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We provide expressions for the nonperturbative matching of the effective field theory describing dark matter interactions with quarks and gluons to the effective theory of nonrelativistic dark matter interacting with nonrelativistic nucleons. We give the leading and subleading order expressions in chiral counting. In general, a single partonic operator already matches onto several nonrelativistic operators at leading order in chiral counting. Thus, keeping only one operator at the time in the nonrelativistic effective theory does not properly describe the scattering in direct detection. Moreover, the matching of the axial--axial partonic level operator, as well as the matching of the operators coupling DM to the QCD anomaly term, naively include momentum suppressed terms. However, these are still of leading chiral order due to pion poles and can be numerically important. We illustrate the impact of these effects with several examples.
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Dark matter could emerge along with the Higgs as a composite pseudo-Nambu-Goldstone boson $chi$ with decay constant $fsim mathrm{TeV}$. This type of WIMP is especially compelling because its leading interaction with the Standard Model, the derivative Higgs portal, has the correct annihilation strength for thermal freeze-out if $m_chi sim O(100)$ GeV, but is negligible in direct detection experiments due to the very small momentum transfer. The explicit breaking of the shift symmetry which radiatively generates $m_chi$, however, introduces non-derivative DM interactions. In existing realizations a marginal Higgs portal coupling $lambda$ is generated with size comparable to the Higgs quartic, and thus well within reach of XENON1T. Here, we present and analyze the interesting case where the pattern of explicit symmetry breaking naturally suppresses $lambda$ beyond the reach of current and future direct detection experiments. If the DM acquires mass from bottom quark loops, the bottom quark also mediates suppressed DM-nucleus scattering with cross sections that will be eventually probed by LZ. Alternatively, the DM can obtain mass from gauging its stabilizing $U(1)$ symmetry. No direct detection signal is expected even at future facilities, but the introduction of a dark photon $gamma_D$ has a number of phenomenological implications which we study in detail, treating $m_{gamma_D}$ as a free parameter. Complementary probes of the dark sector include indirect DM detection, DM self-interactions, and extra radiation, as well as collider experiments. We frame our discussion in an effective field theory, motivating our parameter choices with a detailed analysis of an $SO(7)/SO(6)$ composite Higgs model, which can yield either scenario at low energies.
Beginning with a set of simplified models for spin-0, spin-$half$, and spin-1 dark matter candidates using completely general Lorentz invariant and renormalizable Lagrangians, we derive the full set of non-relativistic operators and nuclear matrix elements relevant for direct detection of dark matter, and use these to calculate rates and recoil spectra for scattering on various target nuclei. This allows us to explore what high energy physics constraints might be obtainable from direct detection experiments, what degeneracies exist, which operators are ubiquitous and which are unlikely or sub-dominant. We find that there are operators which are common to all spins as well operators which are unique to spin-$half$ and spin-1 and elucidate two new operators which have not been previously considered. In addition we demonstrate how recoil energy spectra can distinguish fundamental microphysics if multiple target nuclei are used. Our work provides a complete roadmap for taking generic fundamental dark matter theories and calculating rates in direct detection experiments. This provides a useful guide for experimentalists designing experiments and theorists developing new dark matter models.
In this work we introduce RAPIDD, a surrogate model that speeds up the computation of the expected spectrum of dark matter particles in direct detection experiments. RAPIDD replaces the exact calculation of the dark matter differential rate (which in general involves up to three nested integrals) with a much faster parametrization in terms of ordinary polynomials of the dark matter mass and couplings, obtained in an initial training phase. In this article, we validate our surrogate model on the multi-dimensional parameter space resulting from the effective field theory description of dark matter interactions with nuclei, including also astrophysical uncertainties in the description of the dark matter halo. As a concrete example, we use this tool to study the complementarity of different targets to discriminate simplified dark matter models. We demonstrate that RAPIDD is fast and accurate, and particularly well-suited to explore a multi-dimensional parameter space, such as the one in effective field theory approach, and scans with a large number of evaluations.
The direct detection of sub-GeV dark matter interacting with nucleons is hampered by to the low recoil energies induced by scatterings in the detectors. This experimental difficulty is avoided in the scenario of boosted dark matter where a component of dark matter particles is endowed with large kinetic energies. In this Letter, we point out that the current evaporation of primordial black holes with masses from $10^{14}$ to $10^{16}$ g is a source of boosted light dark matter with energies of tens to hundreds of MeV. Focusing on the XENON1T experiment, we show that these relativistic dark matter particles could give rise to a signal orders of magnitude larger than the present upper bounds. Therefore, we are able to significantly constrain the combined parameter space of primordial black holes and sub-GeV dark matter. In the presence of primordial black holes with a mass of $10^{15}~mathrm{g}$ and an abundance compatible with present bounds, the limits on DM-nucleon cross-section are improved by four orders of magnitude.
We study the capabilities of the MAJORANA DEMONSTRATOR, a neutrinoless double-beta decay experiment currently under construction at the Sanford Underground Laboratory, as a light WIMP detector. For a cross section near the current experimental bound, the MAJORANA DEMONSTRATOR should collect hundreds or even thousands of recoil events. This opens up the possibility of simultaneously determining the physical properties of the dark matter and its local velocity distribution, directly from the data. We analyze this possibility and find that allowing the dark matter velocity distribution to float considerably worsens the WIMP mass determination. This result is traced to a previously unexplored degeneracy between the WIMP mass and the velocity dispersion. We simulate spectra using both isothermal and Via Lactea II velocity distributions and comment on the possible impact of streams. We conclude that knowledge of the dark matter velocity distribution will greatly facilitate the mass and cross section determination for a light WIMP.
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