# Assessing compatibility of direct detection data: halo-independent global likelihood analyses

## Abstract

We present two different halo-independent methods to assess the compatibility of several direct dark matter detection data sets for a given dark matter model using a global likelihood consisting of at least one extended likelihood and an arbitrary number of Gaussian or Poisson likelihoods. In the first method we find the global best fit halo function (we prove that it is a unique piecewise constant function with a number of down steps smaller than or equal to a maximum number that we compute) and construct a two-sided pointwise confidence band at any desired confidence level, which can then be compared with those derived from the extended likelihood alone to assess the joint compatibility of the data. In the second method we define a “constrained parameter goodness-of-fit” test statistic, whose p-value we then use to define a “plausibility region” (e.g. where p≥10%). For any halo function not entirely contained within the plausibility region, the level of compatibility of the data is very low (e.g. p<10%). We illustrate these methods by applying them to CDMS-II-Si and SuperCDMS data, assuming dark matter particles with elastic spin-independent isospin-conserving interactions or exothermic spin-independent isospin-violating interactions.

- Authors:

- Department of Physics and Astronomy, UCLA,475 Portola Plaza, Los Angeles, CA 90095 (United States)
- CERN Theory Division,CH-1211, Geneva 23 (Switzerland)

- Publication Date:

- Sponsoring Org.:
- SCOAP3, CERN, Geneva (Switzerland)

- OSTI Identifier:
- 22572166

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2016; Journal Issue: 10; Other Information: PUBLISHER-ID: JCAP10(2016)029; OAI: oai:repo.scoap3.org:17559; cc-by Article funded by SCOAP3. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 License. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COMPATIBILITY; ISOSPIN; NONLUMINOUS MATTER; PARTICLE IDENTIFICATION; PARTICLE INTERACTIONS; SI SEMICONDUCTOR DETECTORS; SUPERSYMMETRY; UNDERGROUND FACILITIES; WIMPS

### Citation Formats

```
Gelmini, Graciela B., Huh, Ji-Haeng, and Witte, Samuel J.
```*Assessing compatibility of direct detection data: halo-independent global likelihood analyses*. United States: N. p., 2016.
Web. doi:10.1088/1475-7516/2016/10/029.

```
Gelmini, Graciela B., Huh, Ji-Haeng, & Witte, Samuel J.
```*Assessing compatibility of direct detection data: halo-independent global likelihood analyses*. United States. doi:10.1088/1475-7516/2016/10/029.

```
Gelmini, Graciela B., Huh, Ji-Haeng, and Witte, Samuel J. Tue .
"Assessing compatibility of direct detection data: halo-independent global likelihood analyses". United States.
doi:10.1088/1475-7516/2016/10/029.
```

```
@article{osti_22572166,
```

title = {Assessing compatibility of direct detection data: halo-independent global likelihood analyses},

author = {Gelmini, Graciela B. and Huh, Ji-Haeng and Witte, Samuel J.},

abstractNote = {We present two different halo-independent methods to assess the compatibility of several direct dark matter detection data sets for a given dark matter model using a global likelihood consisting of at least one extended likelihood and an arbitrary number of Gaussian or Poisson likelihoods. In the first method we find the global best fit halo function (we prove that it is a unique piecewise constant function with a number of down steps smaller than or equal to a maximum number that we compute) and construct a two-sided pointwise confidence band at any desired confidence level, which can then be compared with those derived from the extended likelihood alone to assess the joint compatibility of the data. In the second method we define a “constrained parameter goodness-of-fit” test statistic, whose p-value we then use to define a “plausibility region” (e.g. where p≥10%). For any halo function not entirely contained within the plausibility region, the level of compatibility of the data is very low (e.g. p<10%). We illustrate these methods by applying them to CDMS-II-Si and SuperCDMS data, assuming dark matter particles with elastic spin-independent isospin-conserving interactions or exothermic spin-independent isospin-violating interactions.},

doi = {10.1088/1475-7516/2016/10/029},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 10,

volume = 2016,

place = {United States},

year = {Tue Oct 18 00:00:00 EDT 2016},

month = {Tue Oct 18 00:00:00 EDT 2016}

}