Optimisation of the S1 simulation using XENON1T data

Optimisation of the S1 simulation using XENON1T data.

Conducted between 30-03-2020 and 10-07-2020 July 14, 2020

NAME Britt Meijer

STUDENT NUMBER 11666137 INSTITUTE Nikhef

UNIVERSITY University of Amsterdam DATE OF SUBMISSION 10-06-2020

EXAMINOR prof. dr. ir. Paul de Jong SUPERVISOR prof. dr. Auke Pieter Colijn

DAILY SUPERVISOR Peter Gaemers CREDITS 15EC

Summaries

Abstract

There are many theories trying to explain the dark matter in our universe. One of these theo-ries is the Weakly Interacting Massive Particle (WIMP). The XENON dark matter experiment uses the XENON1T detector to directly detect such particles. This cylindrical detector is filled with liquid xenon. When dark matter will recoil off a xenon atom, the xenon will then ex-cite and possibly exex-cite neighbours. This causes a light flash which the PMT’s at the top and bottom will detect. This so called S1 signal has been simulated. This has already been done using krypton-I as calibration source. The aim of this thesis is to research the applicability of this simulation and optimise it if necessary. This is done by using other calibration sources such as radon, argon and krypton-II. The goodness of the fit is determined with a KS-test. The resulting KS-value of krypton-I was about three times bigger than the KS-value measured in the thesis that was used for the simulation. This probably due to the fact that different data processors were used. The end part of the S1 simulation is based on the linear template of the waveform. Since this differs for the waveform for this thesis and the thesis of the used simulation, it had significant effect on the KS-values.

Populair wetenschappelijke samenvatting

Sinds de vorige eeuw staan talloze wetenschappers voor een groot vraagstuk: het bestaan van donkere materie. Deze donkere materie zou de verklaring moeten zijn voor alle mis-sende massa in ons heelal. Er zijn talloze verklaringen voor deze materie. Een van deze verklaringen is dat donkere materie bestaat uit Weakly Interacting Massive Particles. Deze WIMPs bestaan uit onbekende deeltjes die geringe interactie hebben met atomen en licht en is alleen meetbaar door gravitatie of door zwakke kernkracht. In Gran Sasso in Italie zijn wetenschappers ook druk bezig dit deeltje te detecteren. Ze maken hiervoor gebruik van een xenon-detector genaamd XENON1T. Deze cillindrische detector is gevuld met xenon en kan hopelijk zo’n WIMP deeltje meten. Wanneer donkere materie op xenon zou inwerken exciteert xenon, wat licht creëert. Boven en onderaan de detector zijn zogenoemde photomultiplier tubes (PMT’s). Deze sensoren meten het licht. Dit kan vervolgens worden omgezet in een signaal, genaamd het S1 signaal. Deze S1 kan vervolgens worden gesimuleerd. Voor dit onderzoek is dit signaal gemodelleerd en geoptimaliseerd om zo meer te leren over de detector.

Contents

1 Introduction 4

1.1 Dark Matter . . . 4

1.2 The xenon experiment and XENON1T . . . 5

2 Project overview 8 2.1 Kolmogorov-Smirnovtest . . . 8 2.2 S1 . . . 9 2.3 S1 simulation . . . 9 2.4 Thesis aim . . . 10 3 Results 12 3.1 S1 and simulation . . . 12

3.2 S1 with best simulation . . . 13

3.3 Height parameter . . . 16

1

Introduction

1.1 Dark Matter

The past century physicists have been struggling to explain one of the biggest scientific mys-teries of our universe: dark matter. Observational evidence for its existence can be found in for example galaxy clusters, velocity dispersion, galaxy rotation curves. It’s existence functions as the explanation for many cosmological measurement anomalies. The first astronomer that was introduced to this problem was Zwicky in 1933 (1)(2). Measuring the mass of the Coma cluster based on the light it emits he found different values than expected. He found that the estimated mass was far too low to correspond to the measured velocities. He came to the con-clusion it would not be possible for the system to be stable with the measured amount of mass, so that there must be more mass, mass that he could not see or measure. This invisible missing matter is what he gave the name ’dark matter’. After him many others came to find the same inconsistencies. For example see figure 1. This figure shows the rotation curve of the M33 (3) and the same aforementioned difference between observed and expected values that Zwicky discovered. Since then there are several theories trying to explain and describe this form of matter of which almost 85% of our universe exists. However, what this non-luminous matter is exactly or how it behaves has not yet been proven.

Figure 1: This figure shows the rotation curve of the M33 disc galaxy. The dashed line represents the expected values and the continuous line represents the measured values. This difference can be accounted for by dark matter.

Today there is much astrophysical evidence that dark matter interacts gravitationally with surrounding particles. One of the proposed explanations that would fit this characteristic is the theory that dark matter consists of Weakly Interacting Massive Particles (WIMPs). It

Figure 2: The figure above shows a schematic illustration of the XENON1T detector that is used to directly detect dark matter particles. Figure taken from (5)

is predicted to exist in extensions to the Standard Model of particle physics. A WIMP only interacts through gravity or other interactions with cross sections lower than the weak scale (4) . And as the name implies it only does so very weakly. Measuring single particles through gravity is very hard. So to detect this particle, it must interact with known matter. For example by the scattering of dark matter off of normal matter.

1.2 The xenon experiment and XENON1T

One of the experiments that tries to find WIMPs using direct detection is the performed in the XENON dark matter project. This project researches the behaviour of atoms caused by scat-tering of passing dark matter particles. The experiment takes place in Gran Sasso, Italy and uses the XENON1T, a dual-phase xenon Time Projection Chamber (TPC), shown in schemat-ically in figure 2. It is a underground double-walled cylindrical vessel filled with 3.2 tonne of xenon. The detector must be very sensitive to low energy particles to successfully detect a WIMP, so reducing noise and background radiation is a very important aspect of this detection experiment.

Figure 3 shows a schematic overview of how a signal is detected. The vessel is filled with liquid xenon (LXe) and gaseous xenon (GXe) at the top. Dark matter travels through the earth and if dark matter were to interact with the xenon in the detector it will transfer its energy into the xenon atom. The particle can transfer its energy to either the nucleus of the xenon

atom, called a nuclear recoil (NR), or to an electron, called an electric recoil (ER). This process will generate excited xenon, xenon-ions and electrons. Then one of two things can happen: an excited xenon atom combines with a neutral xenon atom and forms an excimer state, which will decay and emit light or an electron and a xenon ion will recombine and form an excited xenon atom which will also produce light. At the top and bottom of the detector are sensitive light detectors called photo-multiplier tubes (PMT’s). These are very sensitive light detectors. These will detect the scintillation light emitted by the xenon-atom and will translate the signal into a so called S1 peak, which is the primary signal. Electrons that are freed by ionisation travel upwards due to an electric field towards the gaseous xenon. There they are accelerated by a stronger electric field, causing them to excite more xenon atoms. This creates light which will also be detected by the PMT’s. This secondary signal is called the S2. The time between the S1 and S2 is called the drift time. This drift time can be used to derive the depth of the interaction site. Since the velocity of the electrons in the liquid xenon is constant, the drift time is directly proportional to the depth of the interaction (6).

Xenon is a suitable particle to use in this experiment due several reasons. Firstly, xenon is a very stable noble gas. The reason xenon is chosen over other noble gasses is due to the fact that the energy of the decay products of xenon are very well known and do not fall under the WIMP energy spectrum. The energies of decayed xenon are much to high to be considered a WIMP, which makes the signals very easy to distinguish. This is not the case for the other noble gasses. Furthermore, its relatively high boiling point means that a moderate cryogenic installation is required to liquefy the xenon. Liquid xenon detectors are therefore housed in a vacuum-insulated double-walled vessel. But since xenon has a high density, only a small detector volume needs to be instrumented to reach a relatively high detector mass (6). Lastly, the liquid xenon detectors shield themselves due to the low path length of background radiation in the medium (6).

The XENON1T is the latest of several versions. Currently a new version, XENONnT is in development. This detector will contain up to 9 tonnes of xenon. It is designed to further reduce noise and background radiation. The Nikhef institute in Amsterdam, where this research is conducted, has a smaller replica of this detector called XAMS (Xenon AMSterdam). It is used for research and development purposes.

Figure 3: The figure above shows a schematic representation of the working principle of XENON1T. The cylindrical vessel is filled with liquid and gaseous xenon. When dark matter interacts with the xenon atoms inside the detector, the xenon will cause a light flash. The photo-multiplier tubes at the top and bottom will detect this light. This signal is what is identified as an S1. The electrons that are freed due to ionisation of the xenon will rise to the liquid-gas interface under the influence of an electric field. Here they are accelerated even more and will excite xenon atoms. This will also cause a light flash. This signal is called an S2. Figure taken from (5).

2

Project overview

This chapter will explain all the implements needed for this research. The aim of this thesis is to research the current simulation model for the S1 and tests its applicability. The goodness of the simulation is determined by using a KS-test, explained in 2.1. For comparison the S1 of Kr-83m is shown in section 2.2. A model is already made to simulate the S1 using Kr-83m as calibration source (5) and is explained in section 2.3. For this thesis this model is used on other calibration sources to test its applicability. The simulations and statistical values will be compared and from there the model will be assessed on possible improvements.

2.1 Kolmogorov-Smirnovtest

To test the simulation of the S1 a Kolmogorov-Smirnovtest-test (KS-test) is used. This is a sta-tistical test that is based on the maximum difference between an empirical and a hypothetical cumulative distribution. For this thesis the null hypothesis is that the S1 and the simulation look enough alike to be considered to be from the same distribution.

If the difference satisfies

D_{nm> c(α})r n + m

nm (1)

then there is enough significant statistical evidence against the null hypothesis and it is not allowed to assume that the data sets are from the same distribution and so the null hypothesis must be rejected. Here the Dnm is the maximum KS-distance and n and m the sample sizes

for each distribution. The value of c(α) can be determined by using (7) c(_{α) =} r −1 2ln( α 2) (2)

where_αis the significance level (7). Meaning that if the null hypothesis were to be true and the odds of getting a certain set of data is below this significance threshold, the null hypothesis is to be rejected. The probability of getting that certain set of data is then considered to be significantly low. If the probability of a certain data set were to be higher than the significance level the result would be considered non-significant and then there is not enough statistical evidence to reject the null hypothesis and it is possible that the data are from the same distri-bution. Filling equation 2 into equation 1 will give us the condition

Dnm> 1 p n· s − lnα 2· 1 +mn 2 . (3)

The lower this significance level the more lenient the condition is, because data sets are more easily considered to be non-significant.

2.2 S1

First we will look at the S1 of Kr-83m calibration source. When Kr-83m decays it produces two photons, with energies of 32.2 keV and 9.4 keV. They will be referred to as krypton-I and krypton-II. In figure 4 the S1s of krypton-I and II at different voltages are shown.

Figure 4: Here the plotted S1 of krypton-I (32.2 keV decay energy) and krypton-II (9.4 keV decay energy) are shown for different voltages. Figure taken from (5)

2.3 S1 simulation

As mentioned, for this thesis an existing is used and researched (5). In this section it is sum-marised how this model has been obtained. To find the S1 simulation a million single photo-electron waveforms are extracted from isolated pulses in regular data events. In figure 5 in black the average normalised waveform is shown. The colours in the plot correspond to dif-ferent simulated waveform shapes from three difdif-ferent single-PE pulse models. In green the linear template of the average waveform, in orange an exponentially modified Gaussian plus a boxcart function to describe the late component. This EMG describes the sum of independent normal and exponential random variables. This function is derived using the convolution of the probability functions of these variables. It has two parameters being the mean and the variance. Since the Gaussian is more successful near the peak and the template is more suc-cessful near the tale of the peak they are combined to find the most optimal model. This result is the blue line. This is the exponentially modified Gaussian that switches to the interpolated

template at later times (5).

Figure 5: In the figure above in black the average normalised waveform. Figure taken from (5). In green the linear template of the average waveform, in orange an exponentially modified Gaussian plus a boxcart function to describe the late component. Since the Gaussian is successful near the peak and the template is more successful near the end they are combined to find the most optimal model. This result is the blue line. This is the exponentially modified Gaussian that switches to the interpolated template at later times (5).

For the fit of the simulation over an S1 the krypton-I at 81 V/cm from figure 4 is chosen. The S1 of krypton-II is likely to be contaminated with the S1 of the krypton-I. The fit will be statistically tested using the KS-test. The results of this test will indicate the quality of the four simulated distributions. The parameters of the simulation are chosen to minimise the KS-distance. The parameter values were 41.8 ns for the decay time and 13.6 ns for the Gaussian spread. The results can be seen in figure 6. The KS-distance for these distributions are 5.6 ×10−3(5). Using equation 3 and m = n = 1 this KS-value gives a boundaryα-value of 1.99987. This number indicates the probability of obtaining such a data set if the two plots are from the same distribution with this particular KS-value. This is not a very sensible number since_αis a percentage and should be between 0 and 1, but for the purpose of this thesis this α-values will be accepted and used to compare to other_α-values.

2.4 Thesis aim

As mentioned above the aim of this thesis is to research the current simulation model for the S1 and tests its applicability. To do this the same steps are taken as above but for several calibration sources. The sources that are used are Ra-222, Ar-37, and Kr-83m. When Kr-83m

Figure 6: Above the S1 of krypton-I with its simulation in a 81 V/cm field. Red dashed line shows the same model, but with the single-PE pulse replaced with a delta function. Figure taken from (5)

decays it produces two photons, with energies of 32.2 keV and 9.4 keV. They will be referred to as krypton-I and krypton-II. For each of the four sources the S1 is simulated using the explained simulation model (5). The fit will be statistically tested using a KS-test.

Then the best simulation fit will be chosen. Each simulation will be plotted over all cali-bration sources. Then the sum of the KS-value of all four simulations will be compared. The simulation that gives the lowest sum will be designated as best simulation. The simulation with the best statistical values will be plotted over the other sources. These distributions will be again tested with the KS-test. Depending on the quality of the fit a decision can be made for a possible adaptation of the model in order to retrieve better results.

A parameter that could be considered adding to the model is the z-coordinate of the event. It takes a certain amount of time for the photon to travel from the interaction site to the PMT’s. This time depends on where the xenon atom is located inside the detector. For example, photons from xenon atoms at the bottom of the detector will reach the PMT’s earlier than photons from xenon atoms in the middle of the detector. So far the time differences have been neglected by taking the average time. The time it takes for photons to travel across the detector is about 5.6 ns (5). For this thesis the influence of the height of the interaction site will be researched.

3

Results

3.1 S1 and simulation

Firstly the S1 shapes of the calibration sources are obtained. For radon, argon, krypton-I and krypton-II there were about 9 × 105, 3 × 106 and 5 × 105 peaks total respectively. For each calibration source the peaks are processed to give the average S1 waveform. This processor normalises the peaks and aligns the waveforms to the point when a fixed fraction of area is reached. Then the mean of the peaks is returned. For each source these are shown in figure 7. For krypton-II the median is used instead of the mean. If the average is taken the S1 of krypton-I had a significantly longer tale than the other sources. By taking the median it looks more similar the other S1s. A possible explanation for this might have to do with the relatively low energy of the krypton-I decay. Because the decay energy of this atom is only 9 keV it is more sensitive to noise. By taking the median of the data it reduces the chance of outliers caused by this noise. However, this explanation is not very likely, since argon also has very low energy and does not seem to have this problem.

Also, because of the high energy alpha decay of radon, it had to be downsampled in order to look more similar to the other S1s.

Figure 8 shows the data from figure 7 with their added simulation obtained with the model from section 2.3. For radon no simulation is made. Due to the much higher area values of the S1 the computer was not able to process the data, which is necessary to make a simulation. The parameters of the simulated distribution are chosen to minimise the KS-distance between the simulated and observed average waveform. The parameters used and the resulting KS-values per source can be found in table 1.

Table 1: This table shows the parameters and KS-values for each calibration source. Because of the high energy decay of radon the computer was not able to process the areas.

Source decay time (ns) Gaussian spread (ns) KS-value

Argon 49.25 8.25 _4.03×10−2

Krypton-I 36.00 22.83 _{1.90 ×10}−2 Krypton-II 53.00 8.00 _2.05×10−2

One of the observations that can be made looking at figure 8 is that the peak of the S1 and simulation of krypton-I do not align. The peak of the simulation is lower than that of the data.

Figure 7: This figure shows the S1 of radon, argon, krypton-I and krypton-II. For this the average or median amplitude of all measured peaks is taken. This amplitude is plotted against the time in ns. Due to the high energy of radon the data had to be downsampled to look more similar to the other S1s and for krypton-II the median is taken to reduce outliers.

Also it appears that the shape of argon and krypton-II is slightly skewed. Before 100ns the simulation has lower amplitude and after 100ns the simulation has a higher amplitude.

3.2 S1 with best simulation

To choose the simulation that will give the best results, each simulation is plotted over all sources. Per simulation the KS-values of the four plots are summed. The simulation that gives the lowest sum will be designated as best simulation. Table 2 shows the sum of the KS-value of the corresponding simulation that is plotted over all sources. When using argon it appears to have the lowest sum of KS-values, so this source will be used to plot over the other calibration sources, shown in figure 9.

For each calibration source the KS-distance is calculated again. Using this value, n = m = 1 and equation 3 the boundaryα-value is calculated. The results are shown in table 3.

The calculated_α values, again, are not very sensible since it is a percentage and must be between 0 and 1. But for this thesis they can be compared between themselves. From equation 3, we know that the higher this_α value, the better the fit. Compared to the value of 1.99987

Figure 8: The figure above shows the S1 (green) of figure 7 with their simulations (blue). For radon no simulation is made due to the fact that the processor was not able to process the large area of radon. The parameter values used for radon can be found in table 1.

Table 2: This table shows the sum of the KS-values when using the corresponding calibration source on all S1s.

Simulation used sum of KS-values

Argon 0.123

Krypton-I 0.135 Krypton-II 0.141

Figure 9: The figure above shows the S1s of the calibration sources (green) with the simulation of argon (blue).

Table 3: This table shows the KS-values when using the argon simulation over the corresponding cali-bration source. It also shows theα value using this KS-value in equation 3.

Sources KS-distance α Radon 0.03876 1.99400 Argon 0.04075 1.99337 Krypton-I 0.02298 1.99789 Krypton-II 0.02064 1.99830

Figure 10: The figure above shows the S1 of the the calibration sources per shell. In blue shell, which is the higher third of the detector. In green the second shell and in red the third shell, being the upper third of the detector.

from section 2.3 the simulated waveforms have less favourable values.

3.3 Height parameter

To compare the photon travel time the detector is divided into parts by distinguishing the processed peaks by z-coordinate. All peaks that are created between 0 and 33cm from the top of the detector are designated to the first shell. Peaks created between 33 and 66cm are part of the second shell and peaks created between 66 and 100cm are the third shell. All peaks of each calibration source are separated using these boundaries. The result is shown in figure 10. To test how significant the difference of the plots are we again used the test. The KS-distance is calculated between the S1 of all peaks and each shell. This gives three KS-KS-distances

Table 4: Table to test captions and labels

Source Average KS-value Alpha Radon _{3.13 ×10}−2 1.99609 Argon _{5.53 ×10}−3 1.99988 Krypton-I _{1.54 ×10}−2 1.99905 Krypton-II _{1.10 ×10}−2 1.99954

which are averaged. The average KS-value is used in equation 3 to give a boundaryα value. The results of which are visible in table 4.

Again, comparing this with the alpha value from section 2.3 theαvalues are much closer than, for example, the simulations. For argon it is even higher. Only radon appears to have a significantly lower value.

4

Conclusions and discussion

For this thesis the current S1 simulation model is researched with the aim to find out if it should be adapted or not to make it more applicable for other particles such as radon, argon, krypton-I and II. We therefore research the simulations from figure 9. When looking at these plots it is quite apparent that the simulations are not as good as the simulation from figure 6. For a more quantitative conclusion we use the test. To judge the simulations the KS-distance and equation 3 is used to find a boundary value for α. This value will be compared with the value from section 2.3. Although the value itself is not very reasonable since it does not value between 0 and 1, comparing the number amongst the simulations might give a good enough indication about the quality of the fit. The_α-values found for the simulations are all lower than found in section 2.3.

One explanation for this contrast can be found in the data processors that were used. For this thesis the data was processed differently. This is visible when comparing figures 4 and 7. In the inset plots it is noticeable that especially the tale of the S1’s look significantly dissim-ilar. Radons energy stays relatively high around 500ns. The energy of argon and krypton-II also remains higher compared to figure 4. And krypton-I has several peaks and valleys. It is probable that due to this reason simulating krypton-I gave very different optimal parameter values. This difference can be the reason why the simulations come out with these statistical

values. To conclude, to make accurate simulations more extensive data processing is required. The current manner in which the data is processed gives different ends of the waveform which influences the simulation values.

Concerning adding the height value as a parameter, as seen in figure 10 the height of the interaction site does not seem to have apparent effect on the shape of the S1. The_α-values between the S1 per shell and the average S1 of all peaks also do not differ very largely to the value from section 2.3. Indicating that is does not have large significant effect. This makes sense due to the fact that the photons do not go directly towards the PMT’s. They go in random directions and reflect on the detector walls before they finally reach the PMT. This makes the travelled distance per photon non-dependent on the height of the interaction site. For radon it might seem like there could be a significant difference. This could be possible, but it could probably be explained by the fact that peaks that are created near the PMTs saturate, due to the high energy of the radon decay peaks (8). For the boundaries of radon only peaks that are created in the middle part of the detector (20-80cm) should be considered. Knowing this, the z-parameter should probably not be added to the model. Instead, what could be interesting to look at is the photon travel time. This possibly does have an influence on the shape of the S1 since the photon travel times can be considerately different per interaction.

Acknowledgements

Of course I would not have been able to do this project all by myself. There are a number of people who contributed directly of indirectly to my project.

Firstly, thank you Peter for helping and supporting me almost every day. You always kept believing in me, even when it took me a full week to open a file using my terminal. I’m also very grateful for Auke Pieter Colijn for being my supervisor. Thank you for organising the bachelor theses at NikHef. The projects were conducted during very rare times, so organisationally it went a little different than everyone was used to, but due to your great supervising skills conducting research from a distance it wasn’t a big problem at all. You offered much clarity for the students during very ambiguous times. I would like to thank the dark matter research group for letting me join them the past three months. Unfortunately I never met all of you in person, but you were all very kind and supportive towards me, which I greatly appreciate. Because of you I know what it is like to work in a research group, an experience for which I am grateful. Lastly, I would like to acknowledge my family and friends. Even though you couldn’t help me much with the contents of my research, you helped me complete this project through mental support.

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