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Title: 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:
 [1];  [2];  [1]
  1. Department of Physics and Astronomy, UCLA,475 Portola Plaza, Los Angeles, CA 90095 (United States)
  2. 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}
}
  • We extend and correct a recently proposed maximum-likelihood halo-independent method to analyze unbinned direct dark matter detection data. Instead of the recoil energy as independent variable we use the minimum speed a dark matter particle must have to impart a given recoil energy to a nucleus. This has the advantage of allowing us to apply the method to any type of target composition and interaction, e.g. with general momentum and velocity dependence, and with elastic or inelastic scattering. We prove the method and provide a rigorous statistical interpretation of the results. As first applications, we find that for dark mattermore » particles with elastic spin-independent interactions and neutron to proton coupling ratio f{sub n}/f{sub p}=−0.7, the WIMP interpretation of the signal observed by CDMS-II-Si is compatible with the constraints imposed by all other experiments with null results. We also find a similar compatibility for exothermic inelastic spin-independent interactions with f{sub n}/f{sub p}=−0.8.« less
  • We extend and correct a recently proposed maximum-likelihood halo-independent method to analyze unbinned direct dark matter detection data. Instead of the recoil energy as independent variable we use the minimum speed a dark matter particle must have to impart a given recoil energy to a nucleus. This has the advantage of allowing us to apply the method to any type of target composition and interaction, e.g. with general momentum and velocity dependence, and with elastic or inelastic scattering. We prove the method and provide a rigorous statistical interpretation of the results. As first applications, we find that for dark mattermore » particles with elastic spin-independent interactions and neutron to proton coupling ratio f{sub n}/f{sub p}=−0.7, the WIMP interpretation of the signal observed by CDMS-II-Si is compatible with the constraints imposed by all other experiments with null results. We also find a similar compatibility for exothermic inelastic spin-independent interactions with f{sub n}/f{sub p}=−0.8.« less
  • Results from direct detection experiments are typically interpreted by employing an assumption about the dark matter velocity distribution, with results presented in the m{sub χ}−σ{sub n} plane. Recently methods which are independent of the DM halo velocity distribution have been developed which present results in the v{sub min}−g-tilde plane, but these in turn require an assumption on the dark matter mass. Here we present an extension of these halo-independent methods for dark matter direct detection which does not require a fiducial choice of the dark matter mass. With a change of variables from v{sub min} to nuclear recoil momentum (p{submore » R}), the full halo-independent content of an experimental result for any dark matter mass can be condensed into a single plot as a function of a new halo integral variable, which we call h-til-tilde(p{sub R}). The entire family of conventional halo-independent g-tilde(v{sub min}) plots for all DM masses are directly found from the single h-tilde(p{sub R}) plot through a simple rescaling of axes. By considering results in h-tilde(p{sub R}) space, one can determine if two experiments are inconsistent for all masses and all physically possible halos, or for what range of dark matter masses the results are inconsistent for all halos, without the necessity of multiple g-tilde(v{sub min}) plots for different DM masses. We conduct a sample analysis comparing the CDMS II Si events to the null results from LUX, XENON10, and SuperCDMS using our method and discuss how the results can be strengthened by imposing the physically reasonable requirement of a finite halo escape velocity.« less
  • Results from direct detection experiments are typically interpreted by employing an assumption about the dark matter velocity distribution, with results presented in the m{sub χ}−σ{sub n} plane. Recently methods which are independent of the DM halo velocity distribution have been developed which present results in the v{sub min}− g-tilde plane, but these in turn require an assumption on the dark matter mass. Here we present an extension of these halo-independent methods for dark matter direct detection which does not require a fiducial choice of the dark matter mass. With a change of variables from v{sub min} to nuclear recoil momentummore » (p{sub R}), the full halo-independent content of an experimental result for any dark matter mass can be condensed into a single plot as a function of a new halo integral variable, which we call h-tilde (p{sub R}). The entire family of conventional halo-independent g-tilde (v{sub min}) plots for all DM masses are directly found from the single h-tilde (p{sub R}) plot through a simple rescaling of axes. By considering results in h-tilde (p{sub R}) space, one can determine if two experiments are inconsistent for all masses and all physically possible halos, or for what range of dark matter masses the results are inconsistent for all halos, without the necessity of multiple g-tilde (v{sub min}) plots for different DM masses. We conduct a sample analysis comparing the CDMS II Si events to the null results from LUX, XENON10, and SuperCDMS using our method and discuss how the results can be strengthened by imposing the physically reasonable requirement of a finite halo escape velocity.« less
  • Results from direct detection experiments are typically interpreted by employing an assumption about the dark matter velocity distribution, with results presented in the m χ – σ n plane. Recently methods which are independent of the DM halo velocity distribution have been developed which present results in the v min – g ~ plane, but these in turn require an assumption on the dark matter mass. Here we present an extension of these halo-independent methods for dark matter direct detection which does not require a fiducial choice of the dark matter mass. With a change of variables from v minmore » to nuclear recoil momentum (p R), the full halo-independent content of an experimental result for any dark matter mass can be condensed into a single plot as a function of a new halo integral variable, which we call tilde h(p R). The entire family of conventional halo-independent tilde g ~(v min) plots for all DM masses are directly found from the single tilde h ~(p R) plot through a simple rescaling of axes. By considering results in tildeh ~(p R) space, one can determine if two experiments are inconsistent for all masses and all physically possible halos, or for what range of dark matter masses the results are inconsistent for all halos, without the necessity of multiple tilde g ~(v min) plots for different DM masses. As a result, we conduct a sample analysis comparing the CDMS II Si events to the null results from LUX, XENON10, and SuperCDMS using our method and discuss how the results can be strengthened by imposing the physically reasonable requirement of a finite halo escape velocity.« less