arXiv subjects

Benjamin Lillard

Publications and source records attributed to Benjamin Lillard.

At least 19 recordsLinked to original sources

arXiv2026

The Role of Symmetries in Dark Matter Detector Design

Anisotropic materials have emerged as promising candidates for the next generation of sub-GeV dark matter direct detection experiments, because their intrinsic directionality gives rise to a daily modulation signal as the detector rotates with respect to a dark matter wind. Predicting the shape of the modulation signal requires knowledge of the electronic excited states: however, we show that the amplitude of the modulation can be estimated using only the symmetries of the material. By decomposing the finite momentum dark matter--electron scattering form factor into spherical harmonics, we show that the 230 crystallographic space groups collapse to just 5 classes, distinguished by their suppression of the quadrupole modes of the squared form factor. We apply our symmetry-projection framework to the special case of molecular crystals, and derive an accurate group-theoretic estimator for the loss of daily modulation signal due to crystallisation, which depends only on the symmetries and relative orientations of the molecules within the crystal. Finally, we demonstrate that these estimates are linearly proportional to the absolute magnitude of the modulation signal, allowing us to rank molecular crystals without the need for expensive electronic structure calculations. Together, these results provide a fast and interpretable route to large-scale screening of anisotropic materials for directional dark matter detection.

hep-ph↗

arXiv2026

Statistics of Daily Modulation in Dark Matter Direct Detection Experiments

The time-dependent modulation of the event rate in dark matter direct detection experiments, arising from the motion of the Earth with respect to the Galactic rest frame, is a distinctive signature whose observation is crucial for claiming a discovery of dark matter. While annual modulation has been well studied for decades, daily modulation due to the Earth's rotation has attracted increased attention recently due to the identification of anisotropic solid-state detector materials that yield a direction-dependent scattering rate without sacrificing the overall rate. We perform a statistical analysis of daily modulation in dark matter scattering experiments, with the goal of maximizing the statistical significance of a modulating signal in the presence of an unknown background rate, which may be either flat (non-modulating), or modulating over a 24-hour period with a known or unknown phase. In the background-dominated regime, we find that the discovery significance scales as $f_\text{RMS} \sqrt{T}$, where $T$ is the total exposure time and $f_\text{RMS}$ is the root-mean-square modulation amplitude; in particular, the significance continues to improve with exposure rather than saturating due to systematic uncertainties in the background rate. Using anisotropic trans-stilbene detectors for sub-GeV dark matter as a benchmark example, we provide prescriptions for optimizing the significance for a given total detector mass and location. In an example analysis using three detectors, optimizing the detector orientations can reduce the required exposure by a factor of $\sim 5$ for a desired discovery or exclusion significance, even after profiling over an unknown modulating background phase.

hep-ph↗

arXiv2025

A Numerical Method for the Efficient Calculation of Scattering Form Factors

Scintillating molecular crystals have emerged as prime candidates for directional dark matter detector targets. This anisotropy makes them exquisitely sensitive due to the daily modulation induced by the directional dark matter wind. However, predicting the interaction rate for arbitrary molecules requires accurate modeling of the many-body ground as well as excited states, a task that has been historically computationally expensive. Here, we present a theory and computational framework for efficiently computing dark matter scattering form factors for molecules. We introduce SCarFFF, a GPU-accelerated code to compute the fully three-dimensional anisotropic molecular form factor for arbitrary molecules. We use a full time-dependent density functional theory framework to compute the lowest-lying singlet excited states, adopting the B3YLP exchange functional and a double-zeta Gaussian basis set. Once the many-body electronic structure is computed, the form factors are computed in a small fraction of the time from the transition density matrix. We show that ScarFFF can compute the first 12 form factors for a molecule of 10 heavy atoms in approximately 5 seconds, opening the door to accurate, high-throughput material screening for optimal directional dark matter detector targets. Our code can perform the calculation in three independent ways, two semi-analytical and one fully numeric, providing optimised methods for every precision goal.

hep-ph↗

arXiv2025

Simplified Spin Dependence in Dark Matter Direct Detection

The interactions of dark matter with Standard Model particles can be systematically studied in the language of effective field theories. We investigate dark matter interactions with Standard Model particles, including spin-dependent interactions, for direct detection experiments and demonstrate that, although the scattering rate generally depends on multiple types of material response functions, certain linear combinations of these material response functions vanish if the initial and final electronic states share the same Hamiltonian. We also find that several other response functions vanish in parity-symmetric materials, making these systems as simple as isotropic detectors in some respects. Finally, we present the scattering rate for an anisotropic, possibly chiral detector, for generic dark matter-electron spin interactions. These relations reduce the number of independent response functions needed, thereby simplifying the computational complexity for a broad class of dark matter models. Our results provide a complete and efficient toolkit for analyzing electron recoil signals in diverse detector materials.

hep-ph↗

arXiv2025

Vector Spaces for Dark Matter (VSDM): Fast Direct Detection Calculations with Python and Julia

Anisotropic target materials are promising candidates for dark matter direct detection experiments, providing a directional sensitivity that can be used to distinguish a dark matter (DM) signal from the various Standard Model backgrounds. In this paper we introduce the Julia and Python implementations of \emph{Vector Spaces for Dark Matter} (VSDM), which handle the difficult scattering rate computation for these rotating, three-dimensional response functions by calculating a partial rate matrix for every combination of DM velocity distribution, material response function, and particle DM properties.

hep-ph↗

arXiv2023

Stochastic Gravitational Waves from Early Structure Formation

Early matter-dominated eras (EMDEs) are a natural feature arising in many models of the early universe and can generate a stochastic gravitational wave background (SGWB) during the transition from an EMDE to the radiation-dominated universe required by the time of Big Bang Nucleosynthesis. While there are calculations of the SGWB generated in the linear regime, no detailed study has been made of the nonlinear regime. We perform the first comprehensive calculation of GW production in the nonlinear regime, using a hybrid $N$-body and lattice simulation to study GW production from both a metastable matter species and the radiation produced in its decay. We find that nonlinearities significantly enhance GW production up to frequencies at least as large as the inverse light-crossing time of the largest halos that form prior to reheating. The resulting SGWB is within future observational reach for curvature perturbations as small as those probed in the cosmic microwave background, depending on the reheating temperature. Out-of-equilibrium dynamics could further boost the induced SGWB, while a fully relativistic gravitational treatment is required to resolve the spectrum at even higher frequencies.

astro-ph.CO↗

arXiv2023

Extracting Halo Independent Information from Dark Matter Electron Scattering Data

Direct detection experiments and the interpretation of their results are sensitive to the velocity structure of the dark matter in our galactic halo. In this work, we extend the formalism that deals with such astrophysics-driven uncertainties, originally introduced in the context of dark-matter-nuclear scattering, to include dark-matter-electron scattering interactions. Using mock data, we demonstrate that the ability to determine the correct dark matter mass and velocity distribution is depleted for recoil spectra which only populate a few low-lying bins, such as models involving a light mediator. We also demonstrate how this formalism allows one to test the compatibility of existing experimental data sets (e.g. SENSEI and EDELWEISS), as well as make predictions for possible future experiments (e.g. GaAs-based detectors).

hep-ph↗

arXiv2023

Wavelet-Harmonic Integration Methods

A new integration method drastically improves the efficiency of the dark matter direct detection calculation. In this work I introduce a complete, orthogonal basis of spherical wavelet-harmonic functions, designed for the new vector space integration method. This factorizes the numeric calculation into a ``vector'' that depends only on the astrophysical velocity distribution; a second vector, depending only on the detector form factor; and a scattering matrix defined on the basis functions, which depends on the details of the dark matter (DM) particle model (e.g.~its mass). For common spin-independent DM--Standard Model interactions, this scattering matrix can be evaluated analytically in the wavelet-harmonic basis. This factorization is particularly helpful for the more complicated analyses that have become necessary in recent years, especially those involving anisotropic detector materials or more realistic models of the local DM velocity distribution. With the new method, analyses studying large numbers of detector orientations and DM particle models can be performed more than 10~million times faster. This paper derives several analytic results for the spherical wavelets, including an extrapolation in the space of wavelet coefficients, and a generalization of the vector space method to a much broader class of linear functional integrals. Both results are highly relevant outside the field of DM direct detection.

hep-ph↗

arXiv2023

Partial Rate Matrix for Dark Matter Scattering

I present a highly efficient integration method for scattering calculations, and a ``partial rate matrix'' that encodes the scattering rate as a function of the $SO(3)$ orientation of the detector. This replaces the original multidimensional rate integral with a simple exercise in vector multiplication, speeding up the rate calculation by a factor of around $10^8$. I include a scheme to fully factorize the dark matter particle model, its astrophysical velocity distribution, and the properties of the target material from each other, enabling efficient calculation of the partial rate matrix even in studies comparing large sets of these input functions. This is now the only sensible way to evaluate the dark matter scattering rate in anisotropic detector materials. It is straightforward to generalize this method to other difficult but linear problems.

hep-ph↗

arXiv2023

Neutralizing Topological Obstructions to Bubbles of Nothing

Theories with compact extra dimensions can exhibit a vacuum instability known as a bubble of nothing. These decay modes can be obstructed if the internal manifold is stabilized by fluxes, or if it carries Wilson lines for background gauge fields, or if the instanton is incompatible with the spin structure. In each of these cases the decay can proceed by adding dynamical charged membranes or gauge fields. We give a general, bottom-up procedure for constructing approximate bubble of nothing solutions in models with internal spheres stabilized by flux and study the influence of the brane tension on the tunneling exponent, finding two branches of solutions that merge at a minimal superextremal value of the tension. In the case of Wilson operators and incompatible fermions, the relevant bubble is shown to be the Euclidean Reissner-Nordstrom black hole, and the ordinary decay exponent is modified by $1/g^2$ effects. We examine the Dirac operator on this background and comment on the relevance for models of supergravity with gauged $R$-symmetry.

hep-th↗

arXiv2022

TF08 Snowmass Report: BSM Model Building

We summarize the state of Beyond the Standard Model (BSM) model building in particle physics for Snowmass 2021, focusing mainly on several whitepaper contributions to BSM model building (TF08) and closely related areas.

hep-ph↗

arXiv2022

The Molecular Migdal Effect

Nuclear scattering events with large momentum transfer in atomic, molecular, or solid-state systems may result in electronic excitations. In the context of atomic scattering by dark matter (DM), this is known as the Migdal effect, but the same effect has also been studied in molecules in the chemistry and neutron scattering literature. Here we present two distinct Migdal-like effects from DM scattering in molecules, which we collectively refer to as the molecular Migdal effect: a center-of-mass recoil, equivalent to the standard Migdal treatment, and a non-adiabatic coupling resulting from corrections to the Born-Oppenheimer approximation. The molecular bonds break spherical symmetry, leading to large daily modulation in the Migdal rate from anisotropies in the matrix elements. Our treatment reduces to the standard Migdal effect in atomic systems but does not rely on the impulse approximation or any semiclassical treatments of nuclear motion, and as such may be extended to models where DM scatters through a long-range force. We demonstrate all of these features in a few simple toy models of diatomic molecules, namely ${\rm H}_2^+$, N$_2$, and CO, and find total molecular Migdal rates competitive with those in semiconductors for the same target mass. We discuss how our results may be extended to more realistic targets comprised of larger molecules which could be deployed at the kilogram scale.

hep-ph↗

arXiv2022

Snowmass White Paper: Strong CP Beyond Axion Direct Detection

We sketch recent progress and promising future directions for research connected with the strong CP problem. Topics surveyed include axion dark matter substructure and its gravitational detection; axion model building and the quality problem; experimental tests of ultraviolet solutions; and connections to lattice QCD.

hep-ph↗

arXiv2021

Confinement On the Moose Lattice

In this work we present a new class of N=1 supersymmetric confining gauge theories, with strikingly simple infrared theories that descend from intricate interconnected networks of product gauge groups. A diagram of the gauge groups and the charged matter content of the ultraviolet theory has the structure of a triangular lattice, with $SU(N)$ or $SU(3 N)$ gauge groups at each of the vertices, connected by bifundamental chiral superfields. This structure admits a $U(1)_R$ conserving superpotential with marginal trilinear operators. With the introduction of this superpotential, the $SU(3N)$ and $SU(N)$ gauge groups confine: in the far infrared limit of the supersymmetric theory, the relevant degrees of freedom are gauge invariant "mesons" and "baryons." In this paper we show how the properties of the infrared degrees of freedom depend on the topology and shape of the moose/quiver ``lattice'' of the original gauge theory. We investigate various deformations of the theory, and propose some phenomenological applications for BSM models.

hep-th↗

arXiv2021

Uncovering an Axion Mechanism with the EDM Portfolio

Effective field theory arguments suggest that if BSM sectors contain new sources of CP-violation that couple to QCD, these sources will renormalize the $\theta$ term and frustrate ultraviolet solutions to the strong CP problem. Simultaneously, they will generate distinctive patterns of low-energy electric dipole moments in hadronic, nuclear, atomic, and molecular systems. Observing such patterns thus provides evidence that strong CP is solved by an infrared relaxation mechanism. We illustrate the renormalization of $\theta$ and the collections of EDMs generated in a several models of BSM physics, confirming effective field theory expectations, and demonstrate that measurements of ratios of electric dipole moments at planned experiments can provide valuable input on the resolution of the strong CP problem.

hep-ph↗

arXiv2021

de Sitter Decays to Infinity

Bubbles of nothing are a class of vacuum decay processes present in some theories with compactified extra dimensions. We investigate the existence and properties of bubbles of nothing in models where the scalar pseudomoduli controlling the size of the extra dimensions are stabilized at positive vacuum energy, which is a necessary feature of any realistic model. We map the construction of bubbles of nothing to a four-dimensional Coleman-De Luccia problem and establish necessary conditions on the asymptotic behavior of the scalar potential for the existence of suitable solutions. We perform detailed analyses in the context of five-dimensional theories with metastable $\text{dS}_4 \times S^1$ vacua, using analytic approximations and numerical methods to calculate the decay rate. We find that bubbles of nothing sometimes exist in potentials with no ordinary Coleman-De Luccia decay process, and that in the examples we study, when both processes exist, the bubble of nothing decay rate is typically faster. Our methods can be generalized to other stabilizing potentials and internal manifolds.

hep-th↗

arXiv2021

Bubble of nothing decays of unstable theories

Theories with compact extra dimensions are sometimes unstable to decay into a bubble of nothing -- an instability resulting in the destruction of spacetime. We investigate the existence of these bubbles in theories where the moduli fields that set the size of the extra dimensions are stabilized at a positive vacuum energy -- a necessary ingredient of any theory that aspires to describe the real world. Using bottom-up methods, and focusing on a five-dimensional toy model, we show that four-dimensional de Sitter vacua admit bubbles of nothing for a wide class of stabilizing potentials. We show that, unlike ordinary Coleman-De Luccia tunneling, the corresponding decay rate remains non-zero in the limit of vanishing vacuum energy. Potential implications include a lower bound on the size of compactified dimensions.

hep-th↗

arXiv2021

Dark Matter Daily Modulation With Anisotropic Organic Crystals

Aromatic organic compounds, because of their small excitation energies ~ O(few eV) and scintillating properties, are promising targets for detecting dark matter of mass ~ O(few MeV). Additionally, their planar molecular structures lead to large anisotropies in the electronic wavefunctions, yielding a significant daily modulation in the event rate expected to be observed in crystals of these molecules. We characterize the daily modulation rate of dark matter interacting with an anisotropic scintillating organic crystal such as trans-stilbene, and show that daily modulation is an ~ O(1) fraction of the total rate for small DM masses and comparable to, or larger than, the ~ 10% annual modulation fraction at large DM masses. As we discuss in detail, this modulation provides significant leverage for detecting or excluding dark matter scattering, even in the presence of a non-negligible background rate. Assuming a non-modulating background rate of 1/min/kg that scales with total exposure, we find that a 100 kg yr experiment is sensitive to the cross section corresponding to the correct relic density for dark matter masses between 1.3-14 MeV (1.5-1000 MeV) if dark matter interacts via a heavy (light) mediator. This modulation can be understood using an effective velocity scale v* = Delta E/q*, where Delta E is the electronic transition energy and q* is a characteristic momentum scale of the electronic orbitals. We also characterize promising future directions for development of scintillating organic crystals as dark matter detectors.

hep-ph↗