Search for light dark matter interactions enhanced by the Migdal effect in XENON1T

When a particle elastically scatters off a xenon nucleus, it has been assumed that electron clouds immediately follow the motion of the nucleus, but in reality it takes some time for the atomic electrons to catch up, resulting in ionization and excitation of the atom. This effect is called the Migdal effect, which was predicted by A. B. Migdal and recently reformulated in the context of Dark Matter searches by Ibe. et alWhile the elastic scattering of WIMPs produces nuclear recoils, the Migdal effect predicts secondary electronic recoils that can accompany a nuclear recoil. Unlike nuclear recoils, electronic recoils lose negligible energy as heat, because electrons have small masses compared with xenon nuclei. This results in a lower energy threshold for electronic recoil signals – in XENON1T, down to about 1 keV. Therefore, searching for the electronic recoil signals induced by the Migdal effect enables a significant boost of XENON1T’s sensitivity to low-mass dark matter, based on this lowered threshold. In this search, we adopted an approach that utilizes the ionization signal only (so-called S2-only analysis), as well as both scintillation and ionization signals (S1-S2 analysis), which enables to lower the detection threshold. We interpreted the results in different cases: spin-(in)dependent (SI/SD) WIMP-nucleon interaction and the scenario where the interaction is mediated by a scalar force mediator (light mediator). The results for the spin-(in)dependent WIMP-nucleon interaction are shown in the following figure:
 
We set the most stringent upper limits on the SI and SD WIMP-nucleon interaction cross-sections for masses below 1.8 GeV and 2 GeV, respectively. Together with the standard nuclear recoil search, XENON1T results have thus reached unprecedented sensitivities to both low-mass (sub-GeV) and high-mass (GeV – TeV) WIMPs. An open access pre-print of the paper can of course be found on the arxiv.

Light Dark Matter Search Results from XENON1T

XENON1T recently released a preprint with new world-leading constraints on light dark matter particles.

The challenge of light dark matter

The XENON1T detector aims find the signals of dark matter bouncing off xenon atoms.
If such a collision happens, it produces two signals: a small light flash (S1), and a cloud of free electrons that can be drifted up and extracted out of the detector (S2).

Figure: How dark matter would make S1 and S2 signals in the XENON1T detector.

However, dark matter lighter than about six times the proton mass (6 GeV/c^2) cannot push the heavy xenon atoms (131 GeV/c^2) enough to make efficiently detectable S1s. XENON1T needs both S1 and S2 to accurately reconstruct where in the detector the event happened. The time between the S1 and S2 signals reveals the depth of the event. Events at the top and bottom edge of the detector are common due to radioactive backgrounds. If we cannot reject these events, dark matter searches will not be efficient. Thus, most strong constraints on light dark matter have, until now, come from different detectors, mostly using ultra-low temperature crystals made of Germanium, Silicone, or Calcium Tungstate.

The S2-only technique

XENON1T’s new preprints use an “S2-only analysis”, where events without S1s are still considered. Advances in detector construction and analysis techniques led to a thousand times lower background level than previously achieved in S2-only searches.

For example, the S2 electron cloud becomes broader as it drifts upward, like a drop of ink spreading out in water. The deeper the event, the broader the cloud, and the longer the S2 signal lasts. Thus XENON1T could reject most of the events at the top and bottom, even without the S1, by rejecting very short and very long S2 signals.

The results

Most theorists predict that dark matter would collide with the heavy xenon nuclei and produce “nuclear recoils”. For these, the S2-only technique is sensitive to 2-3x lower energies than traditional analyses. Thus, we get improved constraints on light dark matter:

Figure: New XENON1T limits (black lines) on light dark matter. The colored lines show previous results, including other results from XENON1T in blue.

In some models, dark matter collides with electrons around the nucleus, and produces “electronic recoils”. These make much larger S2 signals than nuclear recoils of the same S1 size. S2-only searches thus improve the energy threshold for these models by as much as a factor of ten. Combined with the lower background, XENON1T’s S2-only results thus improve the constraints on such models by several orders of magnitude:

Figure: New XENON1T limits on scattering of dark matter on electrons. (The dashed line is the same analysis repeated with more conservative assumptions.)

For more information, please see our arXiv preprint at https://arxiv.org/abs/1907.11485.

 

Signal Reconstruction, Calibration and Event Selection in XENON1T

Since the first release of dark matter search results based on the 1 tonne-year exposure of the XENON1T experiment, the collaboration has published more WIMP signal searches based on the same dataset. Those articles are usually written in a brief way and are focusing on the communication of the scientific results.

In order to give more details on the XENON1T dark matter analysis, we have previously published a paper focusing on the signal and background models and the statistical inference using this data. It has been complemented by a new article that reveals details on the challenges of detector characterization and data preparation before it is ready to be used for model building and statistical inference in order to make statements on dark matter.

The XENON1T experiment performed two science runs between October 2016 and February 2018, reaching a total data livetime of 279 days. During that time the detector had to be operated in a very stable mode in order to ensure undistorted signals. If some conditions change over time they have to be modeled over time in order to account for them in the take them into account during data analysis and include them into the models. One example for those changes are the ones at the photosensors. Each sensor has an individual amplification factor, i.e. gain, that is a function of the applied high voltage. few sensors developed malfunctions during the science runs because of which the amplification factor decreased over time or the voltage had to be reduced resulting in a sudden decreased of the amplification. Those variations are shown in red and black for two sensors as a function of time in the following figure while green, blue and magenta show stable sensors which are representative for the majority of the XENON1T light detectors.

 

Measured photosensor amplification factor as a function of time for three representative stable sensors (green, blue and magenta) and two examples where the amplification decreased due to malfunctions (red and black).

As soon as the detector operation conditions are modeled the data is put through selection criteria that reduce the number of background-like signatures and therefore enhance the signal to background ratio. The criteria are grouped into four general types:

 

Acceptance of dark matter signal events after incrementally applying data selection criteria in order to reduce background-like signatures. The acceptance is shown as function of the signal parameters S1 and S2.

Modelling how an electronic or nuclear recoil will look like in the detector is crucial both to know the shape of a WIMP signal, and to model the backgrounds well. XENON1T uses a comprehensive fit to multiple calibration sources to constrain the distributions of  backgrounds and signals in the analysis space; S1, S2 and the radius from the center axis of the detector. Some background components are harder to model directly, and are estimated by using sidebands or other data samples. In the XENON1T analysis, coincidences between unrelated, lone S1 and S2 events were modeled this way, in addition to the surface background– events occurring close to or at the detector wall.

The models of each background and the signal, for two separate science runs, are put together in a likelihood, which is a mathematical function of the WIMP signal strength as well as nuisance parameters. These are unknowns that could change the analysis, such as the true expectation value for each background component. The likelihood also contains multiple terms representing measurements of nuisance parameter, which constrain them when the likelihood is fitted to the data collected by XENON1T. The value of the likelihood evaluated at a specific signal strength has a random distribution which is estimated using simulated realizations of the experimental outcome. The final statistical limits are computed by comparing the likelihood computed on the actual data with the distributions found from the simulations:

Observing the Rarest Decay Process Ever Measured

[Press Release April 2019 – for immediate release. Paper published in Nature and preprint on the arxiv.]

The universe is almost 14 billion years old. An inconceivable length of time by human standards – yet compared to some physical processes, it is but a moment. There are radioactive nuclei that wdecay on much longer time scales. Using our XENON1T detector at the INFN Gran Sasso National Laboratory, we were able to observe the decay of Xenon-124 atomic nuclei for the first time.

The half-life of a process is the time after which half of the radioactive nuclei present in a sample have decayed away. The half-life measured for Xenon-124 is about one trillion times longer than the age of the universe. This makes the observed radioactive decay, the so-called double electron capture of Xenon-124, the rarest process ever seen happening in a detector. “The fact that we managed to observe this process directly demonstrates how powerful our detection method actually is – also for signals which are not from dark matter,” says Prof. Christian Weinheimer from the University of Münster (Germany) whose group lead the study. In addition, the new result provides information for further investigations on neutrinos, the lightest of all elementary particles whose nature is still not fully understood. XENON1T is a joint experimental project of about 160 scientists from Europe, the US and the Middle East. The results were published in the science journal “Nature”.

A sensitive dark matter detector

The Gran Sasso Laboratory of the National Institute for Nuclear Physics (INFN) in Italy, where scientists are currently searching for dark matter particles is located about 1,400 meters beneath the Gran Sasso massif, well protected from cosmic rays which can produce false signals. Theoretical considerations predict that dark matter should very rarely “collide” with the atoms of the detector. This assumption is fundamental to the working principle of the XENON1T detector: its central part consists of a cylindrical tank of about one meter in length filled with 3,200 kilograms of liquid xenon at a temperature of –95° C. When a dark matter particle interacts with a xenon atom, it transfers energy to the atomic nucleus which subsequently excites other xenon atoms. This leads to the emission of faint signals of ultraviolet light which are detected by means of sensitive light sensors located in the upper and lower parts of the cylinder. The same sensors also detect a minute amount of electrical charge which is released by the collision process.

In double electron capture, two electrons and two protons simultaneously convert into two neutrons and two neutrinos. X-rays are emitted when the electron vacancies are subsequently filled.

The new study shows that the XENON1T detector is also able to measure other rare physical phenomena, such as double electron capture. To understand this process, one should know that an atomic nucleus normally consists of positively charged protons and neutral neutrons, which are surrounded by several atomic shells occupied by negatively charged electrons. Xenon-124, for example, has 54 protons and 70 neutrons. In double electron capture, two protons in the nucleus simultaneously “catch” two electrons from the innermost atomic shell, transform into two neutrons, and emit two neutrinos. The other atomic electrons reorganize themselves to fill in the two holes in the innermost shell. The energy released in this process is carried away by X-rays and so-called Auger electrons. However, these signals are very hard to detect, as double electron capture is a very rare process which is hidden by signals from the omnipresent natural radioactivity.

The measurement

The peak at 64keV from double electron capture of Xenon-124 is clearly visible in this plot of the background spectrum from XENON1T.

This is how the XENON collaboration succeeded with this measurement: The X-rays from the double electron capture in the liquid xenon produced an initial light signal as well as free electrons. The electrons were moved towards the gas-filled upper part of the detector where they generated a second light signal. The time difference between the two signals corresponds to the time it takes the electrons to reach the top of the detector. Scientists used this interval and the information provided by the sensors measuring the signals to reconstruct the position of the double electron capture. The energy released in the decay was derived from the strength of the two signals. All signals from the detector were recorded over a period of more than one year, however, without looking at them at all as the experiment was conducted in a “blind” fashion. This means that the scientists could not access the data in the energy region of interest until the analysis was finalized to ensure that personal expectations did not skew the outcome of the study. Thanks to the detailed understanding of all relevant sources of background signals it became clear that 126 observed events in the data were indeed caused by the double electron capture of Xenon-124.

Using this first-ever measurement, the physicists calculated the enormously long half-life of 1.8×1022 years for the process. This is the slowest process ever measured directly. It is known that the atom Tellurium-128 decays with an even longer half-life, however, its decay was never observed directly and the half-life was inferred indirectly from another process. The new results show how well the XENON1T detector can detect rare processes and reject background signals. While two neutrinos are emitted in the double electron capture process, scientists can now also search for the so-called neutrino-less double electron capture which could shed light on important questions regarding the nature of neutrinos.

Status and outlook

XENON1T acquired data from 2016 until December 2018 when it was switched off. The scientists are currently upgrading the experiment for the new “XENONnT” phase which will feature a three times larger active detector mass. Together with a reduced background level this will boost the detector’s sensitivity by an order of magnitude.

 

Modeling and statistical analysis of the XENON1T data

On May 31st 2018, XENON1T released the result of a search for dark matter interacting with xenon atoms using an exposure of 1 tonne-year. Papers presenting the scientific results are written to be brief, and communicate the most important information to the scientific community. Therefore, many details of the instrument, reconstruction of events and analysis work by the entire collaboration must be left out of the science papers. XENON1T has previously published a paper focusing on the operation of the detector itself. A new paper by XENON1T now goes into the details of the analysis of the XENON1T data, and another one, on the event reconstruction and calibration, is being prepared.

XENON1T detects the scintillation light and ionization electrons that energy depositions in the two tonne liquid xenon target produce. In addition to WIMPs, different background sources can produce an S1+S2 signal. The expected S1,S2 distribution may change depending on whether the energy deposition happens by a recoil on an electron of the xenon atom or the nucleus. This is one of the main methods XENON uses to discriminate against backgrounds, since WIMPs, which scatter on the xenon nucleus, have a mean S2 lower than 99.7% of the dominant background component, which is made up of scatters on electrons.

Modelling how an electronic or nuclear recoil will look like in the detector is crucial both to know the shape of a WIMP signal, and to model the backgrounds well. XENON1T uses a comprehensive fit to multiple calibration sources to constrain the distributions of backgrounds and signals in the analysis space; S1, S2 and the radius from the center axis of the detector.
Some background components are harder to model directly, and are estimated by using sidebands or other data samples. In the XENON1T analysis, coincidences between unrelated, lone S1 and S2 events were modeled this way, in addition to the surface background– events occurring close to or at the detector wall.

Models of various backgrounds and the expected WIMP signal in two of the parameters extracted from each even, scintillation S1 and ionization S2 signals.


The models of each background and the signal, for two separate science runs, are put together in a likelihood, which is a mathematical function of the WIMP signal strength as well as nuisance parameters. These are unknowns that could change the analysis, such as the true expectation value for each background component. The likelihood also contains multiple terms representing measurements of nuisance parameter, which constrain them when the likelihood is fitted to the data collected by XENON1T.

The value of the likelihood evaluated at a specific signal strength has a random distribution which is estimated using simulated realizations of the experimental outcome. The final statistical limits are computed by comparing the likelihood computed on the actual data with the distributions found from the simulations: 

Likelihood as function of the signal strength (measured by the WIMP-nucleon cross-section)
The gray area shows likelihoods that corresponds to a 90% exclusion. The confidence interval– the region of signal strength compatible with the observed data– is the region where the likelihood lies below the gray band.


The models and tools used in the XENON1T spin-independent analysis are also used to explore alternative models of dark matter, such as spin-independent interactions and scatterings between WIMPs and pions, with more to come!

 

The first limits on spin-independent WIMP-pion interactions

XENON1T was built to observe the recoil of xenon-atoms, which may be caused by the interaction of a Weakly Interacting Massive Particle (WIMP) as it passes through the detector. A recoiling xenon atom produces scintillation light and ionization that XENON1T detects as an S1 and S2 signal, which carry information of the recoil type, energy and position in the detector. The first results of the XENON1T were published on the spin-independent WIMP-nucleon interaction, which is expected to dominate the WIMP scattering rate. However, models of WIMPs exist where this contribution would be suppressed or vanish. XENON has therefore performed searches for alternative WIMP-recoil spectra, such as the one expected if the scattering depends on the nucleon spins.

A careful accounting of all the possible WIMP-nucleon interactions showed that WIMPs can also interact with pions— subatomic particles that contribute to the strong force that binds atoms together. The figure illustrates a WIMP (χ) scattering via a mediator line on a pion (π) exchanged between a proton and a neutron in the xenon nucleus. The xenon atom recoils from the interaction, which can be observed with our detector. Similarly to the spin-independent recoil, the wimp-pion interaction happens in a way where the WIMP scatters coherently, off the entire xenon atom together. 

A WIMP scattering on a pion exchanged within the xenon nucleus

The analysis was performed with the same tools as the main XENON1T spin-independent WIMP search, and 1 tonne-years of data. No significant evidence for a signal was observed, so we set the first limits on the spin-independent WIMP-pion interaction strength. An open access pre-print of the paper can be found on the arxiv.

XENON1T Result covered by CERN Ccourier

XENON1T results from a 1 ton-year dark matter exposure.

Our latest dark matter results from XENON1T, the most sensitive search for WIMPs with an unprecedented liquid xenon exposure of 1 ton-years and a world-record low background level is featured in the July/August 2018 edition of the CERN Courier, the International Journal of High-Energy Physics. Read the full article here.

 

Search for bosonic super-WIMP interactions with the XENON100 experiment

While the microscopic nature of dark matter in the Universe is largely unknown, the simplest assumption which can explain all existing observations is that it is made of a new, as yet undiscovered particle. Leading examples are weakly interacting massive particles (WIMPs), axions or axion-like particles (ALPs), and sterile neutrinos. WIMPs with masses in the GeV range, as well as axions/ALPs are examples for cold dark matter while sterile neutrinos with masses at the keV-scale are an example for warm dark matter. Cold dark matter particles were nonrelativistic at the time of their decoupling from the rest of the particles in the early universe. In contrast, warm dark matter particles remain relativistic for longer, retain a larger velocity dispersion, and thus more easily free-stream out from small-scale perturbations. Astrophysical and cosmological observations constrain the mass of warm dark matter to be larger than about 3keV/c2, with a more recent lower limit from Lyman-alpha forest data being 5.3keV/c2. Another example for warm dark matter particles are bosonic super-WIMPs. These particles, with masses at the keV-scale, could couple electromagnetically to standard model particles via the axioelectric effect, which is an analogous process to the photoelectric effect, and thus be detected in direct detection experiments.

The limit derived from the XENON100 experiment on the coupling of SuperWIMPs.

We searched for vector and pseudo-scalar bosonic super-WIMPs with the XENON100 experiment. The super-WIMPs can be absorbed in liquid xenon and the expected signature is a monoenergetic peak at the super-WIMP’s rest mass. A profile likelihood analysis of data with an exposure of 224.6 live days × 34kg showed no evidence for a signal above the expected background. We thus obtained new upper limits in the (8 − 125) keV/c2 mass range, excluding couplings to electrons with coupling constants of gae > 3 × 10−13 for pseudo-scalar super-WIMPs and α′/α > 2 × 10−28 for vector super-WIMPs, respectively. We expect to improve upon these results with the XENON1T detector, which operates a larger mass of liquid xenon with reduced backgrounds. Our results were published in Physical Review D 96, 122002 (2017) and are of course also available at the arxiv.

Intrinsic backgrounds from Rn and Kr in the XENON100 experiment

XENON1T is currently the largest liquid xenon detector in the search for dark matter. To fully exploit the capabilities of the ton-scale target mass, a thorough understanding of radioactive background sources is required. In this paper we use the full data of the main science runs of the XENON100 experiment that were taken over a period of about 4 years to asses the target-intrinsic background sources radon (Rn-222), thoron (Rn-220) and krypton (Kr-85). We derive distributions of the individual radionuclides inside the detector (see Figure below) and quantify their abundances during the main three science runs. We find good agreement with external measurements of radon emanation and krypton concentrations, and report an observed reduction in concentrations of radon daughters that we attribute to the plating-out of charged ions on the negatively biased cathode.

The preprint of the full study is available on arXiv:1708.03617.

Figure: Spatial distributions of the various radon populations identified in XENON100.

Search for WIMP Inelastic Scattering Off Xenon Nuclei With XENON100

Most direct detection searches focus on elastic scattering of galactic dark matter particles off nuclei, where the keV-scale nuclear recoil energy is to be detected. In this work, the alternative process of inelastic scattering is explored, where a WIMP-nucleus scattering induces a transition to a low-lying excited nuclear state. The experimental signature is a nuclear recoil detected together with the prompt de-excitation photon. We consider the scattering of dark matter particle off 129Xe isotope, which has an abundance of 26.4\% in natural xenon, and when excited to it lowest-lying 3/2+ state above the ground state it emits a 36.9 keV photon. This electromagnetic nuclear decay has a half-life of 0.97 ns.

The WIMP inelastic scattering  is complementary to spin-dependent, elastic scattering, and dominates the integrated rates above 10 keV of deposited energy. In addition, in case of a positive signal, the observation of inelastic scattering would provide a clear indication of the spin-dependent nature of the fundamental interaction.

The search is performed using XENON100 Run-II science data, which corresponds to an exposure of 34×224.6 kg×days. No evidence of dark matter is found and a limit on dark matter inelastic interaction cross section is set. Our result, shown in the Figure, is the most stringent limit for the spin-dependent inelastic scattering to date, and set the stage for a sensitive search of inelastic WIMP-nucleus scattering in running or upcoming liquid xenon experiments such as XENON1T, XENONnT, LZ, and DARWIN.

Full details may be found in this article: Phys. Rev. D 96, 022008 and on the arxiv.