The time distribution of hits is involved in the reconstruction of the main features of the event: the clustering and the total number of hits in the event, the position reconstruction, the particle identification using pulse shape discrimination algorithms (see Sec. 3.4.2 and Sec. 3.5). In order to be able to simulated these high-level features, the time distribution of the hit PMTs (henceforth time distributions) must be simulated with at least 5% agreement with data, for each time bin and in the energy range used in the analysis. In particular, the mean and the peak of the time distribution should be reproduced with 1 ns accuracy, and the other momenta of the distribution should not disagree more then few nanosecond.
The parameters that influences the most the time distribution are: the scintillation parameters (τi, qi), the PPO re-emission probability, the scaling factors for the PPO
and PC attenuation lengths, the reflection probability of the SSS, concentrators and PMT cathode. The Scintillation light parameters (τi, qi) are the one with the largest
impact on the shape of the time distribution: they affect the profile from the first nanoseconds to tail of the distribution. PC and PPO scaling factors and attenuation lengths and PPO re-emission probability affects the rise of the time distribution and the width of its peak. They are also responsible for the uniformity of the energy response respect to the position of the event. The reflection probability of the source of the SSS, of the PMT concentrators and of PMT cathode affects the time distribution with a secondary structure of hits at 50-70 ns. For what concerns the simulation of the PMTS and the electronics (see Sec. 4.2.6), the parameters that affects the time distribution are the PMT transition time spread and the PMT afterpulse probability and its time distribution. Both of them have been measured and included in the simulation. The transition time spread affects the rise time of the distribution and the width of its peak, and it is responsible of a secondary bump at ∼ 60 ns after the peak. The PMT afterpulse affects the time distribution with secondary hits from 140 ns to the end of the pulse.
4.3 The tuning of the Borexino Monte Carlo 59
Most of these parameters, with the exception of the τi and qi for α events, have
been fine-tuned using the following γ-ray source runs as reference: 85Sr in 8 positions,
54Mn, 65Zn and 40K at centre and at z = ±3m. The use of calibration data provides
a set of advantages: calibration source runs ensure high statistics samples of pure and monochromatic and point-like events, allowing to study the dependence of the accuracy of the simulation of the time distribution with respect to the energy and position of the event. The ensemble of this source scans the relevant energy and position range for 7Be ν analysis. The γ-ray sources have been employed to optimise the simulation of the time distribution of β events because the time distributions of β and γ events are very similar. In fact, γ-rays undergo Compton scattering on the electrons of the scintillator. Recoil electrons loose energy and produce scintillation light. Hence, the γ-ray is detected as superpositions of electron events of lower energy, close in space and time. Once the whole set of parameters have been tuned for β events, the α decay times and weights have been tuned using 214Po events in 222Rn sources.
The following iterative procedure has been followed. From a given calibration data run, the time distribution is built. The events coming from the calibration source are selected cutting events reconstructed outside a sphere of 1 m from the nominal source position. Only events with reconstructed energy around the nominal energy on the source are considered. Muons events and muon daughters are rejected using the external muon veto and the standard analysis cuts (see [105] and Sec. 5.5.1).
The very same calibration run is then simulated (see Sec. 4.2.1.4) with a given set of optical parameters. Great care was devoted to simulate the electronics configuration in the same configuration of the real run. In particular we have included the pattern the PMTs that were disabled during the run, the measured dark noise of the PMTs, based to the rate of random triggers during that run, the gain of each PMT, taken from to the electronics calibrations of the real run. The procedure of event selection described in the previous paragraph is performed on the simulated events. The time distributions of the selected simulated events are then compared to the corresponding distribution for real data events. For sources located at z = ±3 m from the centre of the detector, the time distributions are also compared using only the time distribution of hits in a subset of PMTs near or far from the source.
The optical parameters that leads to the best accordance between simulated and real time distributions are then selected. The comparison is done with the method of the least squares. Direct comparison using the eyes (that are the best tool of pattern recognition at present time) is also performed to select the final choice of configuration parameters.
A final overall check for β and α time distributions is done using the sample given by the 214BiPo coincidences on normal runs (see Sec. 3.5). These events are distributed in the whole volume of the Inner Vessel. This allow to check the goodness of the simulation on the overall fiducial volume, instead of a point-like source. The inhomogeneity of the position of 214BiPo events along the vertical axis is taken in account with the method of rejection.
60 The Borexino detector response and simulation