Right: Top graph shows Brem data and MC comparison and bottom graph shows data/MC ratio. List of Figures xxxvii 6.6 Left: The top graph shows the DiF data and the MC comparison and the bottom graph.
The Weak Interaction
Due to V −A theory, the weakly charged current interaction allows the coupling to only left-handed chiral fermions and therefore the right-handed coupling to charge current interaction disappears. The coupling of left-handed and right-handed neutrino to Z0 is respectively ∝ Iz−qsin2θW and ∝ qsin2θW, where θW is the Weinberg angle and q is the electric charge.
Mass of Neutrino
Taking this into account, the Majorana term can be written in the form, . 1.10) where superscript c stands for charge conjugation. Now suppose L= 0 ,(otherwise it would require a Higgs triplet which is not available in Standard Model), mR>> mD, the mass eigenvalues reduce to-.
Neutrino Oscillations
Eq.1.38 is the survival probability for a muon neutrino of energy E after traveling a distance of L km. For the value of Ne in Eq. 1.51, the mixing can therefore become maximum (the effective angle in the matter can become π/2), which is the MSW effect.
Experimental Evidence for Neutrino Oscillations
The combined fit (Fig.1.6) to all the solar neutrino data gives the best fit oscillation parameter with a precision of 3.5 % as,. It was found, as shown in Fig.1.8, that the neutrinos coming from the bottom (cosθ = −1) are less in number than the predictions.
Future Experiments
The mass hierarchy of neutrino mass eigenstates has yet to be determined by neutrino oscillation experiments. In order to observe CP asymmetry, the initial and final taste states must be different, i.e. α 6= β as shown in Equation 1.63 and must be separated from the mass hierarchy.
Current Status of Oscillation Parameters
Relevance of the Thesis Work
Chapter Summary
NOνA distant detector is located 810 km downstream of the beam production point, as shown in Figure 2.1. Apart from the size, the near and far detector are made of the same type of materials and design. Due to matter between the near and far detector and due to the availability of both neutrino and anti-neutrino beams, NOνA can measure the sign of atmospheric mass splitting and Dirac-CP violation of the phase, δCP.
NuMI Beam
The NuMI neutrino energy spectrum depends on the off-axis angle, θ, which is measured from the beam direction as shown in Fig.2.4. The neutrino energy spectrum depends on the off-axis angle and is given by the following equation, 2Replace 0.43 with 0.96 to get the energy versus off-axis angle spectrum of the neutrino coming from the kaons.
NOν A Detectors
PVC extrusions are made from 16 unit cells joined side by side, as shown in Fig.2.10. The corners of the extrusions are rounded to reduce stress on the PVC structure from its weight. Fig. 2.12 shows the 3-D schematic diagram of NONA detectors which are made of alternative planes.
Data Acquisition (DAQ) System
The applied voltage creates a temperature difference on the two sides of the device according to the Peltier Effect. The raw data is first linked, based on the geometric location of the detectors, in Data Concentrator Modules (DCMs). The facts and rules form the knowledge base for Message Analyzer and can be written in the form of a configuration file.
Simulations
As an output, the neutrinos and the parent information are stored in the flux files. Using the information from the previous step, neutrino interactions in the detectors are simulated using the GENIE generator. Rock muons produced in the surrounding rock of the near detector are simulated separately as.
Calibration
Three-cell hits are those hits that have two adjacent hits on the muon orbit. An event, in the form of hits, must be reconstructed so that the useful physics information can be extracted. Since the thesis is related to νe-appearance analysis, a detailed description of the νe-CC reconstruction method is given in the next chapter.
Chapter Summary
To extract useful physics information from the hits deposited by the particles in the detector, we need to associate particle information with the hits. These particles and processes manifest themselves as EM bursts, tracks or teeth in the detector, as shown in Figure 3.1. The reconstruction for this channel in NOνA consists of several steps, as shown in Figure 3.2 [81], which are described in detail in the following sections.
Slicer
This is achieved in NOνA by implementing a density-based clustering algorithm (DBSCAN) algorithm. The first term penalizes hits if they are far apart in time, the second and third terms penalize the hits which are far apart in space, M inP ts, , Dpen, P Epen are free parameters and have been set. Purity is defined as the fraction of hits that come from the leading interaction in the slice.
Tracking
In the tracking process, input hits that are 4 cells apart are used as seeds for the algorithm. A pair of hits (downstream in the beam direction) in the cut is used to estimate the position and inclination of the track. This method takes the input of an object constructed by the previously mentioned methods in the reconstruction chain.
Chapter Summary
To make the details in the signal-like region visible, the y-axis cuts off a lot of the background peak. In NOνA, the signal for the νe-CC interaction is the appearance of an electron signal in the distant detector. Upon production, the electron in the far detector produces an EM shower in the detector.
Bremsstrahlung Muons Track Preselection
4.1) When a muon undergoes a bremsstrahlung process, the amount of energy deposition increases along the way in the detector. Therefore, the planes with EM shower hits in the detector will have more energy than the planes with muon hits. As in Fig.4.2, it can be seen that the energy deposition in the detector planes increases for the EM shower region.
EM Shower Finding in NOν A Detector
In the detector the muon is a minimal ionizing particle2 (MIP) and the energy corresponding to a MIP in the NOνA detector is 1.57 M eV/cm. We used this property of bremsstrahlung in extracting the EM shower described in the next section. To achieve this, a new muon algorithm has been developed that removes the muon hits from the track, as described in the next section.
Muon Removal Algorithm
As it is visible, at about 4400 cm on the Z-axis, the energy deposition increased (number of . colored hits increased) due to EM shower energy deposition.
Data/MC Comparison
Fig.4.14 shows the plot of the probability difference between e and γ and we can see that the peak in the plot is towards the positive side, which indicates that Brem events are more likely to be electron type than γ type. Fig.4.15 shows the plot of the probability difference between e and μ and we can see that the peak in the plot is clearly towards the positive side, which indicates that Brem events are more likely to be electron-type than μ-type. Similarly, Fig.4.16 shows the plot of the difference in probability between e and π0 and we can see that the peak in the plot is towards the positive side in the transverse probability than the longitudinal probability.
Reweighing Method
We also process our sample via another particle ID, LEM and CVN, and Fig. 4.18 and Fig. 4.19 show the output of the LEM and CVN respectively. To address the above problem, we developed a reweighting method to make the Brem shower sample equivalent to the νe shower by constructing a matrix, based on a bin-by-bin comparison of brem and νe-CC- energy and angular distribution (reweighing is discussed in the following paragraphs). We can also see in Figure 4.23 that there is virtually no effect of reweighting the shower length, because the shower length is independent of the angle.
Signal Selection Efficiency in the Far Detector
As can be seen from Fig.4.40 and Fig.4.41, the signal selection efficiency in Y and Z direction for CVN is quite flat. In Fig.4.39 the selection efficiency in the X direction has a slope but that is well modeled in the simulations. In Fig.4.42 the selection efficiency in the X direction has a slope but that is well modeled in the simulations.
Bremsstrahlung EM Shower from Rock Muons in Near Detector
The plots show good data and MC agreement, showing that the EM showers are well modeled by the ND MC. This implies that most of the EM showers in the mountains are of the bi type. We also see the LID output from the rock muon brem EM shower and from Fig.4.61 it is clear that most of the rock muon Brem EM showers are classified as νe-CC type to a large extent.
Chapter Summary
In the next chapter, we discuss the decay in flight (DiF) muon-induced EM shower, which is a much cleaner shower sample. The new shower exactly mimics the νe-CC initiated EM shower as discussed in the next chapter. As discussed in the previous chapter, the bremsstrahlung EM shower sample has been used to benchmark several tools in the νe-CC analysis.
Motivation
Next, we will present the results on the comparison study of some aspects of the νe-CC analysis using the DiF EM shower sample. The EM shower from in-flight muon decay may serve as a similar source of these EM showers. DiF, unlike Brem, with no muon or very little contamination, can serve as an ideal sample of the EM shower.
DiF EM Shower Selection in FD
After the selection of the muon candidate, the muon track is searched for dump region. The distribution for this variable is shown in Fig.5.5 for both the brake and DiF EM shower. Fig.5.7 shows the reduction of signal and background as a function of different selection criteria applied to extract the EM shower.
DiF Variables and Data/MC comparison
As can be seen in the plots, then-e-CC MC is relatively higher in energy than the DiF sample (red). This is due to the fact that most of the muon tracks come from the direction upwards at the detector while the direction of the beam is horizontal. This is due to the fact that the shower characteristics in the core (longitudinal direction) in γ, e and π0 look almost the same.
Signal Selection Efficiency
The results are limited by limited statistics, but the agreement between the data and MC in terms of detector efficiency as a function of X, Y, and Z is well within 4%. In this subsection, the selection efficiencies for a reweighted DiF shower with a PID value >0.7 are plotted. The results are limited by limited statistics, but the agreement between the data and MC in terms of detector efficiency as a function of X, Y, and Z is within 4%.
Chapter Summary
Fig.6.1 shows the energy distribution for DiF EM shower and brake EM shower side by side. Fig.6.2 shows the angle (w.r.t to beam) distribution for DiF EM shower and Brem EM shower. Fig. [6.3-6.5] shows the probability differences under certain particle hypothesis for DiF and Brem EM shower sample.
Comparison with ν e and Reweighing
Fig.6.9 shows the radius distribution of all samples before and after reweighing and both showers match well with one sample. It is clear from Fig.6.9 and Fig.6.10 that even with one-dimensional reweighting, the DiF sample is performing better than the Brem EM shower sample. Fig.6.11 shows the particle-ID distributions of DiF and Brem together with νe-CC, before and after reweighting which clearly show the performance of the PID algorithm at.
Detector Efficiency as a function of Vertex Position
By also considering the error on the ratio, a conservative estimate of about 4% can be attributed to systematic uncertainty about the detector performance. Also considering the error on the ratio, a conservative estimate of about 4% can also be assigned as systematic uncertainty on the detector performance, based on Brem EM dump sample. Right: Upper plot shows the Brem data and MC comparison and νe and lower plot shows the Brem after reweighting.
Conclusions
Right: The upper graph shows the reweighted Brem and MC data comparing detector performance, for LID >0.7, as a function of vertex position X and . Right: the upper graph shows the reweighted Brem and MC data comparing the detector efficiency, for LID >0.7, as a function of Y and peak position. Right: The top graph shows the reweighted Brem and MC data comparing the detector efficiency, for LID >0.7, as a function of vertex position Z and .
