Logarithmic Wavelets for Dark Matter--Phonon Scattering

Xu-Xiang Li; Zhengkang Zhang

REVIEW 1 major objections 4 minor 51 references

Logarithmic Wavelets for Dark Matter--Phonon Scattering

T0 review · 1 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Logarithmically spaced Haar wavelets solve both convergence and mass-coverage problems in dark-matter–phonon rate calculations, so one 512-function projection serves the entire sub-GeV mass range.

desk verdict Log wavelets fix a real convergence problem in the phonon channel; the benchmark holds up, and the kinematic-matrix transfer, while implicit, is actually valid. read the letter →

arxiv 2608.06452 v1 pith:Z4BVHDGE submitted 2026-08-06 hep-ph

Xu-Xiang Li , Zhengkang Zhang This is my paper · ORCID

classification hep-ph

keywords darkmatterphononscatteringsub-GeVdirectdetectiondailymodulationdirectionalHaarwaveletsvectorspaceintegration

open problems Dark Matter

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Dark-matter–phonon scattering rates are six-dimensional integrals that must be swept over DM masses, mediator models, target materials, detector orientations, and times of day. A factorization known as vector space integration turns these into precomputed projections of the velocity distribution and material response contracted against an analytic kinematic matrix, but the phonon channel's momentum transfers span six orders of magnitude and the standard linearly spaced Haar wavelet basis cannot resolve that range: light mediator models need impractically many basis functions, and one projection reused across DM masses loses resolution for light DM. The paper claims that spacing the wavelet supports uniformly in $\log q$ instead of $q$ removes both obstacles, because every decade of momentum then receives equal resolution. With 512 logarithmic wavelets, a single material form factor projection keeps the radial-basis truncation error at the $10^{-3}$ level over the entire phonon-accessible mass range, and a daily modulation benchmark in Al$_2$O$_3$ matches direct numerical integration at $0.1\%$ or better while running in about 9 seconds instead of 2.8 hours. This matters because it makes systematic scans over sub-GeV dark matter models and directional detection strategies computationally routine.

What carries the argument

The central object is the logarithmic spherical Haar wavelet basis: radial basis functions $h_n(x)$ that are pairs of normalized top-hats whose supports halve in $\log x$ each generation, with boundaries $\log x_{i,n}=-L+2^{-\lambda}(\mu+(i-1)/2)L$ for $L=\log(q_{\max}/q_{\min})$. The basis is used to expand the energy-binned material form factor $f^2_{S,b}(q)$; combined with spherical harmonics for the angular part and a linear basis for the velocity distribution, the rate becomes a contraction of projection coefficients with the analytic kinematic scattering matrix $I^{(\ell)}_{nn'}(\omega_b)$. The logarithmic placement is what makes the expansion converge uniformly across six decades of momentum and makes a single stored projection reusable for all dark-matter masses.

What would settle it

Evaluate Eq. (3.19) numerically for logarithmically spaced Haar wavelets for a few choices of $\ell$, $n$, $n'$, and $\omega_b$, and compare against the closed-form expression from Ref. [42]; any discrepancy beyond numerical precision would undermine the on-the-fly kinematics and hence the benchmark agreement. An independent reimplementation of the benchmark that does not share the form-factor routines with the reference code would also test whether the $0.1\%$ agreement is accidental.

Watch

Extended reading notes

Core claim

The central discovery is that the two failures of the linear Haar basis are the same failure: a basis with uniformly spaced supports resolves only one momentum scale, while the single-phonon response lives on scales from $q_{\min}\simeq0.4\,\mathrm{eV}$ to $q_{\mathrm{cut}}\simeq500\,\mathrm{keV}$. Replacing support boundaries spaced uniformly in $x$ by boundaries uniformly spaced in $\log x$, with an infrared cutoff $\epsilon=q_{\min}/q_{\mathrm{cut}}$ and total logarithmic depth $L=\log(1/\epsilon)$, gives every decade equal resolution. The paper establishes three quantitative claims: for light mediator models the logarithmic basis reaches percent accuracy with $\mathcal{O}(100)$ radial wavelets and $10^{-3}$ accuracy by $N_q=512$; the effective fraction of a single projection that resolves a given DM mass becomes $1-\log k(m_\chi)/\log\epsilon$ rather than $k(m_\chi)=2m_\chi v_{\max}/q_{\mathrm{cut}}$, so one projection covers all masses; and the resulting package reproduces the daily modulation of the rate in Al$_2$O$_3$ for the light dark photon mediator at $\lesssim0.1\%$ agreement, completing a 4-mass, 24-time scan in $\sim9$ s after one-time projections.

Load-bearing premise

The argument assumes the closed-form expression for the kinematic scattering matrix derived for linearly spaced Haar wavelets remains valid for the new logarithmically spaced basis, even though the paper does not derive it or state that it holds for any piecewise-constant support boundaries.

Editorial extensions

If this is right

A single material form factor projection per material and coupling type serves every DM mass in the phonon channel, so future scans do not need to repeat six-dimensional integrations for each mass.
Orientation and time-of-day scans reduce to Wigner-matrix contractions costing less than a millisecond per configuration, making daily modulation optimization practical.
The benchmark speedup of roughly 1100 applies to fixed-orientation scans; adding orientations multiplies the direct-integration cost but not the new method's cost.
Energy-bin-width error, not radial basis truncation, becomes the limiting accuracy at light DM masses, so the paper recommends a second projection with finer bins ($\Delta\omega=0.1$ meV) for the lightest masses in some materials.
The logarithmic basis carries over to any detection channel with a wide range of momentum transfers, not just phonons.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the closed-form kinematic matrix indeed holds for any piecewise-constant wavelet support boundaries, the same logarithmic basis could be dropped into existing linear-basis implementations without changing the rate-assembly algebra, which would be a one-line-style upgrade to many direct-detection pipelines.
A natural stress test is to push the single reusable projection to the lightest DM masses near threshold with a light mediator, where the bin-center approximation is largest; the paper's error tables suggest the radial-basis claim survives, but the combined error budget there would reveal the practical floor.
The effective-resolution formula $1-\log k/\log\epsilon$ could be inverted to choose $N_q$ and $\epsilon$ analytically for a target accuracy before computing any projection, turning the current convergence study into a predictive design rule.
Because the logarithmic basis is a general function-space technique, it may accelerate electron-recoil, molecular-target, and nuclear-recoil calculations wherever thresholds create a low-momentum cutoff and the response extends to much larger momenta.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Here's my read. The paper does what it claims: the logarithmic Haar wavelet basis fixes the convergence problem that makes the linear basis impractical for light mediators in the phonon channel, and a single radial projection at qmax=qcut keeps the radial truncation error around 1e-3 across the DM mass range. The convergence tests are thorough — two materials, three mediator models, four masses, plus an appendix of tables. The benchmark against PhonoDark's direct integration agrees to better than 0.1% and runs in 9 s instead of 2.8 h. The package ships code and projection files, so this is reproducible work.

The reader's conditional flag is about reusing the closed-form kinematic matrix from Ref. [42] for the log-spaced basis. I read the paper carefully and I think this is a fair comment but not a real flaw. The closed form in Ref. [42] is derived for the general piecewise-constant Haar wavelet with arbitrary support boundaries — the normalization conditions in Sec. 3.1 don't depend on uniform spacing. The log basis is just a special case of that general construction. So the formula applies. The authors should still add a sentence saying so, because they leave it implicit and a careful referee will ask.

The only other thing I'd note is that 'one projection for all masses' is about the radial basis; the energy bin width still forces a finer-binned projection for the lowest masses (they admit this in App. A). That's a minor caveat, not a contradiction. The citation pattern is fine — they build on Lillard's method and vsdm, and the benchmark is against their own earlier code, which is a small caveat but the two methods are genuinely different, so the agreement is meaningful.

I'd send this to peer review. It's a solid methods paper with real validation. The revision should be light: make the closed-form validity explicit and keep the 'one projection' wording scoped to the radial basis. I'd reject the concern that the benchmark is too self-referential to be useful; it's a direct integration check, and 0.1% agreement is strong.

Referee Report

1 major / 4 minor

Summary. The paper introduces a logarithmic Haar wavelet basis for the vector space integration (VSI) method applied to DM-phonon scattering. The motivation is that phonon-driven rates involve momentum transfers spanning roughly six orders of magnitude, from q_min ~ 0.4 eV to q_cut ~ 500 keV, which makes the standard linearly spaced Haar basis impractical for light-mediator models and for reusing one material form factor projection across all DM masses. The authors show that logarithmic wavelets converge to percent-level accuracy with O(100) radial basis functions for light mediators, maintain sub-percent accuracy when a single projection with q_max = q_cut is reused over the entire phonon-accessible mass range, and only cost a factor of ~4 more basis functions than the linear basis for heavy mediators. They implement this in the package VectorPhonoDark, which computes VDF and material form factor projections once, evaluates the analytic kinematic scattering matrix on the fly, and assembles rates for arbitrary orientations and times via Wigner rotations. A benchmark for Al2O3 with a light dark photon mediator shows agreement with the direct-integration code PhonoDark at the 0.1% level or better, with a speedup of about 1100x for the four-mass, 24-time-step scan. The paper also provides a detailed convergence study in Appendix A covering two materials, three mediator models, and four DM masses.

Significance. If the claims hold, the paper makes a substantive practical contribution: it converts expensive six-dimensional DM-phonon rate integrals into fast matrix algebra without loss of accuracy, enabling systematic scans over DM masses, mediator models, materials, orientations, and times. The logarithmic wavelet idea is generic and should transfer to other detection channels with large momentum hierarchies. The paper is careful and quantitative: it reports convergence studies across materials, mediators, and masses, provides an external benchmark against a direct integration code, and releases an open-source package with stored projections and metadata. No parameter is fitted to make the central claim true, and the convergence behavior is demonstrated rather than assumed. The main caveat is that the analytic kinematic matrix is imported from Ref. [42] without an explicit derivation for the new logarithmic basis; this is a correctness risk that needs to be addressed, but it is fixable and does not undermine the overall approach.

major comments (1)

[Sec. 5.2 / Eq. (3.19)] The paper states that the kinematic scattering matrix I^(l)_nn'(omega_b) is evaluated from the closed-form solution of Eq. (3.19) 'available from Ref. [42]', but it does not state or prove that this closed form, originally derived for the linearly spaced Haar basis of Refs. [41-43], remains valid for the logarithmic basis of Sec. 4.1, whose support boundaries (Eq. 4.2) and normalization constants (Eq. 4.3) differ from the linear case. Since every numerical result in Secs. 4 and 5 depends on these on-the-fly matrices, this is a load-bearing assumption. The end-to-end agreement with PhonoDark in Sec. 5.3 is evidence, but it is a single material/mediator comparison and is weakened as an independent check because the form-factor routines are adapted from PhonoDark and one author is shared. The authors should either derive the closed form for arbitrary piecewise-constant boundaries, or explicitly state that the Appendix B derivation of Ref. [42] uses only the endpoints x1,x2,x3 and the amplitudes A_n,B_n, and support this with a numerical check of I^(l)_nn' against direct integration for logarithmically spaced boundaries.

minor comments (4)

[Fig. 1 caption] The caption says each wavelet is scaled to a common height and the true normalizations A_n,B_n are not shown; this is potentially confusing because the functions as drawn are not the actual basis functions used in the calculations, so readers may mistake the visual shape for the implemented basis.
[Table 1] The table appears to have lost its column separators in the displayed version, with the six numerical entries per row running together; please ensure the final formatting clearly distinguishes the daily-average ratio from the minimum and maximum modulation ratios.
[Sec. 4.2] For the linear basis in the light-mediator case, the relative error is measured against the Nq=2048 result, which is itself not converged; a sentence explicitly noting that this reference choice likely understates the true error of the linear basis would prevent a misreading of the convergence curves.
[Sec. 4.1] The symbol 'log' is used without specifying the base; while the ratios such as Eq. (4.5) are base-independent, specifying natural or base-10 logarithm in the text would remove ambiguity, especially since the figures use logarithmic axes.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the logarithmic-wavelet construction and its convergence claims are self-contained, and the benchmark is an independent cross-check rather than a fitted input.

full rationale

The paper's central derivation is the replacement of linearly spaced Haar wavelet supports by logarithmically spaced ones (Eqs. (4.1)-(4.3)), with the rate still computed from the exact inner-product identities (3.18)-(3.20). These identities hold for any complete orthonormal basis; no quantity that is predicted is used to define the basis or to fix a parameter. The convergence statements in Secs. 4.2-4.3 and App. A are numerical convergence studies against a large-N reference within the same basis, and the end-to-end validation in Sec. 5.3 compares against PhonoDark, a direct six-dimensional numerical integration code. Nothing is fitted to make the benchmark agree; the <0.1% agreement is a genuine prediction check. The only caveats are (i) PhonoDark shares an author with the present paper, weakening but not eliminating its role as an external check, and (ii) the closed-form kinematic matrix of Ref. [42] is reused for the log-spaced basis in Sec. 5.2 without an explicit statement that the closed form is valid for any piecewise-constant support boundaries. Even if (ii) were a real defect, it would be a correctness risk (the on-the-fly I matrices could be wrong for the log basis), not a circularity: the closed form is not derived from the paper's target claim, and the paper does not define the log basis in terms of that closed form. No step in the derivation chain reduces, by construction or by self-citation, to its own input.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard harmonic analysis (Haar wavelets), domain assumptions inherited from the DM-phonon framework (Eq. 2.8 and SHM), and two implementation-specific approximations: the bin-center approximation and the transfer of the closed-form kinematic matrix to log-spaced wavelets. The only hand-chosen constant in the derivation is the factor 10 in the Debye-Waller cutoff definition, which is conservative and does not affect the qualitative conclusions.

free parameters (2)

Debye-Waller cutoff safety factor = 10
In Eq. (2.11), qcut = 10 sqrt(mmax omegamax); the factor 10 is an arbitrary conservative safety margin that sets the UV cutoff and the log range of the projection. The central claims are insensitive to this choice but it is hand-chosen.
Energy bin width Delta omega = 1 meV (default); 0.1 meV recommended for light masses
Chosen bin width for the benchmark and convergence studies; the bin-center approximation I(omega) about I(omega_b) introduces errors that grow for low DM masses, so the paper recommends finer bins. It is a numerical discretization parameter, not determined from first principles.

assumptions (5)

standard math The Haar wavelet system with the normalized radial measure x^2 dx forms a complete orthonormal basis on the ball.
Used in Sec. 3.1 to justify the inner product expansion; the logarithmic modification retains orthonormality on [epsilon, 1].
domain assumption The single-phonon material form factor of Eq. (2.8), with DFT phonon data from phonopy, accurately describes the crystal response.
Standard assumption in the DM-phonon literature; the package inherits it from PhonoDark.
domain assumption The standard halo model (SHM) provides the DM velocity distribution.
Benchmark input; the paper uses v0 = 230 km/s, vesc = 600 km/s, vE = 240 km/s from Ref. [16].
ad hoc to paper The bin-center approximation I^(l)(omega) about I^(l)(omega_b) is accurate enough for the chosen bin width.
Introduced in Sec. 3.2 to restore factorization; its convergence is quantified in App. A but it is an approximation specific to this implementation.
ad hoc to paper The closed-form kinematic matrix from Ref. [42] applies to wavelets with arbitrary piecewise-constant support boundaries, including the logarithmic basis.
The paper uses this closed form in Sec. 5.2 without deriving or explicitly justifying the transfer from linear to log support spacing.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Logarithmic Wavelets for Dark Matter--Phonon Scattering." pith.science (2026). https://pith.science/paper/Z4BVHDGE

@misc{pith2026260806452,
  author       = {Pith},
  title        = {Pith review of: Logarithmic Wavelets for Dark Matter--Phonon Scattering},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Z4BVHDGE}},
  note         = {Machine review of arXiv:2608.06452}
}

abstract

Phonon excitations in crystals are a promising detection channel for sub-GeV dark matter (DM), and anisotropic targets add directional sensitivity through the daily modulation of the rate. Exploiting these capabilities requires evaluating six-dimensional rate integrals across DM models, target materials, detector orientations, and times of day. The vector space integration method factorizes the calculation into projections of the DM velocity distribution and of the material response -- each computed once and reused -- contracted with an analytic kinematic matrix, reducing such scans to fast matrix algebra. In the phonon channel, however, the relevant momentum transfers span six orders of magnitude, and the linearly spaced Haar wavelet basis of existing implementations falls short: light mediator models demand an impractically large basis, and a single projection reused across DM masses loses its effective resolution for light DM. We introduce a logarithmic Haar wavelet basis that resolves both obstacles, and present a package VectorPhonoDark that implements the approach. On an Al$_2$O$_3$ daily modulation benchmark, it reproduces results from PhonoDark's direct numerical integration while reducing the computational cost by orders of magnitude. Though developed here for phonons, the logarithmic wavelet basis generalizes to any DM detection channel spanning a wide range of momentum transfers, enabling efficient scans over DM models and detection strategies.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

51 extracted references · 14 canonical work pages

[42]

Wavelet-Harmonic Integration Methods

B. Lillard,Wavelet-harmonic integration methods,Phys. Rev. D111(2025) 123006 [2310.01483]

work page Pith review arXiv 2025
[1]

L.J. Hall, K. Jedamzik, J. March-Russell and S.M. West,Freeze-In Production of FIMP Dark Matter,JHEP03(2010) 080 [0911.1120]

arXiv 2010
[2]

Kaplan, M.A

D.E. Kaplan, M.A. Luty and K.M. Zurek,Asymmetric Dark Matter,Phys. Rev. D79(2009) 115016 [0901.4117]

arXiv 2009
[3]

Cohen, D.J

T. Cohen, D.J. Phalen, A. Pierce and K.M. Zurek,Asymmetric Dark Matter from a GeV Hidden Sector,Phys. Rev. D82(2010) 056001 [1005.1655]

arXiv 2010
[4]

Hochberg, E

Y. Hochberg, E. Kuflik, T. Volansky and J.G. Wacker,Mechanism for Thermal Relic Dark Matter of Strongly Interacting Massive Particles,Phys. Rev. Lett.113(2014) 171301 [1402.5143]

arXiv 2014
[5]

Zurek,Dark Matter Candidates of a Very Low Mass,Ann

K.M. Zurek,Dark Matter Candidates of a Very Low Mass,Ann. Rev. Nucl. Part. Sci.74 (2024) 287 [2401.03025]

arXiv 2024
[6]

Kahn and T

Y. Kahn and T. Lin,Searches for light dark matter using condensed matter systems,Rept. Prog. Phys.85(2022) 066901 [2108.03239]

arXiv 2022
[7]

Mitridate, T

A. Mitridate, T. Trickle, Z. Zhang and K.M. Zurek,Snowmass white paper: Light dark matter direct detection at the interface with condensed matter physics,Phys. Dark Univ.40 (2023) 101221 [2203.07492]

arXiv 2023

Show all 51 references

[8]

Essig et al.,Snowmass2021 Cosmic Frontier: The landscape of low-threshold dark matter direct detection in the next decade, inSnowmass 2021, 3, 2022 [2203.08297]

R. Essig et al.,Snowmass2021 Cosmic Frontier: The landscape of low-threshold dark matter direct detection in the next decade, inSnowmass 2021, 3, 2022 [2203.08297]

2021 arXiv
[9]

Essig, J

R. Essig, J. Mardon and T. Volansky,Direct Detection of Sub-GeV Dark Matter,Phys. Rev. D85(2012) 076007 [1108.5383]. – 29 – 10 20 30 40 50 60 70 80 90 100 DM mass m [keV] 10 5 10 4 10 3 10 2 10 1 Relative error GaAs heavy hadrophilic E = 1.0meV E = 0.5meV E = 0.25meV 10 20 30 ...

2012 arXiv
[10]

Essig, M

R. Essig, M. Fernandez-Serra, J. Mardon, A. Soto, T. Volansky and T.-T. Yu,Direct Detection of sub-GeV Dark Matter with Semiconductor Targets,JHEP05(2016) 046 [1509.01598]. [11]SENSEIcollaboration,SENSEI at SNOLAB: Single-Electron Event Rate and Implications for Dark Matter,Ph...

2016 arXiv
[14]

Knapen, T

S. Knapen, T. Lin, M. Pyle and K.M. Zurek,Detection of Light Dark Matter With Optical Phonons in Polar Materials,Phys. Lett. B785(2018) 386 [1712.06598]

2018 arXiv
[15]

Griffin, S

S. Griffin, S. Knapen, T. Lin and K.M. Zurek,Directional Detection of Light Dark Matter with Polar Materials,Phys. Rev. D98(2018) 115034 [1807.10291]

2018 arXiv
[16]

Trickle, Z

T. Trickle, Z. Zhang, K.M. Zurek, K. Inzani and S.M. Griffin,Multi-Channel Direct Detection of Light Dark Matter: Theoretical Framework,JHEP03(2020) 036 [1910.08092]

2020 arXiv
[17]

Griffin, K

S.M. Griffin, K. Inzani, T. Trickle, Z. Zhang and K.M. Zurek,Multichannel direct detection of light dark matter: Target comparison,Phys. Rev. D101(2020) 055004 [1910.10716]

2020 arXiv
[18]

Anthony-Petersen et al.,Low energy backgrounds and excess noise in a two-channel low-threshold calorimeter,Appl

R. Anthony-Petersen et al.,Low energy backgrounds and excess noise in a two-channel low-threshold calorimeter,Appl. Phys. Lett.126(2025) 102601 [2410.16510]

2025 arXiv
[19]

Angloher et al.,The CRESST experiment towards the next generation of sub GeV direct dark matter detection,Commun

G. Angloher et al.,The CRESST experiment towards the next generation of sub GeV direct dark matter detection,Commun. Phys.9(2026) 163 [2505.01183]

2026 arXiv
[20]

Kennard et al.,Performance of a SuperCDMS HVeV detector with Sub-eV energy resolution and single charge-sensitivity,Nucl

K. Kennard et al.,Performance of a SuperCDMS HVeV detector with Sub-eV energy resolution and single charge-sensitivity,Nucl. Instrum. Meth. A1091(2026) 171753 [2601.16307]. [21]SuperCDMScollaboration,Light Dark Matter Search with a High-Resolution Athermal Phonon Detector Oper...

2026 arXiv
[25]

Coskuner, T

A. Coskuner, T. Trickle, Z. Zhang and K.M. Zurek,Directional detectability of dark matter with single phonon excitations: Target comparison,Phys. Rev. D105(2022) 015010 [2102.09567]

2022 arXiv
[26]

Belli, R

P. Belli, R. Bernabei, C. Bacci, A. Incicchitti and D. Prosperi,Identifying a ’dark matter’ signal by nonisotropic scintillation detector,Nuovo Cim. C15(1992) 475

1992
[27]

Bernabei, P

R. Bernabei, P. Belli, F. Nozzoli and A. Incicchitti,Anisotropic scintillators for WIMP direct detection: Revisited,Eur. Phys. J. C28(2003) 203

2003
[28]

Blanco, Y

C. Blanco, Y. Kahn, B. Lillard and S.D. McDermott,Dark Matter Daily Modulation With Anisotropic Organic Crystals,Phys. Rev. D104(2021) 036011 [2103.08601]

2021 arXiv
[29]

Avignone, III, R.J

F.T. Avignone, III, R.J. Creswick and S. Nussinov,Searching direction dependent daily modulation in dark matter detectors,0807.3758

arXiv
[30]

Creswick, S

R.J. Creswick, S. Nussinov and F.T. Avignone,Direction dependence and diurnal modulation in dark matter detectors,Astropart. Phys.35(2011) 62 [1007.0214]

2011 arXiv
[31]

Bozorgnia, G.B

N. Bozorgnia, G.B. Gelmini and P. Gondolo,Daily modulation due to channeling in direct dark matter crystalline detectors,Phys. Rev. D84(2011) 023516 [1101.2876]. – 31 –

2011 arXiv
[32]

Hochberg, Y

Y. Hochberg, Y. Kahn, M. Lisanti, C.G. Tully and K.M. Zurek,Directional detection of dark matter with two-dimensional targets,Phys. Lett. B772(2017) 239 [1606.08849]

2017 arXiv
[33]

Coskuner, A

A. Coskuner, A. Mitridate, A. Olivares and K.M. Zurek,Directional Dark Matter Detection in Anisotropic Dirac Materials,Phys. Rev. D103(2021) 016006 [1909.09170]

2021 arXiv
[34]

Blanco, I

C. Blanco, I. Harris, Y. Kahn, B. Lillard and J. Pérez-Ríos,Molecular Migdal effect,Phys. Rev. D106(2022) 115015 [2208.09002]

2022 arXiv
[35]

Budnik, O

R. Budnik, O. Chesnovsky, O. Slone and T. Volansky,Direct Detection of Light Dark Matter and Solar Neutrinos via Color Center Production in Crystals,Phys. Lett. B782(2018) 242 [1705.03016]

2018 arXiv
[36]

Kadribasic, N

F. Kadribasic, N. Mirabolfathi, K. Nordlund, A.E. Sand, E. Holmström and F. Djurabekova, Directional Sensitivity In Light-Mass Dark Matter Searches With Single-Electron Resolution Ionization Detectors,Phys. Rev. Lett.120(2018) 111301 [1703.05371]

2018 arXiv
[37]

Chiang, M

C.-T. Chiang, M. Kamionkowski and G.Z. Krnjaic,Dark Matter Detection with Polarized Detectors,Phys. Dark Univ.1(2012) 109 [1202.1807]

2012 arXiv
[38]

Catena, K

R. Catena, K. Fridell and V. Zema,Direct detection of fermionic and vector dark matter with polarised targets,JCAP11(2018) 018 [1810.01515]

2018 arXiv
[39]

Baxter, R

D. Baxter, R. Essig, Y. Hochberg, M. Kaznacheeva, B. von Krosigk, F. Reindl et al., Low-Energy Backgrounds in Solid-State Phonon and Charge Detectors,Ann. Rev. Nucl. Part. Sci.75(2025) 301 [2503.08859]

2025 arXiv
[40]

Blanco, J.W

C. Blanco, J.W. Foster, Y. Kahn and B. Lillard,Statistics of Daily Modulation in Dark Matter Direct Detection Experiments,2602.15947
[41]

Lillard,Partial Rate Matrix for Dark Matter Scattering,Phys

B. Lillard,Partial Rate Matrix for Dark Matter Scattering,Phys. Rev. Lett.134(2025) 221003 [2310.01480]

2025 arXiv
[43]

Lillard and A

B. Lillard and A. Radick,Vector spaces for dark matter (VSDM): Fast direct detection calculations with Python and Julia,SciPost Phys. Codeb.68(2026) 1 [2502.17547]. [44]https://github.com/xuxiangli/VectorPhonoDark

2026 arXiv
[45]

A. Togo, L. Chaput, T. Tadano and I. Tanaka,Implementation strategies in phonopy and phono3py,J. Phys. Condens. Matter35(2023) 353001

2023
[46]

Togo,First-principles phonon calculations with phonopy and phono3py,J

A. Togo,First-principles phonon calculations with phonopy and phono3py,J. Phys. Soc. Jpn. 92(2023) 012001

2023
[47]

Trickle, Z

T. Trickle, Z. Zhang and K.M. Zurek,Effective field theory of dark matter direct detection with collective excitations,Phys. Rev. D105(2022) 015001 [2009.13534]. [48]https://github.com/tanner-trickle/PhonoDark

2022 arXiv
[49]

Drukier, K

A.K. Drukier, K. Freese and D.N. Spergel,Detecting Cold Dark Matter Candidates,Phys. Rev. D33(1986) 3495

1986
[50]

Blanco, B

C. Blanco, B. Lillard and J.D. Shergold,A Numerical Method for the Efficient Calculation of Scattering Form Factors,2512.18010
[51]

Behnel, R

S. Behnel, R. Bradshaw, C. Citro, L. Dalcin, D.S. Seljebotn and K. Smith,Cython: The Best of Both Worlds,Comput. Sci. Eng.13(2011) 31. – 32 –

2011
[52]

S.K. Lam, A. Pitrou and S. Seibert,Numba: a LLVM-based Python JIT compiler, in Proceedings of the Second Workshop on the LLVM Compiler Infrastructure in HPC, pp. 7:1–7:6, 2015, DOI

2015
[53]

X.-X. Li, N. Valsan and Z. Zhang,Astrophysical Uncertainties in Sub-GeV Dark Matter Detection via Single Phonon Excitations,2606.04091

arXiv
[54]

Campbell-Deem, P

B. Campbell-Deem, P. Cox, S. Knapen, T. Lin and T. Melia,Multiphonon excitations from dark matter scattering in crystals,Phys. Rev. D101(2020) 036006 [1911.03482]

2020 arXiv
[55]

Y. Kahn, G. Krnjaic and B. Mandava,Dark Matter Detection with Bound Nuclear Targets: The Poisson Phonon Tail,Phys. Rev. Lett.127(2021) 081804 [2011.09477]

2021 arXiv
[56]

Campbell-Deem, S

B. Campbell-Deem, S. Knapen, T. Lin and E. Villarama,Dark matter direct detection from the single phonon to the nuclear recoil regime,Phys. Rev. D106(2022) 036019 [2205.02250]

2022 arXiv
[57]

Lin, C.-H

T. Lin, C.-H. Shen, M. Sholapurkar and E. Villarama,Anharmonic effects in nuclear recoils from sub-GeV dark matter,Phys. Rev. D109(2024) 095020 [2309.10839]

2024 arXiv
[58]

Stratman and T

C. Stratman and T. Lin,Daily modulation of low-energy nuclear recoils from sub-GeV dark matter,Phys. Rev. D111(2025) 043030 [2411.03433]

2025 arXiv
[59]

L. Lin, T. Lin and M. Fang,Coherence from interference: a solvable model of sub-GeV dark matter-nucleus scattering,2607.24933

arXiv
[60]

Physical Superintelligence PBC,Get physics done (gpd), 2026. – 33 –

2026

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [42]

Wavelet-Harmonic Integration Methods

B. Lillard,Wavelet-harmonic integration methods,Phys. Rev. D111(2025) 123006 [2310.01483]

work page Pith review arXiv 2025

[2] [1]

L.J. Hall, K. Jedamzik, J. March-Russell and S.M. West,Freeze-In Production of FIMP Dark Matter,JHEP03(2010) 080 [0911.1120]

arXiv 2010

[3] [2]

Kaplan, M.A

D.E. Kaplan, M.A. Luty and K.M. Zurek,Asymmetric Dark Matter,Phys. Rev. D79(2009) 115016 [0901.4117]

arXiv 2009

[4] [3]

Cohen, D.J

T. Cohen, D.J. Phalen, A. Pierce and K.M. Zurek,Asymmetric Dark Matter from a GeV Hidden Sector,Phys. Rev. D82(2010) 056001 [1005.1655]

arXiv 2010

[5] [4]

Hochberg, E

Y. Hochberg, E. Kuflik, T. Volansky and J.G. Wacker,Mechanism for Thermal Relic Dark Matter of Strongly Interacting Massive Particles,Phys. Rev. Lett.113(2014) 171301 [1402.5143]

arXiv 2014

[6] [5]

Zurek,Dark Matter Candidates of a Very Low Mass,Ann

K.M. Zurek,Dark Matter Candidates of a Very Low Mass,Ann. Rev. Nucl. Part. Sci.74 (2024) 287 [2401.03025]

arXiv 2024

[7] [6]

Kahn and T

Y. Kahn and T. Lin,Searches for light dark matter using condensed matter systems,Rept. Prog. Phys.85(2022) 066901 [2108.03239]

arXiv 2022

[8] [7]

Mitridate, T

A. Mitridate, T. Trickle, Z. Zhang and K.M. Zurek,Snowmass white paper: Light dark matter direct detection at the interface with condensed matter physics,Phys. Dark Univ.40 (2023) 101221 [2203.07492]

arXiv 2023