We show that the rate for dark-matter-electron scattering in an arbitrary material is determined by an experimentally measurable quantity, the complex dielectric function, for any dark matter interaction that couples to electron density. This formulation automatically includes many-body effects, eliminates all systematic theoretical uncertainties on the electronic wave functions, and allows a direct calibration of the spectrum by electromagnetic probes such as infrared spectroscopy, x-ray scattering, and electron energy-loss spectroscopy. Our formalism applies for several common benchmark models, including spin-independent interactions through scalar and vector mediators of arbitrary mass. We discuss the consequences for standard semiconductor and superconductor targets and find that the true reach of superconductor detectors for light mediators exceeds previous estimates by several orders of magnitude, with further enhancements possible due to the low-energy tail of the plasmon. Using a heavy-fermion superconductor as an example, we show how our formulation allows a rapid and systematic investigation of novel electron scattering targets.
Bibliographical noteFunding Information:
Gordon and Betty Moore Foundation American Physical Society Aspen Center for Physics National Science Foundation Fermilab U.S. Department of Energy High Energy Physics Israel Science Foundation United States-Israel Binational Science Foundation Planning and Budgeting Committee of the Council for Higher Education of Israel Azrieli Foundation U.S. Department of Energy
We thank Carlos Blanco, Vinayak Dravid, Rouven Essig, Sinéad Griffin, Adolfo Grushin, David Huse, Simon Knapen, Belina von Krosigk, Jonathan Kozaczuk, Eric David Kramer, Tongyan Lin, Mariangela Lisanti, Andrea Mitridate, Lucas Wagner, and Kathryn Zurek for enlightening discussions. Y. K. is indebted to Peter Abbamonte for relentlessly (and correctly) emphasizing the importance of the loss function and plasmon excitations for dark matter scattering. The idea for this work was conceived via an email exchange during the New Directions in Light Dark Matter workshop at Fermilab, supported by the Gordon and Betty Moore Foundation and the American Physical Society, and via a Skype call taken during the workshop “Quantum Information and Systems for Fundamental Physics” at the Aspen Center for Physics, which is supported by National Science Foundation Grant No. PHY-1607611. This project was supported in part by the Fermi National Accelerator Laboratory, managed and operated by Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with the U.S. Department of Energy, through the Office of High Energy Physics QuantISED program. The work of Y. H. is supported by the Israel Science Foundation (Grant No. 1112/17), by the Binational Science Foundation (Grant No. 2016155), by the I-CORE Program of the Planning Budgeting Committee (Grant No. 1937/12), and by the Azrieli Foundation. The work of Y. K. is supported in part by DOE Award No. DE-SC0015655. Parts of this document were prepared by N. K. using the resources of the Fermi National Accelerator Laboratory (Fermilab), a U.S. Department of Energy, Office of Science, HEP User Facility. Fermilab is managed by Fermi Research Alliance, LLC (FRA), acting under Contract No. DE-AC02-07CH11359. The work of B. V. L. is supported in part by DOE Award No. DE-SC0010107. T. C. Y. is supported by the U.S. Department of Energy under Award No. DE-AC02-76SF00515. K. K. B. acknowledges support for the later stages of the work from the Fermi Research Alliance, LLC (FRA) and the U.S. Department of Energy (DOE) under contract No. DE-AC02-07CH11359; the initial stages of the work were supported by the DOE under the QuantiSED program, Award No. DE-SC0019129.
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