TT participated in the conception of this project, helped derive the new formulas for the dark matter induced electronic absorption rate, created the Fortran package EXCEED-DM to calculate the dark matter electron absorption rates, created all the figures and participated to writing the manuscript. TT participated in the conception of this project, helped develop the Python package, PhonoDark, to calculate the scattering rate of single phonons in dark matter, and participated in writing the manuscript.
LIST OF ILLUSTRATIONS
This term derives from the NLO operator in NR EFT (underlined in Table 9.1) and cannot be directly related to the optical properties of the target (ie, the complex conductivity/dielectric function). P.1, the Ecut parameters in the legend correspond to the values used for the low/high E regions.
LIST OF TABLES
The (effective) currents are defined by L ⊃ gXφJX (X = S, P) or gXVµJXµ (X =V, A,edm,mdm,ana, V2), after integration of parts in the last four cases. The leading-order non-vanishing coefficients c(ψ)i for the operators Oi(ψ) (defined in Table 7.3) are listed in the penultimate column.
INTRODUCTION
The Evidence for Dark Matter
However, not only the temperature of the CMB is measured, fluctuations in this temperature are as well. The evolution of the scale factor is determined by Friedmann equations and depends on the cosmological content of the universe.
Theoretical Motivation for Light Dark Matter Models
This is not very attractive as a production mechanism for the DM abundance, since the value is precisely tuned to the initial state of the action field, which previously rolled around in the flat potential. Then the action field will essentially be a random value in different regions of the universe.
Direct Detection Preliminaries
Let pχ be the momentum of the incoming DM particle, and p0χ=p−q be the momentum of the outgoing DM particle,4 where q is the momentum leaving the DM system (and entering the detector). Usually this is given in terms of the DM velocity, vχ since pχ = mχvχ in the non-relativistic limit.
Summary
Furthermore, we show how this basis can be used for both DM single phonon scattering and single magnon scattering. We show that these effects can be important for states near the band gap.
MULTI-CHANNEL DIRECT DETECTION OF LIGHT DARK MATTER
THEORETICAL FRAMEWORK
Introduction
We show how this is done in three cases – nuclear recoils, electron transitions and single phonon excitations. Our general framework allows us to derive single phonon excitation rates for arbitrary SI couplings from first principles, such as phonon excitation by coupling to electrons.
General Framework for Spin-Independent Dark Matter Scattering
In the case of the MB distribution in Eq. 2.17), the η function can be evaluated analytically, which gives 2.26). In the case of a vector mediator, effects in medium can cause screening and directly affect detection rates.
Nuclear Recoils
However, in a crystal target, the nuclei are not free, but interact with the neighboring nuclei in the crystal structure. The instantaneous interaction approximation in the standard nuclear recoil calculation is valid when the energy deposition is much higher than the energies of all phonon modes, i.e.
Electron Transitions
Consequently, the speed is essentially independent of the direction of the incoming DM's speed. In ground-based experiments, as the target rotates with the Earth, the DM wind comes from different directions at different times of the day, resulting in a diurnal velocity modulation. Due to the layered crystal structure, the velocity strongly depends on the angle between the DM wind and the layers.
Single Phonon Excitations
For electrons, on the other hand, this is generally not true, as electron wave functions are distorted when an atom/ion is displaced relative to the other atoms/ions in the crystal lattice. For mχ = 1MeV and 10 MeV, Umklapp processes dominate the rate in the heavy mediator case, as the momentum integral is dominated by large q. In the case of a vector mediator, the coupling conditions shown in Eq. 2.104) should incorporate in-medium screening effects according to Eq.
Conclusions
As an example, we calculated the range for DM scattering via a mildly hadrophobic scalar or U(1)B−L vector mediator (Fig. 2.6), where single phonon excitations provide a complementary search channel with competitive sensitivities to previous proposals [10]. ]. We pointed out that the sensitivity of the single phonon excitation channel is not limited to sub-MeV DM. (Fig. 2.5), and single phonon excitations and nuclear recoil play complementary roles in exploring the DM parameter space (Fig. 2.4).
TARGET COMPARISON
Introduction
To achieve this goal, we perform a detailed comparison of target materials in Sections 3.3 and 3.4, focusing on two comparative DM scenarios to illustrate how to optimize target selection for the best sensitivity. The technical aspects of these calculations are discussed in Appendix B, where we also present our calculated electronic band structures and phonon dispersions for the target materials. Results for materials not presented in the main text can be found in Appendix C, along with other parameters assumed in the range calculation.
Detection Channels
For an isotropic target, the dynamic structure factor depends only on the magnitude but not on the direction of q, so that the velocity integral can be evaluated independently, which gives At large q, the dynamic structure factor is suppressed by the Debye-Waller factor that determines it. In contrast, out-of-phase oscillations associated with gap phonon modes differentially increased the sensitivity to DM coupling with atoms/ions in the same primitive cell.
Target Comparison: Kinetically Mixed Light Dark Photon Mediator
227], in the low q limit (which dominates the momentum integral for a light mediator since Fmed2 ∝ q−4), the interaction is described via the Born effective charges of the ions, Z∗j (which is generally 3×3 matrices are ),. Only polar materials, or materials that have differently charged ions in the primitive cell, can couple phonon modes to the dark photon, which explains the absence of phonon range curves for Si and Ge in figure. As explained in the previous section, optical phonon modes involve out-of-phase oscillations and a gap exists.
Target Comparison: Hadrophilic Scalar Mediator
Since hωi is usually related to cs, the order of the curves is the same as in the previous regime. The low mass behavior of the achievement curves is understood in the same way. 3.29)), and lighter elements are favorable. We also see how in the case of acoustic phonons, achieving lower energy thresholds is essential for improving alignment.
Conclusions
Collective Excitations
DIRECTIONAL DETECTABILITY OF DARK MATTER WITH SINGLE PHONON EXCITATIONS: TARGET COMPARISON
- Introduction
- Directional Detection With Single Phonon Excitations Excitation RateExcitation Rate
- Target Comparison
- Conclusions
As explained in the text, the anisotropy factor Yj·ν,k,j in Eq. 4.7) is the dominant factor in determining the daily modulation pattern. The distinct diurnal modulation curves can be understood from the differential velocity plot in the right panel of the figure. Meanwhile, the orientation of the crystal determines the function ve(t) and thus the daily modulation pattern.
DETECTING LIGHT DARK MATTER WITH MAGNONS
- Introduction
- Magnons In Magnetically Ordered Materials
- Magnon Excitation From Dark Matter Scattering
- Projected Reach
- Discussion
- Conclusions
As a first demonstration of the detection concept, we consider a yttrium iron garnet (YIG, Y3Fe5O12) target. For simplicity, we set the DM wind direction to be parallel (perpendicular) to the ground-state spins for the magnetic dipole and anapole (pseudo-mediated) models, which increases the event rate. Consequently, only non-gap modes can be excited, i.e. Goldstone modes of broken rotational symmetry.
DETECTABILITY OF AXION DARK MATTER WITH PHONON POLARITONS AND MAGNONS
Introduction
6.4).3 In the case of phonon excitation, the true energy eigenmodes in a polar crystal, at the low momentum transfers relevant for dark matter absorption, are phonon polaritons due to the mixing between the photon and phonons. We take this mixing into account, while still often referring to the gapped polaritons as phonons, since their phonon components are much larger. Among them, two are particularly promising: the coupling of the gradient of the action field to the electron spin,gaee, allows for magnon excitation, while the action-induced electric field in the presence of an external magnetic field, due to the action - photon coupling gaγγ, can generate phonon polaritons.
General Formalism For Absorption Rate Calculations
For a polar crystal, since the ions are electrically charged, some of the phonon states mix with the photon. However, near the center of the 1BZ, where k .ω – relevant for DM absorption – the photon-phonon mixing modifies the dispersions to avoid a level crossing. The phonon-like states at k ω do not have the same energies as away from the polariton regime: TO phonon-like states become degenerate with the longitudinal optical (LO) phonon state atωLOask→0, whereas there is a LO-TO splitting, ωTO 6=ωLO, at k ω .
Selection Rules And Ways Around Them
The magnetic unit cell contains three Fe3+ magnetic ions with spin 5/2, which form a triangle in the x-y plane. In the simplest and most common case of magnetic ions with quenched orbital angular momenta (i.e. `j'0), we recover the usual result gj = 2. As in the case of phonons, additional selection rules usually exist due to crystal symmetries.
Axion Couplings And Detection Channels
The assembly of the axion wind with the electron spin leads to the assembly with the spin component Fig. In summary, for axion couplings independent of external fields, we found that excitation of magnons via axion wind coupling with electrons is the only viable detection channel. In the presence of a direct magnetic fieldB, the axion field induces oscillating electromagnetic fields via aFF˜ coupling.
Projected Sensitivity
6.3, but with an external magnetic field directed in the xˆ(ˆz) direction on the left (right) plate. The strength of the axion-phonon couplings depends on the orientation of the magnetic field, and different resonances can be selected by changing the direction of the magnetic field. The idea of using an external magnetic field to lift the gapless mode is one adopted in the QUAX experiment [91–93] .
Conclusions
In each case, only one of the 19 gap magnon modes, namely 7 meV and 76 meV, is found to contribute to axon absorption. The single gap mode that couples to the DM action corresponds to the out-of-phase precessions of the tetrahedral and octahedral rotations. On the material side, we would like to make more accurate predictions of detection rates through an improved understanding of phonon and magnon resonance shapes, and explore the possibility of scanning resonance frequencies from material engineering properties, so to fully exploit the discovery potential. of a DM action search experiment based on phonon and magnon excitations.
EFFECTIVE FIELD THEORY OF DARK MATTER DIRECT DETECTION WITH COLLECTIVE EXCITATIONS
Introduction
Within this framework, starting from a UV model consisting of relativistic operators coupling the DM to the proton, neutron and/or electron, we can systematically calculate direct detection rates via single phonon and magnon excitations in various target materials . Finally, in the third step, we quantize the scattering potential to obtain the phonon and magnon modes in a specific target material and calculate the matrix elements for their excitation. These calculations highlight the complementarity between phonon and magnon excitations, and between different targets, in the search of DM light theory space.
Effective Field Theory Calculation of Dark Matter Induced Collective Ex- citationscitations
In each model, the DM χ and an SM fermion ψ each couple to the mediator via a linear combination of the currents in the last column of Table 7.1, whose NR limits can be direct. We now fit the effective operators O(ψ)i to lattice degrees of freedom (highlighted for clarity) appearing in the DM ion scattering potentialsV˜lj. It is generic, since point-like and composite responses arise from the first two terms in the expansion iq·xα = 1 +iq·xα+.
Application to Benchmark Models
As we will see, written in terms of the dimensionless quantities FX,ν(ψ) and EX,ν defined above, Σν(q) can be expressed in a concise form for each benchmark model. Our final results will be presented in terms of the rate per unit target mass, R = 1. The size of the 1BZ is determined by the inverse lattice spacing a−1, and is typically O(keV).
This explains the m−1χ scaling of the purple curves beyond mχ ∼ MeV in the left panel of Fig.7.2. A comparison of the phonon range in these models is shown in the left panel of Fig.7.3. The middle and right panels of Fig.7.3 zoom in on the magnetic dipole and anapole DM models, respectively, and compare the range of phonon and magnon excitations.
Electronic Excitations
EXTENDED CALCULATION OF DARK MATTER ELECTRON SCATTERING IN CRYSTAL TARGETS
Introduction
Electronic states near the band gap deviate significantly from atomic orbitals and must be calculated numerically. On the other hand, our modeling of core (3d) states is similar to the semi-analytical approach of Ref. 35] overestimates the rate at smaller mχ due to reduced accuracy in modeling valence and conduction states.
Electronic States
