadwick showed that a spectrum of electrons emitted in the β-decays is continuous [1]: N → X + e−, where N and X stand for the initial and final nucleus states.
• The β-decays are now used to set a limit on the mass of the emitted neutrino by accurately measuring electron momentum and nuclear recoil energy.
• In the 1960s, Davis used this reaction for the first time to detect neutrinos produced in the sun [9].
• In 1964, Murray Gell-Mann and George Zweig proposed the idea that this family of particles4, which included pions and protons but not leptons, is composed of even more elementary constituents called quarks.
• The theory predicted the existence of the heavy gauge bosons, W± and Z0, which mediate charged-current (CC) and neutral-current (NC) interactions.

1.2 Theory of neutrino oscillations

• The Standard Model describes all existing data on the weak, electro- magnetic and strong interactions [5].
• There are no experimental measurements to suggest a lepton number violation for the charged leptons [5].
• 6See Reference [23] for a comprehensive review of different scenarios.
• Experimental data suggest two very different scales for the mass differences squared, ∆m232 ∆m212.

1.3 Experimental evidence for neutrino oscillations

• Neutrino oscillations are investigated using an intense source of neutri- nos and a large neutrino detector.
• Neutrino oscillation experiments compare a number of neutrino interactions in the detector with an expected interaction rate, assuming that neutrinos travel directly from the source to the detector without oscillations.
• A detailed understanding of the neutrino source is required to compute the expected interaction rate.
• For neutrinos produced by the sun or cosmic rays, computation of the predicted rate presents a complex experimental and theoretical problem.
• Man-made sources of neutrinos are 12 easier to understand, but they generate less intense neutrino fluxes.

1.3.1 Electron neutrinos from the sun

• A first hint of neutrino oscillations came from the radiochemical exper- iment at Homestake Gold Mine, South Dakota, led by Davis.
• Through this period the experiment measured a consistent rate of argon capture, and the final result for the production of argon atoms per day was 2.56±0.16(stat)±0.16(syst) SNU (1 SNU = 1 Solar Neutrino Unit = 1 capture per second and per 1,036 target atoms).
• The sun generates energy via the nuclear conversion reaction, which schematically is expressed as: 4p →4 He + 2e+ + 2νe (1.14) Two neutrino are produced in each fusion reaction.
• New experiments were constructed to study the electron neutrinos pro- duced by the sun.
• The Kamiokande detector was built in the late 1980s.

1.3.2 Electron anti-neutrinos from nuclear reactors

• A remarkable confirmation of the solar neutrino oscillation hypothesis was carried out by the Kamioka Liquid-scintillator Anti-Neutrino Detector .
• This experiment observes interactions of electron anti-neutrinos through the inverse β-decay reaction: ν̄e + p → e+ + n (1.16) The positron deposits energy in the scintillator and then annihilates.
• The average distance between KamLAND and the reactors is 180 km.
• In addition, Bugey [37], Palo Verde [38], and CHOOZ [39] collabora- 20 tions searched for neutrino oscillations using reactor nuclear plants as a source of electron anti-neutrinos.

1.3.3 Atmospheric neutrinos

• In the 1990s, several deep underground neutrino experiments measured fluxes of atmospheric neutrinos.
• The underground detectors measured the ratio of muon neutrinos to electron neutrinos, R = Nνµ+Nν̄µ Nνe+Nν̄e , for neutrino energies of few GeV.
• The distance L is a reconstructed distance from the detector to the point in the Earth’s atmosphere where the muon neutrino was produced.
• The recent MINOS result [46] disfavors these two models compared to the neutrino oscillation hypothesis.

1.3.4 Man-made muon neutrino beams

• The first man-made, neutrino beam was constructed at Brookhaven, Upton, New York.
• Neutrino beam facilities were later constructed at CERN, Fermilab, KEK, Los Alamos, and Serpukhov, where they were utilized to study weak interactions.
• In the early 1990s, atmospheric neutrino experiments provided the first hints for the muon neutrino oscillations with L/E around 400 km/GeV (∆m2 ≈ 10−3eV2).
• A chief advantage of the man-made neutrino beams is the significant reduction of systematic errors in the measurement of the neutrino oscillation parameters.
• A smaller (near) detector is placed very close to the neutrino source, and a larger (far) detector is placed a few hundred km away from the neutrino source.

1.4 Summary of neutrino oscillations

• Experimental data provide compelling evidence that neutrinos do os- cillate between three mass states.
• The values of the mass differences among these states are illustrated in Figure 1.8.
• These experiments do not tell us which of these two oscillation scenarios is realized in Nature.
• The atmospheric, accelerator, and reactor neutrino data are consistent with pure νµ → ντ oscillations with |∆m2| = 2.44 × 10−3eV2.
• The MINOS experiment provides the most precise current measurement of |∆m2| [46].

1.5 Outline of the dissertation

• This dissertation presents a measurement of muon neutrino disappear- ance using the MINOS detectors and NuMI neutrino beam.
• The detectors and beamline facility are briefly discussed in Chapter 2.
• This near detector analysis computes corrections to neutrino flux and cross-section models.
• These corrections are used in Chapter 8 to compute a predicted event rate at the far detector assuming there are no oscillations.
• 29 Chapter 2 NuMI facility and detectors The Main Injector Neutrino Oscillation Search experiment [52] is a two-detector neutrino experiment that uses an intense muon neutrino beam to study neutrino oscillations.

2.2 NuMI facility

• The NuMI is a neutrino beamline facility [53,57,58] constructed at the Fermi National Accelerator Laboratory in Batavia, Illinois.
• The horns are pulsed simultaneously with a proton pulse reaching a 200 kA peak current and generating a maximum 30 kG magnetic field.
• 34 35 The transport line from the Main Injector to the target is instrumented with beam position monitors and beam profile monitors.
• The accepted window was defined to select proton pulses with charatestics as similar as possible to the NuMI design specifications.
• Figure 2.5 shows the contributions to the predicted MC neutrino spec- trum at the near detector from the pion and kaon decays for different beam configurations.

2.3 MINOS detectors

• MINOS consists of two iron and scintillator detectors designed as hadronic sampling calorimeters with a muon tracking capability.
• Fully instrumented planes contain 96 scintillator strips connected to two PMTs.
• This detector was exposed to test beams at CERN, and the results of the tests showed that a calibrated response of the near and far detector readout systems are equal [65].
• The near detector electronics [66] continuously record signals from 44 all detector channels during a neutrino beam spill.
• 45 The near detector DAQ permanently records all detector hits within a spill window without any preconditions.

2.4 Detector calibration

• A precise measurement of the oscillation parameters requires accurate calibration of two spatially separated detectors.
• In the far detector, the attenution corrections vary by approximately 30% for an 8 m scintillator strip (for a sum of signals from both strip-ends).
• 52 Chapter 3 Neutrino interactions in the MINOS detectors.
• These detectors hits are examined using reconstruction algorithms for patterns that match muon tracks and hadronic cascades .
• In Section 3.6, detector hits from the data and MC simulation are examined to validate the MC simulation.

3.1 Event reconstruction

• The event reconstruction procedure uses the topology and timing of de- tector hits to identify neutrino interactions inside the detector or surrounding rock.
• The uncertainty of the muon momentum measurement via curvature is estimated using the stopping muon tracks by comparing the muon momentum via the range with the muon momentum via curvature.
• Reconstructed showers and tracks are assigned 56 to a reconstructed event based on the start position of the track and shower and the timing of the track and shower hits.
• The vertex positions of the selected νµ charged-current events for the data and MC simulation are shown in Figures 3.2 and 3.3 for the near and far detectors, respectively.
• In the far detector, a demultiplexing algorithm identifies which of the eight possible scintillator strips are associated with each far detector hit [77].

3.2 Charged-current muon neutrino interactions

• The total νµ charged-current cross-section includes contributions from three processes2: quasielastic scattering (QES), resonance production (RES), 1100 ADC ≈ 1 photoelectron.
• Figure 3.9 shows a typi- cal reconstructed QES event.
• The absence of the visible hadronic energy is an efficient signature of the QES events in the MINOS detectors [80].
• RES interactions produce muons and baryon resonances.
• These interactions can change the multiplicity and the particle type of the hadrons produced in neutrino interactions.

3.3 Selection of QES, RES, and DIS events

• A method to select QES, RES, and DIS events is devel- oped, using events from the Monte-Carlo simulation.
• The QES and RES events can be used to measure precisely the shape of the neutrino energy spectrum, as discussed in Chapter 9.
• The protons and pions, with momenta around 1 GeV, were observed to produce only a few detector hits [72].
• The three categories of events are defined using reconstructed variables; each category is enriched with either QES, RES, or DIS events.
• Approximately 40% of the QES events have no reconstructed hadronic energy.

3.4 Energy reconstruction in QES, RES, and DIS events

• The reconstructed event energy is examined for QES, RES, and DIS events, using events from the Monte-Carlo simulation.
• The true values are generated by the MC simulation.
• 79 Figure 3.18 shows the energy resolution computed for the true QES, RES, and DIS events .
• If the nuclear effects are ignored, the QES interaction is a two-body scattering process; this is illustrated in Figure 3.9.
• The standard method estimates the neutrino energy as the sum of hadronic shower energy and muon energy.

3.5 Monte-Carlo simulation

• The MC simulation of the MINOS experiment is used to develop anal- ysis methods and to compute a predicted event rate the far detector.
• The neutrino interactions in the MINOS detectors are modeled using the NEUGEN neutrino event generator [78].
• Final state leptons are allowed to leave the target nucleus without addi- tional interactions and are passed directly to the detector simulation.
• The secondary particles produced in these interactions are traced through the realistic model of the MINOS detectors, 85 including the effects of the magnetic field.
• The energy depositions within the active detector elements (scintillator strips) are passed to the MC simulation of the detector response.

3.6 Study of near detector hits in the data and MC

• This section compares a number of neutrino induced hits in the near detector data and the MC simulation.
• This effect was first observed in 2005 when it was noticed that the near detector channels for a few percent of the hits record an additional hit following the earlier hit in the same channel.
• These two figures do not include hits from the channels that have 8 or more hits in a single spill; the hits from these channels are shown in Figures 3.22b and 3.22d.
• The number of high signal hits agrees with the MC simulation.

3.7 Summary

• This chapter opened with the description of the event reconstruction and followed with the discussion of the νµ charged-current interactions in the MINOS detectors.
• The absolute QES and RES cross-sections are constrained by the previous neutrino experiments, but the normalization uncertainties are greater than the statistical precision of the MINOS near detector data.
• A simple method was developed to select QES, RES, and DIS events.
• The MC simulation is used to develop analysis techniques and to compute a prediction for the νµ charged-current event rate at the far detector without oscillations.
• These events are identified by the observation of a muon track.

4.1 Reconstructed muon and non-muon tracks

• This section provides a framework for the subsequent analysis of recon- structed muon and non-muon tracks in the MINOS detectors.
• In the MC simulation, each energy deposit is tagged with a unique code for the particle associated with that energy deposit.
• First, only tracks that have at least 5 scintillator plane hits in each detector view were considered.
• Qualitative observations of the true νµ charged- 100 current events that fail this requirement indicate that these muon tracks are obscured by the associated hadronic shower.
• The second preselection requires that a track vertex (see Section 3.1 for a definition) is contained within the fiducial volume of the detector.

4.2 Improving sensitivity to muon tracks

• In these interactions, the muons are produced in association with the hadronic shower.
• Figure 4.1 shows a νµ charged-current event and neutralcurrent events that contain a reconstructed track.
• Figure 4.2 shows the mean pulse height of track segments plotted as a function of the track length.
• Removing the hadronic shower hits closest to the track vertex might improve a muon identification algorithm.
• All available parameters were varied in this fashion to minimize the figure of merit for the three variables described in Section 4.3.

4.3 Track based muon identification variables

• Four variables were constructed to distinguish muon tracks from non- muon tracks.
• The pattern of the muon energy loss in the scintillator strips provides another muon track signature.
• These four figures are discussed in the following four subsections.
• A variable sensitive to this signature was developed [95].
• All histograms were normalized to the unit area.

4.3.1 Number of track scintillator planes

• The number of track scintillator planes is plotted in Figure 4.4.
• This variable is proportional to the length of the muon track within the detector.
• First, a multidimensional likelihood method (described in Section 4.4) is employed for an event classification; this method compares reconstructed tracks of a similar length.
• Second, a muon carries only a fraction of the total reconstructed neutrino energy, where the fraction is determined planes is used.

4.3.2 Mean pulse height of track hits

• The mean pulse height of track hits measures the average energy loss in the MINOS scintillator strips.
• This variable is computed using hits located away from the track vertex.
• The above-mentioned optimization procedure was used to determine the fraction of the excluded planes.
• The mean pulse height variable is computed as follows: Exclude 30% of the track scintillator planes closest to the track vertex; Compute the mean pulse height of the track hits in the remaining scin- tillator planes.
• Events with large energy depositions by muons are infrequent; thus, this variable has a narrow distribution for the muon tracks.

4.3.3 Signal fluctuation

• The third variable, Rf , measures fluctuations in the energy deposited in the MINOS scintillator strips.
• The signal fluctuation variable is computed as follows: Exclude 30% of the track scintillator planes closest to the track vertex; .
• Sort the selected hits in ascending order by pulse height.
• The fraction where the two parts are divided is a tunable parameter used for the sensitivity optimization procedure; Compute the mean of the low pulse height hits and the mean of the high pulse height hits.
• The peak of the muon distribution is located on the right of the peak of the non-muon distribution.

4.3.4 Transverse track profile

• The fourth variable is the transverse track profile, Rt. A scintillator plane is made from closely packed 4.1 cm wide scintillator strips.
• A typical hadronic shower has a transverse profile a few strips wide, so it deposits energy in multiple 111 112 strips within one scintillator plane [72].
• The following three adjustable parameters determine this variable: (a) the fraction of the excluded planes; (b) the number of strips in the window around a track; (c) the time span of the window around a track.
• In the remaining scintillator planes with track hits, select all detector hits, Salli , that fall within a 4 strip window and within a 37.36 ns time window around the track hits, Strackj , including hits that belong to the track.
• The transverse track profile variable is the ratio of the track signal over the signal of all the selected hits: Rt = ∑M j=1 S track j ∑N i=1 S all i , (4.2) where Strackj is the pulse height of the track hits, and S all i is the pulse height of all the selected hits (including track hits).

4.4 Event classification with the k-nearest neighbor al-

• Gorithm A typical classification problem has two classes: signal and background.
• The knn algorithm uses a training set to estimate a density for the sig- nal and background events in a small neighborhood around the query event.
• A value of k determines the average size of the neighborhood over which probability density functions are evaluated.
• For their analysis, the number of the muon tracks included within the training set was reduced to match the number of non-muon tracks for the following two reasons.
• This search algorithm requires 3The code developed for the knn algorithm was contributed to the TMVA project [97].

4.5 Identification of muon neutrino charged-current events

• Reconstructed events in the MINOS detectors are classified using in- formation from a reconstructed track.
• Both νµ charged-current and ν̄µ charged-current interactions are included into one category since the track classification variables do not distinguish between µ+ and µ− tracks.
• For the far detector, the training set contains 163,838 muon tracks and an equal number of non-muon tracks.
• The discriminant variable is shown in Figure 4.10 for the near detector and in Figure 8.6 for the far detector.
• Figure 4.11 shows the selection efficiency and the background rejection; these two quantities do not depend on k, for k = 20, 60, 100.

4.6 A study of event selection for several beam config-

• The energy dependence of the muon selection efficiency is examined.
• The MC events used to create a training set are generated using the MC simulation of the low energy beam configuration.
• The classification algorithm includes the number of planes variable, which depends on muon momentum.
• Figure 4.12 shows the efficiency and purity (defined in Section 3.3) for the three beam configurations.
• The purity for the high energy beam is lower, because the number of neutral-current background events from the high energy tail is increased.

4.7 Comparison of muon tracks for data and MC

• The excess of low pulse height hits in the near detector data (see Sec- tion 3.6) implies differences between the data and MC simulation in topology and pulse height of detector hits.
• This section evaluates a systematic error resulting from the excess of low pulse height hits.
• This algorithm uses hits with pulse heights greater than 2 photoelectrons to create track clusters; this requirement significantly reduces the dependence of the track finding algorithm on low pulse height hits.
• The number of the selected νµ chargedcurrent data events is greater than the number of MC events, consistent with the results of tuning muon neutrino flux and cross-sections models in Chapter 7.
• A fraction of events that pass the original method and fail the modified method, and vice versa, is consistent with both the data and the MC simu- 128 129 130 lation.

4.8 Summary

• A new method to the select νµ charged-current and ν̄µ charged-current events in the MINOS detectors was introduced.
• This method uses the k-nearest neighbor algorithm and the four track based variables.
• The 131 selected νµ charged-current events at the far detector include the estimated 0.6% background contamination from the neutral-current interactions [46].
• The near and far detectors have a similar response to physical detector hits, so these results are appliacable to far detector analysis.
• It is shown that this variable is sensitive to the muon charge sign and that it reduces a number of the background νµ charged-current events, among the selected ν̄µ charged-current events.

5.1 Charge-sign measurement using fitting algorithm

• The MINOS detectors are muon tracking detectors; muons leave visi- ble tracks in the detectors, as illustrated in Figure 4.1.
• The track finding and track fitting algorithms are described in Section 3.1.
• The first two variables are computed together as the q/p ratio.
• For some tracks, the q/p ratio cannot be unambiguously computed; such tracks are assigned a “failed fit” 134 135 flag.
• The fitting algorithm correctly determines the muon charge sign for a majority of reconstructed tracks.

5.2 New method for charge-sign measurement

• The selection of the ν̄µ charged-current events requires an efficient mea- surement of the muon charge sign.
• An improved method for the measurement of the muon charge sign is described.
• The majority of the µ− tracks move toward the coil, where many of these tracks stop.
• The muon direction at the track vertex is determined by the track fitting algorithm.
• These two variables are plotted in Figure 5.6.

5.3 Charge-sign for non-muon tracks

• It is interesting to note that the curvature of the non-muon tracks does not depend on the magnetic field.
• Figure 5.9 shows the azimuthal angle φ and the polar radius for the muon and non-muon tracks, and Figure 5.9 shows these variables for the π− and π+ tracks.
• The non-muon tracks do not experience significant deflections in the magnetic field.
• For these tracks, the 143 deflections are independent of the charge sign.
• Figure 4.4 shows a number of track planes for the non-muon tracks; these tracks are typically very short and do not have a sufficient number of hits to measure the track curvature.

5.4 Selecting muon neutrino and anti-neutrino events

• In this section a new charge-sign method is examined using the MC simulation.
• The standard charge-sign selection uses the q/p variable computed by the track fitting algorithm for the reconstructed track in the event.
• It was implemented to remove tracks with errors measuring the q/p value.
• Figure 5.11b shows the true ν̄µ charged-current events.
• The conclusion is that the new charge-sign method does not affect the selection of the νµ charged-current events.

5.5 Summary

• A new and improved method for the measurement of the muon charge sign in the MINOS detectors was introduced.
• This selection can be further improved by requiring that the tracks contain at least 20 hits in each detector view.
• This work resulted in an improved understanding of the magnetic field in the MINOS detectors and reduced the systematic error for the measurement of the muon momentum from the curvature.
• Initial observations show substantial disagreements between the data and MC simulation.
• In Section 6.3, the νµ charged-current events in the near detector are examined.

6.1 Calibration of the near detector magnetic field

• The near detector magnetic field is calibrated using muon tracks.
• The procedure takes into account effects from 1The track fitting algorithm used in this section was developed by Sergei Avvakumov and it is based on techniques described in [102].
• A comparison of the muon momentum from the range, Prange, with the muon momentum from the curvature, Pcurv, provides a tool for the calibration of the magnetic field strength in the near detector.
• For the old magnetic field map, there is an approximately 5% shift between the data and MC simulation.
• This observation prompted an investigation of the magnetic field properties in the near detector and far detectors; this work produced the new magnetic field maps, discussed earlier.

6.2 Selecting near detector events

• The reconstructed events are required to contain at least one recon- structed track to be selected for their analysis.
• This fiducial volume was adopted to minimize reconstruction errors and improve the measurement of event energy [103].
• The νµ charged-current events can be further subdivided into the QES, RES, and DIS events using the technique developed in Section 3.3.
• This se- lection method can be altered by changing the selection requirements listed in Table 6.1.
• A complete analysis of the near detector data is performed for each of the nine additional sets of events.

6.3 Near detector data

• The authors analysis uses all the near detector data recorded between May 2005 and July 2007.
• These figures show events from the Run I and Run II data, recorded in the low energy beam configuration.
• This fact suggests that in this energy region the neutrino cross-sections are not correctly modeled.
• The agreement between the data and the MC simulation significantly improved after the tuning, especially for the invariant mass squared variable that is used to select the RES events.
• The reconstructed energy spectra for the selected QES, RES, and DIS events are shown in Figures 6.11 and 6.13.

6.4 Summary

• This chapter examined the near detector νµ charged-current events.
• The near detector data are utilized to compute this prediction.
• This usage of the MINOS near detector data results in a partial cancellation of systematic errors from the incorrect modeling of the detector, neutrino flux, and cross-sections, as well as the mismeasurement of event observables [58].
• The present analysis uses a tuning method.
• These events are separated into three categories, using the technique described in Chapter 3.

7.2 Parameterization of the cross-section model

• The neutrino interaction rate in the detector is a function of the product of the neutrino flux and cross-section.
• The ν̄µ charged-current events are dominated by DIS events.
• The three separate scale factors for the QES, RES, and DIS events measure the energy scale uncertainty for different regions of neutrino energy.
• The 6 tuning parameters are summarized in Table 7.1, where the last column lists the uncertainty of these parameters.
• In addition, their results indicate that simple scale factors for the normalization of the QES and RES events are sufficient to describe the near detector data.

7.3 Fit description and χ2 function

• This section briefly describes the fit procedure (fit) used to minimize the differences between the data and MC simulation.
• The χ2 function depends on the flux and cross-section parameters via the MC event importance weights.
• The weights of data events are always set to unity.
• The fit is an iterative procedure consisting of these steps: Step 1 Compute the MC event weights using the current tuning parameters.
• Fill the histograms with the MC and data events.

7.4 Kernel method and χ2 function

• The χ2 function is a different function of the energy scale and all other parameters, and this difference affects a minimization procedure.
• The energy scale parameters change reconstructed event energy.
• A discontinuous χ2 function presents a problem for the MINUIT program because MINUIT searches for a minimum by following a gradient descent.
• This method introduces a finite event width so that one event can contribute some weight to multiple histogram bins.
• The kernel smoothing method uses the “kernel” function.

7.5 Tuning results

• This section presents results of the near detector fits.
• These tables show the χ2 values and the number of events before (default MC) and after tuning (tuned MC).
• The number of true RES events is scaled down by approximately 13%.
• The additional systematic errors for these two parameters are discussed in Section 7.6.
• Figures 6.11 and 6.13 show the reconstructed energy for the selected QES, RES, and DIS events for the data and tuned MC simulation.

7.6 Study of different fit approaches

• The fit parameters listed in Table 7.4 are the corrections for the MC simulation.
• The average interaction probability of the secondary pions with the nucleus was increased by approximately 8% [110, 111].
• For the previous MC version, the QES scale factor is 1.48 compared to 1.23 for the current MC version.
• The MC simulation also uses the magnetic field map to simulate the passage of muons through the detector.
• The Eν formula (defined in Equation 3.1) and EQES formula (defined in Equation 3.5) are used to reconstruct the energy of the selected QES events in the data and MC simulation.

7.7 Summary

• The systematic errors from the nuclear effects were estimated: approximately ±0.24 for the QES events, and approximately ±0.11 for the RES events.
• The detector energy scale was adjusted by approximately 2%, within the estimated 5% uncertainty.
• This chapter discusses the differences in the neutrino interaction rate between the near and far detectors.
• The selected νµ charged-current events in the far detector are examined by comparing these events with the expected event distributions.

8.1 Extrapolation from near to far detectors

• The far detector is located 734.3 km away from the near detector.
• The distance and the direction from the neutrino source to the detector determine the rate of neutrino interactions and predict differences between the two detectors.
• Tuning methods use the near detector data to adjust the parameters of the MC simulation.
• The present analysis employs the tuning method, described in Chapter 7.
• The errors on the predicted far detector event rate were determined to be less than 3%, if the near detector data were used to compute this predicted rate [101].

8.2 Selecting far detector events

• The far detector events are selected using the expected arrival time of the neutrino beam spills (see Section 2.3).
• The far detector events, within a 50 µs timing window of the neutrino spill time, are subject to additional analysis cuts.
• The direction of the reconstructed track at the vertex is required to be within 53.1◦ angle with the detector Z axis.
• The two methods predicted less than 0.5 background events for the Run I data [58].

8.3 Far detector data

• The MINOS collaboration follows a blind analysis policy for the far detector events produced by the NuMI neutrino beam.
• This policy was implemented to minimize a potential physicist bias.
• Then, simple event distributions were examined for the entire data set to check for any potential problems [46, 52, 58].
• The present analysis uses the subset of the νµ chargedcurrent events2 selected by the collaboration for the recent measurement of the muon neutrino disappearance [46].

8.4 Summary

• The event selection procedure for the far detector events was described.
• The selection requirements are similar to the requirements for the near detector events, with three exceptions.
• The selected far detector data events are accurately described using the oscillation hypothesis.
• This exposure includes only the data from the low energy beam configuration.
• Assuming there are no neutrino oscillations, the expected number of νµ charged-current events is 910.

9.1 Description of the fit method

• The data events are analyzed using a simple two-neutrino oscillation hypothesis.
• The procedure to select νµ charged-current events removes many ντ charged-current and νe charged-current events because these interactions look similar to background neutral-current events.
• The computation of the χ2 function defined in Equation 9.2 depends on histogram binning for the reconstructed neutrino energy.
• This fit does not separate the DIS events from the QES and RES events.

9.2 Measurement of neutrino oscillations parameters

• The two oscillation parameters, |∆m2| and sin2 2θ, are derived from a fit to the selected νµ charged-current events.
• Figures 9.4 and 9.6 show the ratios of the data spectra and the os- cillated MC spectra to the MC spectra without oscillations as a function of the reconstructed neutrino energy.
• Figure 9.8 shows the allowed 68% C.L. regions for the primary and secondary fit methods.
• The kinematic formula reduces the energy reconstruction bias for the selected QES events.
• This comparison of the two approaches suggests a presence of systematic effect possiblly not modeled by the MC simulation.

9.3 Statistically independent pseudo-experiments

• The fit procedure is tested using MC pseudo-experiments.
• The pseudo-experiments are created following this procedure: 1. Apply the corrections derived in Chapter 7 to all the MC events.
• These oscillation parameters are listed in Table 9.1.
• These pseudo experiments are fitted using the primary and secondary fit methods.

9.4 Treatment of the systematic errors

• The systematic uncertainties can be broadly separated into two cate- gories.
• These 1200 pseudo-experiments are compared to the 100 pseudo-experiments without the systematic uncertainties.
• This set is generated by requiring simultaneous ± shifts for the 6 systematic uncertainties, described above.
• The systematic error of measuring the oscillation parameters is com- puted using differences between two best fit parameters.

9.5 MINOS results

• The oscillation results obtained in this dissertation are compared with the latest published result by the MINOS collaboration [46].
• For the MINOS result, Figure 9.21 shows the reconstructed energy spectrum for the far detector data, the MC prediction without oscillations, and the MC spectrum weighted by the best fit oscillation parameters.
• Two analyses are compatible and have measured the same values for the oscillation parameters.
• The systematic errors measured with the present analysis are larger than the errors for the MINOS analysis.

9.6 Conclusions

• This thesis presented a complete analysis of the MINOS near and far detector data.
• The study of the neutrino interactions in the near detector led to the development of a simple method to identify quasi-elastic, resonance production, and deep inelastic scattering νµ charged-current events.
• The fit to the far detector data was performed using the oscillation hypothesis for the two massive neutrinos.
• The fit gives an excellent description of the data.

Figures

Figure 3.5: Reconstructed shower energy (top), muon momentum (middle), and muon angle (bottom) for the selected νµ charged-current events for the far detector data and MC simulation. The event selection procedure is described in Chapter 8. The MC simulation includes flux and cross-section corrections computed in Chapter 7 and corrections for the neutrino oscillations computed in Chapter 9.

Figure 3.24: Response of the near detector to neutrino beam spills. The figures show the mean signal of detector hits with the signal below (left) and above (right) the signal threshold, as labeled on each plot. The X axis labels use “strips” to stand for hits.

Figure 9.16: Illustrations of the statistical errors for the four sets of pseudoexperiments with several values of the number of protons on target (POT). The figures show the area contained within the 90% C.L. (see Figure 9.15) for one hundred pseudo-experiments at each fixed number of POT. The two fit methods are compared in these figures. The primary fit method is shown with a black line, labeled as “Separate.” The secondary fit method is shown with a red histogram, labeled as “All events.”

Table 7.3: This table lists the beam configuration, the selection type, and the number of histogram bins. The table also lists the χ2 values and the number of events in the data and MC simulation, before and after the fit. This fit includes all of the Run II LE data in addition to the data from other beam configurations.

Figure 9.4: These figures show the data spectra and the oscillated MC spectra divided by the expected MC spectra without oscillations. The top figure shows QES and RES events. The bottom figure shows the DIS events. These figures show the sum of Run I and Run II data events.

Figure 3.18: Energy resolution for Eν (top), Eµ (middle), and Ehad (bottom). Figures (a), (c), and (e) show the energy resolution computed for the true QES, RES, and DIS events in the MC simulation. Figures (b), (d), and (f) show the energy resolution computed for the selected QES, RES, and DIS events, as discussed in the text. The selected QES, RES, and DIS categories include the contributions from the true QES, RES, and DIS events, as illustrated in Figure 3.16.

Figure 6.6: Energy spectra for the Run I and Run II data. The target position in Run II was approximately 1 cm closer to the first horn. This shift changes focusing characteristics for the secondary pions and produces fewer neutrinos. To account for this difference in target position, separate analysis procedures were performed for the Run I and Run II data.

Figure 4.4: Number of track scintillator planes. Figure (a) shows the reconstructed muon and non-muon tracks. Figure (b) shows the three categories of events, as discussed in the text.

Figure 8.4: Timing of the far detector events, relative to the arrival time of the nearest beam spill. The left plot shows separately events from Run I and Run II. The right plot shows all events. Visible in the right plot is the batch structure of the primary proton beam in the Main Injector.

Figure 9.14: Results of 600 statistically independent pseudo-experiments. Fit parameters are not constrained to the physical region, but with the requirement sin2 2θ ≤ 2. (a) the χ2 values for the data and MC without oscillations. (b) the χ2 values for the data and best oscillation fit. (c) and (d) the best fit parameters. (e) and (f) 90% C.L. statistical errors for best fit parameters. Values obtained from the fit to the real far detector data are shown with red lines. Black dotted lines show the true values of oscillation parameters used to generate the pseudo-experiments.

Figure A.3: The Eν spectra for several values of Q 2. The X variable is constrained within this range: 0 < X < 0.13.

Figure 2.9: Raw and calibrated mean scintillator strip signal induced by muons produced in beam neutrino interactions in the near detector. The continuous line shows the raw signal before any corrections. Open circles show the signal with corrections accounting for variations in channel gain, attenuation in optical fiber, and strip light output. The solid histogram includes additional corrections for a non-uniform response of the scintillator and WLS fiber. This figure was taken from [52].

Figure 5.1: Variables computed by the track fitting algorithm are shown for the true MC µ− and µ+ tracks. The top figure shows q/p. The middle figure shows σq/p. The bottom figure shows q/p divided by σq/p. The histograms are normalized to the unit area.

Figure 5.10: Azimuthal angle φ, the new charge-sign variable defined in Figure 5.4b, plotted after the standard (default) charge-sign selection for the µ+ and µ− tracks. Figure (a) shows the azimuthal angle for the reconstructed tracks with q/p < 0. Figure (b) shows the azimuthal angle for the reconstructed tracks with q/p > 0

Figure 6.7: Reconstructed event energy Eν , hadronic shower energy Ehad, muon momentum Pµ and reconstructed muon angle for the selected νµ chargedcurrent events. These figures show the Run I near detector data. The right plots show the data divided by the default and tuned MC simulation.

Figure 2.4: Reconstructed neutrino energy distributions in the MINOS near detector. The figure shows the νµ charged-current data events (discussed in Chapters 4 and 6), recorded using 3 target positions, with the target placed 10 cm, 150 cm and 250 cm away from the 1st horn (see Figure 2.3). The horns are pulsed at 185 kA or 200 kA current, producing a maximum 30 kG toroidal magnetic field. The number of events is normalized to 1018 protons on target (POT).

Figure 2.3: Drawing of a baffle, a target, and two magnetic horns (separated by 10 m). The NuMI horns are pulsed in “forward” polarity, focusing positively charged secondary hadrons. The baffle and target can be moved together further upstream (to the left) of the horns to focus higher momentum secondary hadrons and to produce a higher energy neutrino beam (see Figure 2.4). The vertical scale is 4 times greater than the horizontal scale. This figure was taken from [58].

Figure 1.4: Flux of µ+ τ neutrinos versus flux of electron neutrinos. CC, NC and ES flux measurements are indicated by the filled bands. The predicted 8B solar neutrino flux [27] is shown as dashed lines, and that measured with the NC channel is shown as the solid band parallel to the prediction. The narrow band parallel to the SNO ES result corresponds to the Super-Kamiokande result [31]. The intercepts of these bands with the axes represent the ±1σ uncertainties. The non-zero value of φµτ provides strong evidence for neutrino flavor transformation. The point represents φe from the CC flux and φµτ from the NC-CC difference with 68%, 95%, and 99% C.L. contours included. The figure and caption were taken from [32].

Figure 6.3: These figures show the ratio of the muon momentum from the range over the muon momentum from the curvature, Prange/Pcurv for the three magnetic field maps, as discussed in the text. The muon momentum from the curvature, Pcurv, is computed using the standard fitting algorithm. These figures show the tracks for the near detector data and MC simulation. The number of the data tracks is scaled down to match the number of the MC tracks.

Figure 9.20: Systematic errors for the three sets of pseudo-experiments. Each figure shows a difference between two fit parameters. First fit parameter is obtained from a fit with a pseudo experiment without systematic effects. Second fit parameter is obtained from a fit with a pseudo experiment that includes one or more systematic shifts, as described in the text. In both cases, the same statistical pseudo experiment is used. Figures (a) and (b) show differences for the near detector systematic effects. Figures (c) and (d) show differences for the far detector correlated systematic effects. Figures (e) and (f) show differences for the far detector uncorrelated systematic effects. Blue lines mark a symmetric region that includes 68% of the pseudo-experiments.

Table 1.1: Three generations (or flavors) of fermions in the Standard Model. The table shows the most current mass measurements and limits [5]. The quark mass measurements contain significant uncertainties because quarks are confined within hadrons, and, unlike leptons, their masses can not be measured directly. The neutrino mass limits are obtained from direct measurements. The squared neutrino mass differences are measured precisely by neutrino oscillation experiments.

Full text

Copyright
by
Rustem Ospanov
2008

The Dissertation Committee for Rustem Ospanov
certifies that this is the approved version of the following dissertation:
A measurement of muon neutrino disappearance with
the MINOS detectors and NuMI beam
Committee:
Karol Lang, Supervisor
Duane Dicus
Karl Gebhardt
Sacha Kopp
Jack Ritchie

A measurement of muon neutrino disappearance with
the MINOS detectors and NuMI beam
by
Rustem Ospanov, B.S., M.A.
DISSERTATION
Presented to the Faculty of the Graduate School of
The University of Texas at Austin
in Partial Fulfillment
of the Requirements
for the Degree of
DOCTOR OF PHILOSOPHY
THE UNIVERSITY OF TEXAS AT AUSTIN
December 2008

Dedicated to my family.

A measurement of muon neutrino disappearance with
the MINOS detectors and NuMI beam
Publication No.
Rustem Ospanov, Ph.D.
The University of Texas at Austin, 2008
Supervisor: Karol Lang
MINOS is a long-baseline two-detector neutrino oscillation experiment
that uses a high intensity muon neutrino beam to investigate the phenomena
of neutrino oscillations. The neutrino beam is produced by the NuMI facility
at Fermilab, Batavia, Illinois, and is observed at near and far detectors placed
734 km apart. The neutrino interactions in the near detector are used to
measure the initial muon neutrino flux. The vast majority of neutrinos travel
through the near detector and Earth matter without interactions. A fraction
of muon neutrinos oscillate into other flavors resulting in the disappearance of
muon neutrinos at the far detector. This thesis presents a measurement of the
muon neutrino oscillation parameters in the framework of the two-neutrino
oscillation hypothesis.
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