cor-responds to a certain number of detector planes. A wider binning groups the events per module, resulting in a total of 5 L-bins. For a data set with higher statistics, a finer binning per 2 detector planes, giving a total of 25 bins, could be chosen. In addition, the detected events vary in energy and the gathered data is binned in measured energy E. As the detector and reconstruction effects have so far been excluded, the signal prediction as given by equation 3.22, can be binned in terms of the true distanceLνe and true neutrino energy Eνe.
The expected number of IBD events for theith length bin [Li,Li+1] and jth neutrino energy bin [Ej,Ej+1], where we have dropped the νe-subscript for simplicity, is written as
Nint(ij) = and, as explained in the previous section, can be modified with the oscillation probability Pνe→νe for those values of L and E. Note that the range of the
To provide representative neutrino spectra that allow a comparison with the measured data, a dedicated framework for the generation of large numbers of neutrino events was designed by the SoLid collaboration. The framework is called SoLO and, as described above, it has to combine the BR2 reactor flux model, the detector acceptance and the neutrino interaction process in the detector. On the one hand, the results of the reactor core simulations, such as the spatial fission distributions, the fission rates and the related energy spectra, are fed to the SoLO code. On the other hand, the full detector ge-ometry is loaded from a GDML file.3 SoLO thus acts as an interface between the reactor and detector simulations and uses this information to generate a detailed signal prediction.
3GDML stands for Geometry Description Markup Language, and is a code specifically designed for the modelling of complex detectors. The GDML file with the SoLid detector geometry is based on the Geant4 detector simulation, described in chapter 4.
74 CHAPTER 3. SIGNAL PREDICTION The generation of neutrino interaction vertices happens on a voxel-by-voxel basis, where the detector volume is split in voxel-by-voxels of 5×5×5 cm3. We would like to emphasise that apart from the SoLid detector cubes, that nicely match one such voxel, all surrounding, inactive material in the simulation is also divided in these voxels. The neutrino generator code then carries out the following steps for each voxel:
1. The signal normalisation is calculated for each isotope k, as deduced from equation 3.24.
2. According to the normalisation, a number of signal events is gener-ated per isotope k. A 100 times more events are generated to reduce statistical fluctuations.
3. For each signal event :
(a) A position inside the reactor core is picked, according to the given fission map.
(b) A neutrino energy value is drawn, according to the predicted Eνe spectrum.
(c) An interaction point inside the detector voxel is picked.
The SoLO code thus generates events with a certain energyE, momentum~p, a precise reactor-detector distanceLbased on the fission position in the reactor and the picked interaction point (x,y,z) in the detector. This information allows us to determine the L/E distributions of the neutrinos interacting in each of our detection cells. We should note that the resulting number of events and related histograms need to be scaled back with a factor 100, to obtain the correct normalisation.
The neutrino predictions are generated for each cycle of the BR2 reactor, taking into account the specific power history and the core loading map of that cycle. Table 3.3 shows the predicted number of IBD events in the SoLid detector for the first 5 BR2 reactor cycles of 2018.
An illustration of the distribution of antineutrino interactions over the SoLid detector volume is given in figure 3.8. First of all, the materials with a high proton density, such as the frame lining and shielding plates from HDPE, as well as the cell structure of the PVT cubes are clearly visible in this figure. In addition, one can see the expected quadratic reduction of the num-ber of interacting neutrinos with distance L (= z in the figure), as described in section 3.1.3.
After the antineutrino event generation, the next step is to reproduce the kinematics of the IBD reaction products (e+, n) and to simulate the particle
3.3. NEUTRINO GENERATOR 75
Table 3.3:The first 5 BR2 reactor cycles of 2018, with the start and end date, and the corresponding number of calculated reactor fissions and predicted number of IBD events in the active material of the SoLid detector. [115]
Reactor cycle Start date End date Nfiss [1024] NIBD Cycle 1/18 06/02/18 27/02/18 3.12 24159.3 Cycle 2/18 24/04/18 22/05/18 4.63 35729.4 Cycle 3/18 12/06/18 10/07/18 4.08 31558.6 Cycle 4/18 21/08/18 11/09/18 3.24 25083.3 Cycle 5/18 02/10/18 23/10/18 3.13 24232.0
Monte&Carlo+sample
0 500 1000 1500 2000 2500
x in cm
0 500 1000 1500 2000 2500
y in cm
Figure 3.8:The distribution of antineutrino interactions in the SoLid detector volume for a large Monte Carlo sample of O(105) events: front view (left), side view (top right), top view (bottom right).
76 CHAPTER 3. SIGNAL PREDICTION transport in the detector, which is carried out by the Geant4 detector simula-tion. The resulting information is then combined with the modelling of the response of our detector in terms of detection efficiency, energy resolution, electronics noise, etc. and the effects of the signal reconstruction algorithms, finally allowing to compare the predicted signal with the measured data.
These detector simulation and signal reconstruction steps are discussed in the following chapter.
3.4 Summary
This chapter gave an overview of the inputs required for the IBD signal pre-diction in the SoLid detector.
A crucial part are the reactor-related calculations, which determine the expected produced antineutrino flux. As discussed in sections 3.1.1 and 3.1.2, these calculations involve the knowledge of an enormous amount of parame-ters, that are not always directly available. For the SoLid experiment, the error budget on the determination of the flux is mainly driven by the uncertainty on the BR2 reactor power measurement.
In sections 3.1.3 and 3.1.4, the number of interacting antineutrinos was derived by combining the emitted number of antineutrinos with the geomet-rical efficiency of the SoLid detector, its proton content and the IBD cross section. Equation 3.21 summarises the prediction of the expected IBD signal for the data taking period of the experiment. As discussed in section 3.2, this prediction is in practice binned in the two parameters Eνe andLνe, which are the neutrino energy and its distance travelled.
The implementation of the prediction is fully based on Monte Carlo sim-ulations, which are combined in and partly performed by the SoLO frame-work. In section 3.3 the neutrino generation method of the SoLO code is treated, showing how the SoLid experiment builds a set of neutrino events for a sterile neutrino search.
Detector response
and event reconstruction 4
In the previous chapter, the full chain of calculations for the signal prediction was described. The resulting prediction gives a number of expected IBD interactions in the SoLid detector, but - as explained - this does not include the detector response yet. Since the detection and reconstruction effects can not be treated analytically, they are studied and accounted for using Monte Carlo simulations. This chapter briefly describes the detector and readout simulations in the first sections. Next the reconstruction algorithms, that are also applied on real data, are detailed. Further on, a tool to efficiently account for these detector effects when building the signal prediction, called the migration matrix, is discussed.
4.1 Geant4 detector Monte Carlo
The SoLid detector is simulated with a Geant4 [116] Monte Carlo (MC) code, called SoLidSim. It models the transport of particles through the detector materials and determines the energy deposits in the scintillators.
For the implementation of the geometry of the experimental set-up, three levels can be distinguished, according to the degree of detail required and their relative scales [82]:
• The full Phase I detector is simulated with a high level of accuracy. The detailed geometry and composition of the detection cells, the optical fi-bres, MPPCs and mirrors, the aluminium frames and neutron reflectors are implemented.
• The main volumes and components of the container, including the full instrumentation inside it, are modelled without reproducing the fine patterns, but with the objective of a positioning of the material that is
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78 CHAPTER 4. DETECTOR RESPONSE AND EVENT RECONSTRUCTION close to reality. An exception is made for the CROSS calibration system, that is modelled with precision, because of its proximity to the detector.
• The BR2 reactor and its water basin, plus the experimental hall as well as the confinement building are reproduced schematically. These struc-tures affect the transport of cosmic radiation, such as muons and neu-trons, and are thus necessary for the estimation of the background ra-diation in the detector.
Given the geometry and depending on the input particles and the selected physics processes, the particle transport through these implemented volumes is simulated next.
As discussed in section 3.3 of the previous chapter, the collaboration has developed a dedicated neutrino event generator to produce IBD events ac-cording to the BR2 specific neutrino energy spectrum and the position distri-bution of the interaction vertices provided by the SoLO code.
For each of these IBD events, the positron scintillation and annihilation, as well as the neutron thermalisation and capture, are simulated by the SoLid-Sim code. The modelling of the energy deposited by the positron is relatively straightforward and is based on the standard physics processes available in Geant4. For the neutron modelling in the SoLid detector, however, no an-alytical models are available. This is a consequence of the particular SoLid detector concept, where the IBD neutrons are thermalised to an energy of about 0.025 eV before they can be captured on 6Li. To simulate the elas-tic scattering of these thermal neutrons, the collaboration therefore relies on reference cross-sections measured for polyethylene [117], the chemical com-position of which is very close to that of PVT. These features are imported in GEANT4 via dedicated neutron libraries.
In addition to these IBD-related generators and other, more standard ones already implemented in the Geant4 software, the collaboration added particle generators for the reproduction of the following calibration sources:
• the252Cf and AmBe neutron sources, with the radiation energy spectra taken from the ISO reference [118],
• the 22Na, 137Cs and 207Bi gamma and positron sources and their ra-dioactive decay,
and the following experimental backgrounds, see section 5.2:
• the bismuth-polonium decay chain,
• the cosmic muons, with the CRY generator [119], cross-checked with the Guan [120] and Reyna [121] models,
• atmospheric neutrons, using the Gordon parametrisation [122].
4.2. READOUT SIMULATION 79