Tag Archives: inference

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!