The Dark Matter Inverse Problem: Extracting Particle Physics from Scattering Events
Samuel D. McDermott, Hai-Bo Yu, Kathryn M. Zurek

TL;DR
This paper investigates how well future dark matter direct detection experiments can identify the underlying particle physics interactions from scattering spectra, highlighting the importance of multiple targets and high event counts.
Contribution
It demonstrates the potential and limitations of extracting particle physics operators from scattering data, emphasizing the role of multiple targets and large event samples.
Findings
Single target with 300 events has limited discrimination power.
Multiple targets or more events improve operator discrimination.
High mass dark matter candidates are easier to distinguish with fewer events.
Abstract
The primary observable in dark matter direct detection is the spectrum of scattering events. We simulate multiple positive direct detection signals (on germanium, xenon, and argon targets) to explore the extent to which the underlying particle physics, manifested in the momentum dependence of the operator mediating the scattering, can be extracted. Taking into account realization (Poisson) noise, a single target nucleus with 300 events has limited power to discriminate operators with momentum dependence differing by q^\pm2 for a wide range of dark matter masses from 10 GeV to 1 TeV. With the inclusion of multiple targets (or a factor of several more events on a single target), the discrimination of operators with different momentum dependence becomes very strong at the 95% C.L. for dark matter candidates of mass 50 GeV and above. On the other hand, operator discrimination remains poor…
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