arXiv subjects

Zhengkang Zhang

Publications and source records attributed to Zhengkang Zhang.

At least 19 recordsLinked to original sources

arXiv2026

Logarithmic Wavelets for Dark Matter--Phonon Scattering

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.

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arXiv2026

Astrophysical Uncertainties in Sub-GeV Dark Matter Detection via Single Phonon Excitations

We present the first systematic study of how local dark matter velocity distribution uncertainties propagate into direct detection rates for dark matter--single phonon scattering. We consider three benchmark halo models -- Standard Halo Model, Tsallis and empirical -- and vary the astrophysical parameters within observationally motivated ranges. To compare halo models on equal footing, we introduce an rms-matching prescription that holds the mean dark matter kinetic energy fixed across models. With this prescription, differences between halo models prove subdominant to parameter variations within each model, so that astrophysical uncertainties can be effectively captured by varying parameters within the Standard Halo Model alone. We find $\mathcal{O}(1\%)$ to $\mathcal{O}(100\%)$ fractional deviations in the predicted rates across the dark matter mass range of interest. For the daily modulation signal, astrophysical parameter variations rescale the amplitude but leave the phase robust. These results provide timely input for reliably interpreting upcoming phonon-based direct detection experiments targeting sub-GeV dark matter.

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arXiv2026

Optimal Architecture and Fundamental Bounds in Neural Network Field Theory

Neural network field theory (NNFT) represents fields as neural networks and samples field configurations by drawing network parameters from a probability distribution. We identify a previously unexplored architectural freedom in NNFT, parameterized by $α$, that leaves the infinite-width theory invariant but dramatically affects finite-width errors in the calculation of correlation functions. For a massive scalar field, we show that $α=0$, corresponding to propagator-weighted neuron momenta and constant neuron amplitudes, is optimal: it minimizes finite-width variance and uniquely removes IR-sensitive corrections in the interacting theory. Even at $α=0$, relative errors from both bias and variance grow exponentially with distance beyond the correlation length. The bias can be removed by extrapolating to infinite width, which we demonstrate numerically, while the variance imposes a fundamental bound on the achievable signal-to-noise ratio as in lattice field theory. These results chart a path toward developing NNFT into a practical tool for the numerical study of field theories.

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arXiv2025

Geometric Building Blocks of Effective Field Theory Amplitudes

On-shell amplitudes are invariant under field redefinitions. Nonderivative field redefinitions have a natural interpretation as coordinate transformations on the target manifold. General field redefinitions, which may involve derivatives, can be viewed as coordinate transformations on the field configuration manifold. We present a unified perspective for the geometry of both the target manifold and the field configuration manifold for scalar effective field theories. In both cases, we identify vertices that can be used to build the tree-level amplitudes, with the property that they transform covariantly in the vacuum and on-shell limits. We identify a choice of metric on the field configuration manifold, for which amplitude expressions on the target manifold can be easily reproduced from their counterparts on the field configuration manifold. This clarifies the relation between the well-established framework of field space geometry and recent proposals for functional geometry.

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arXiv2025

What is the Geometry of Effective Field Theories?

We elaborate on a recently proposed geometric framework for scalar effective field theories. Starting from the action, a metric can be identified that enables the construction of geometric quantities on the associated functional manifold. These objects transform covariantly under general field redefinitions that relate different operator bases, including those involving derivatives. We present a novel geometric formula for the amplitudes of the theory, where the vertices in Feynman diagrams are replaced by their geometrized counterparts. This makes the on-shell covariance of amplitudes manifest, providing the link between functional geometry and effective field theories.

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arXiv2024

The Geometric Universal One-Loop Effective Action

We derive universal formulae for integrating out heavy degrees of freedom in scalar field theories up to one-loop level in terms of covariant quantities associated with the geometry of the field manifold. The universal matching results can be readily applied to phenomenologically interesting extensions of the Standard Model, as we demonstrate using a singlet scalar example. We also discuss the role of field redefinitions in effective field theory matching and simplifications resulting from going to a field basis where interactions are encoded in a nontrivial metric on the field manifold.

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arXiv2024

Neural Scaling Laws From Large-N Field Theory: Solvable Model Beyond the Ridgeless Limit

Many machine learning models based on neural networks exhibit scaling laws: their performance scales as power laws with respect to the sizes of the model and training data set. We use large-N field theory methods to solve a model recently proposed by Maloney, Roberts and Sully which provides a simplified setting to study neural scaling laws. Our solution extends the result in this latter paper to general nonzero values of the ridge parameter, which are essential to regularize the behavior of the model. In addition to obtaining new and more precise scaling laws, we also uncover a duality transformation at the diagrams level which explains the symmetry between model and training data set sizes. The same duality underlies recent efforts to design neural networks to simulate quantum field theories.

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arXiv2023

Structures of Neural Network Effective Theories

We develop a diagrammatic approach to effective field theories (EFTs) corresponding to deep neural networks at initialization, which dramatically simplifies computations of finite-width corrections to neuron statistics. The structures of EFT calculations make it transparent that a single condition governs criticality of all connected correlators of neuron preactivations. Understanding of such EFTs may facilitate progress in both deep learning and field theory simulations.

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arXiv2023

Anomaly Cancellation in Effective Field Theories From the Covariant Derivative Expansion

We extend our recently-proposed formalism for calculating anomalies of global and gauge symmetries using the Covariant Derivative Expansion to include a general class of operators that can appear in relativistic Effective Field Theories (EFTs). This allows us to prove that EFT operators involving general scalar, vector, and tensor couplings to fermion bilinears only give rise to irrelevant anomalies, which can be removed by an appropriate choice of counterterms, thereby confirming the absence of new constraints from anomaly cancellation on the Standard Model EFT.

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arXiv2023

Anomalies From the Covariant Derivative Expansion

We revisit the calculation of anomalies for global and gauge symmetries in the framework of the Covariant Derivative Expansion (CDE). Due to the presence of UV divergences, the result is an ambiguous quantity that depends on the regularization procedure and the renormalization scheme. We introduce a class of regulators that facilitate a straightforward evaluation of the anomaly exclusively in $d=4$ spacetime dimensions using the CDE methodology. We derive a master formula for the anomaly that integrates various known results into a unified framework.

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arXiv2022

LHC EFT WG Note: Precision matching of microscopic physics to the Standard Model Effective Field Theory (SMEFT)

This note gives an overview of the tools for the precision matching of ultraviolet theories to the Standard Model effective field theory (SMEFT) at the tree level and one loop. Several semi- and fully automated codes are presented, as well as some supplementary codes for the basis conversion and the subsequent running and matching at low energies. A suggestion to collect information for cross-validations of current and future codes is made.

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arXiv2022

Snowmass Theory Frontier: Effective Field Theory

We summarize recent progress in the development, application, and understanding of effective field theories and highlight promising directions for future research. This Report is prepared as the TF02 "Effective Field Theory" topical group summary for the Theory Frontier as part of the Snowmass 2021 process.

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arXiv2022

Snowmass Theory Frontier: Astrophysics and Cosmology

We summarize progress made in theoretical astrophysics and cosmology over the past decade and areas of interest for the coming decade. This Report is prepared as the TF09 "Astrophysics and Cosmology" topical group summary for the Theory Frontier as part of the Snowmass 2021 process.

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arXiv2022

Snowmass White Paper: Effective Field Theories for Dark Matter Phenomenology

The quest to discover the nature of dark matter continues to drive many of the experimental and observational frontiers in particle physics, astronomy, and cosmology. While there are no definitive signatures to date, there exists a rich ecosystem of experiments searching for signals for a broad class of dark matter models, at different epochs of cosmic history, and through a variety of processes with different characteristic energy scales. Given the multitude of candidates and search strategies, effective field theory has been an important tool for parametrizing the possible interactions between dark matter and Standard Model probes, for quantifying and improving model-independent uncertainties, and for robust estimation of detection rates in the presence of large perturbative corrections. This white paper summarizes a wide range of effective field theory applications for connecting dark matter theories to experiments.

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arXiv2022

Snowmass White Paper: Effective Field Theory Matching and Applications

Mapping UV theories onto low energy effective descriptions is a procedure known as matching. The last decade has seen tremendous progress in the development of new tools for efficiently performing matching calculations, by relying on so-called functional methods. This white paper summarizes the status of functional matching. Specifically, matching for relativistic theories is a fully solved problem up to one-loop order in perturbation theory, and to arbitrary order in the effective field theory expansion. A streamlined prescription that has been partially automated facilitates the application of functional matching to phenomenological studies in the Standard Model EFT framework.

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arXiv2022

Snowmass White Paper: Light Dark Matter Direct Detection at the Interface With Condensed Matter Physics

Direct detection experiments for light (sub-GeV) dark matter are making enormous leaps in reaching previously unexplored theory space. The need for accurate characterizations of target responses has led to a growing interplay between particle and condensed matter physics. This white paper summarizes recent progress on direct detection calculations that utilize state-of-the-art numerical tools in condensed matter physics and effective field theory techniques. These new results provide the theoretical framework for interpreting ongoing and planned experiments using electronic and collective excitations, and for optimizing future searches.

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arXiv2022

Dark Matter Direct Detection in Materials with Spin-Orbit Coupling

Semiconductors with $\mathcal{O}(\text{meV})$ band gaps have been shown to be promising targets to search for sub-MeV mass dark matter (DM). In this paper we focus on a class of materials where such narrow band gaps arise naturally as a consequence of spin-orbit coupling (SOC). Specifically, we are interested in computing DM-electron scattering and absorption rates in these materials using state-of-the-art density functional theory (DFT) techniques. To do this, we extend the DM interaction rate calculation to include SOC effects which necessitates a generalization to spin-dependent wave functions. We apply our new formalism to calculate limits for several DM benchmark models using an example ZrTe$_{5}$ target and show that the inclusion of SOC can substantially alter projected constraints.

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arXiv2022

Directional Detectability of Dark Matter With Single Phonon Excitations: Target Comparison

Single phonon excitations are sensitive probes of light dark matter in the keV-GeV mass window. For anisotropic target materials, the signal depends on the direction of the incoming dark matter wind and exhibits a daily modulation. We discuss in detail the various sources of anisotropy, and carry out a comparative study of 26 crystal targets, focused on sub-MeV dark matter benchmarks. We compute the modulation reach for the most promising targets, corresponding to the cross section where the daily modulation can be observed for a given exposure, which allows us to combine the strength of DM-phonon couplings and the amplitude of daily modulation. We highlight Al$_2$O$_3$ (sapphire), CaWO$_4$ and h-BN (hexagonal boron nitride) as the best polar materials for recovering a daily modulation signal, which feature $\mathcal{O}(1 - 100)\%$ variations of detection rates throughout the day, depending on the dark matter mass and interaction. The directional nature of single phonon excitations offers a useful handle to mitigate backgrounds, which is crucial for fully realizing the discovery potential of near future experiments.

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