Eugenio Del Nobile - The Theory of Direct Dark Matter Detection: A Guide to Computations

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The nature of dark matter (DM), invisible matter whose existence is only inferred through its gravitational influence on other objects, is one of the biggest mysteries in modern physics and astronomy. A vast experimental program is currently in place to establish detection through non-gravitational DM signatures, at the forefront of which are direct searches. Unlike other detection strategies which rely on indirect evidences of its existence, direct detection experiments aim at directly uncovering DM, traditionally by observing recoils of detector nuclei struck by passing DM particles. The rate and energy spectrum of these nuclear recoils can then be matched with what is predicted by theoretical models to pin down the properties of DM. This highlights the need of performing accurate theoretical computations to be compared with experimental data.

These notes have been written with the aim to provide extensive guidance for computations in direct DM detection phenomenology. They are a pedagogical yet general and model independent manual, with examples from standard and non-standard particle DM models. They feature self-contained chapters on non-relativistic (NR) expansion, elastic and inelastic scattering kinematics, DM velocity distribution, hadronic matrix elements, nuclear form factors, cross sections, rate spectra, and parameter-space constraints as well as a handy two-page summary and Q&A section for a quick reference.

Direct detection experiments are traditionally concerned with DM in the form of weakly interacting massive particles (WIMPs); for this reason, in these notes, we use DM as a synonym for WIMP. We do not, however, enforce any strict definition of WIMPs, rather thinking of them in broad terms, as DM particles that can be detected on Earth through scattering off nuclei. In this sense, we will not delimit the range of WIMP mass a priori, but rather work out what masses experiments can be sensitive to. Likewise, we will not focus on any specific WIMP candidate, but rather try to be as general and model independent as possible.

These notes are organized as follows. We first discuss the general grounds of direct DM detection in Chap. , which also features a handy Q&A section.

These notes ideally follow the spirit of the Review of mathematics, numerical factors, and corrections for dark matter experiments based on elastic nuclear recoil by J. D. Lewin and P. F. Smith , although without its convenient conciseness. Computations are worked out in all their crucial steps, and a number of examples are presented throughout to complement and illustrate the theoretical arguments. A code for generating most of the figures of these notes is also publicly available on this working as a frame to the various parts.

An effort has been made to present the material of these notes in a form compatible with the different notations adopted in the literature, so that it is readily comparable with results found elsewhere. The discussion is kept as general as possible; however, we restrict ourselves to elementary DM particles with spin 0 and 12 in our examples in Chaps.. Assumptions are spelled out systematically, and our notation is summarized in a stand-alone chapter for a quick reference.