Unified halo-independent formalism from convex hulls for direct dark matter searches
Abstract
Using the Fenchel-Eggleston theorem for convex hulls (an extension of the Caratheodory theorem), we prove that any likelihood can be maximized by either a dark matter 1- speed distribution F(v) in Earth's frame or 2- Galactic velocity distribution fgal(), consisting of a sum of delta functions. The former case applies only to time-averaged rate measurements and the maximum number of delta functions is (-1), where is the total number of data entries. The second case applies to any harmonic expansion coefficient of the time-dependent rate and the maximum number of terms is . Using time-averaged rates, the aforementioned form of F(v) results in a piecewise constant unmodulated halo function 0BF(vmin) (which is an integral of the speed distribution) with at most (-1) downward steps. The authors had previously proven this result for likelihoods comprised of at least one extended likelihood, and found the best-fit halo function to be unique. This uniqueness, yet, cannot be guaranteed in the more general analysis applied to arbitrary likelihoods. Thus we introduce a method for determining whether there exists a unique best-fit halo function, and provide a procedure for constructing either a pointwise confidence band, if the best-fit halo function is unique, or a degeneracymore »
- Authors:
-
- Univ. of California, Los Angeles, CA (United States)
- European Organization for Nuclear Research (CERN), Geneva (Switzerland)
- Univ. of California, Los Angeles, CA (United States); Consejo Superior de Investigaciones Cientificas (CSIC), Valencia (Spain). Inst. de Física Corpuscular (IFIC) and Univ. of Valencia
- Publication Date:
- Research Org.:
- Univ. of California, Los Angeles, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP); National Research Foundation of Korea (NRF)
- OSTI Identifier:
- 1608997
- Grant/Contract Number:
- SC0009937
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Cosmology and Astroparticle Physics
- Additional Journal Information:
- Journal Volume: 2017; Journal Issue: 12; Journal ID: ISSN 1475-7516
- Publisher:
- Institute of Physics (IOP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; dark matter theory; dark matter experiment
Citation Formats
Gelmini, Graciela B., Huh, Ji-Haeng, and Witte, Samuel J. Unified halo-independent formalism from convex hulls for direct dark matter searches. United States: N. p., 2017.
Web. doi:10.1088/1475-7516/2017/12/039.
Gelmini, Graciela B., Huh, Ji-Haeng, & Witte, Samuel J. Unified halo-independent formalism from convex hulls for direct dark matter searches. United States. https://doi.org/10.1088/1475-7516/2017/12/039
Gelmini, Graciela B., Huh, Ji-Haeng, and Witte, Samuel J. Wed .
"Unified halo-independent formalism from convex hulls for direct dark matter searches". United States. https://doi.org/10.1088/1475-7516/2017/12/039. https://www.osti.gov/servlets/purl/1608997.
@article{osti_1608997,
title = {Unified halo-independent formalism from convex hulls for direct dark matter searches},
author = {Gelmini, Graciela B. and Huh, Ji-Haeng and Witte, Samuel J.},
abstractNote = {Using the Fenchel-Eggleston theorem for convex hulls (an extension of the Caratheodory theorem), we prove that any likelihood can be maximized by either a dark matter 1- speed distribution F(v) in Earth's frame or 2- Galactic velocity distribution fgal(), consisting of a sum of delta functions. The former case applies only to time-averaged rate measurements and the maximum number of delta functions is (-1), where is the total number of data entries. The second case applies to any harmonic expansion coefficient of the time-dependent rate and the maximum number of terms is . Using time-averaged rates, the aforementioned form of F(v) results in a piecewise constant unmodulated halo function 0BF(vmin) (which is an integral of the speed distribution) with at most (-1) downward steps. The authors had previously proven this result for likelihoods comprised of at least one extended likelihood, and found the best-fit halo function to be unique. This uniqueness, yet, cannot be guaranteed in the more general analysis applied to arbitrary likelihoods. Thus we introduce a method for determining whether there exists a unique best-fit halo function, and provide a procedure for constructing either a pointwise confidence band, if the best-fit halo function is unique, or a degeneracy band, if it is not. Using measurements of modulation amplitudes, the aforementioned form of fgal(), which is a sum of Galactic streams, yields a periodic time-dependent halo function BF(vmin, t) which at any fixed time is a piecewise constant function of vmin with at most downward steps. In this case, we explain how to construct pointwise confidence and degeneracy bands from the time-averaged halo function. Lastly, we show that requiring an isotropic Galactic velocity distribution leads to a Galactic speed distribution F(u) that is once again a sum of delta functions, and produces a time-dependent BF(vmin, t) function (and a time-averaged 0BF(vmin)) that is piecewise linear, differing significantly from best-fit halo functions obtained without the assumption of isotropy.},
doi = {10.1088/1475-7516/2017/12/039},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 12,
volume = 2017,
place = {United States},
year = {Wed Dec 27 00:00:00 EST 2017},
month = {Wed Dec 27 00:00:00 EST 2017}
}
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text, January 2014
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text, January 2018
- Ibarra, Alejandro; Kavanagh, Bradley J.; Rappelt, Andreas
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