Unified halo-independent formalism from convex hulls for direct dark matter searches

Journal Article · Wed Dec 27 00:00:00 EST 2017 · Journal of Cosmology and Astroparticle Physics

DOI:https://doi.org/10.1088/1475-7516/2017/12/039· OSTI ID:1608997

Gelmini, Graciela B. ^[1]; Huh, Ji-Haeng ^[2]; Witte, Samuel J. ^[3]

---

1. Univ. of California, Los Angeles, CA (United States)
2. European Organization for Nuclear Research (CERN), Geneva (Switzerland)
3. 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

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 f^gal(), 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 ⁰_BF(v_min) (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 f^gal(), which is a sum of Galactic streams, yields a periodic time-dependent halo function _BF(v_min, t) which at any fixed time is a piecewise constant function of v_min 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(v_min, t) function (and a time-averaged ⁰_BF(v_min)) that is piecewise linear, differing significantly from best-fit halo functions obtained without the assumption of isotropy.

• Research Organization: Univ. of California, Los Angeles, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP); National Research Foundation of Korea (NRF)
• Grant/Contract Number: SC0009937
• OSTI ID: 1608997
• Journal Information: Journal of Cosmology and Astroparticle Physics, Vol. 2017, Issue 12; ISSN 1475-7516
• Publisher: Institute of Physics (IOP)
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
dark matter theory
dark matter experiment