Center for Theoretical Physics Publications

Understanding the detailed structure of energy flow within jets, a field known as jet substructure, plays a central role in searches for new physics, and precision studies of QCD. Many applications of jet substructure require an understanding of jets initiated by heavy quarks, whose description has lagged behind remarkable recent progress for massless jets. In this Letter, we initiate a study of correlation functions of energy flow operators on beauty and charm jets to illuminate the effects of the intrinsic mass of the elementary particles of QCD. We present a factorization theorem incorporating the mass of heavy quarks, and show that the heavy quark jet functions for energy correlators have a simple structure in perturbation theory. Our results achieve the very first full next-to-leading-logarithmic calculation of the heavy quark jet substructure observable at the LHC. Using this framework, we study the behavior of the correlators, and show that they exhibit a clear transition from a massless scaling regime, at precisely the scale of the heavy quark mass. This manifests the long-sought-after dead-cone effect and illustrates fundamental effects from the intrinsic mass of beauty and charm quarks in a perturbative regime, before they are confined inside hadrons. Our theoretical framework for studying energy correlators using heavy jets has many exciting applications for improving the description of mass effects in next generation parton shower event generators, probing the QGP, and studying heavy flavor fragmentation functions.

We explore machine learning-based jet and event identification at the future Electron-Ion Collider (EIC). We study the effectiveness of machine learning-based classifiers at relatively low EIC energies, focusing on (i) identifying the flavor of the jet and (ii) identifying the underlying hard process of the event. We propose applications of our machine learning-based jet identification in the key research areas at the future EIC and current Relativistic Heavy Ion Collider program, including enhancing constraints on (transverse momentum dependent) parton distribution functions, improving experimental access to transverse spin asymmetries, studying photon structure, and quantifying the modification of hadrons and jets in the cold nuclear matter environment in electron-nucleus collisions. We establish first benchmarks and contrast the estimated performance of flavor tagging at the EIC with that at the Large Hadron Collider. We perform studies relevant to aspects of detector design including particle identification, charge information, and minimum transverse momentum capabilities. Additionally, we study the impact of using full event information instead of using only information associated with the identified jet. These methods can be deployed either on suitably accurate Monte Carlo event generators, or, for several applications, directly on experimental data. We provide an outlook for ultimately connecting these machine learning-based methods with first principles calculations in quantum chromodynamics.

We compute the soft-drop jet-mass distribution from \(pp\) collisions to NNLL accuracy while including nonperturbative corrections through a field-theory based formalism. Using these calculations, we assess the theoretical uncertainties on an \(\alpha_s\) precision measurement due to higher order perturbative effects, nonperturbative corrections, and PDF uncertainty. We identify which soft-drop parameters are well-suited for measuring \(\alpha_s\), and find that higher-logarithmic resummation has a qualitatively important effect on the shape of the jet-mass distribution. We find that quark jets and gluon jets have similar sensitivity to \(\alpha_s\), and emphasize that experimentally distinguishing quark and gluon jets is not required for an \(\alpha_s\) measurement. We conclude that measuring \(\alpha_s\) to the 10% level is feasible now, and with improvements in theory a 5% level measurement is possible. Getting down to the 1% level to be competitive with other state-of-the-art measurements will be challenging.

We introduce a \(\mathbb{Z}_N\) stabilizer code that can be defined on any spatial lattice of the form \(\Gamma\times C_{L_z}\), where \(\Gamma\) is a general graph. We also present the low-energy limit of this stabilizer code as a Euclidean lattice action, which we refer to as the anisotropic \(\mathbb{Z}_N\) Laplacian model. It is gapped, robust (i.e., stable under small deformations), and has lineons. Its ground state degeneracy (GSD) is expressed in terms of a "mod \(N\)-reduction" of the Jacobian group of the graph \(\Gamma\). In the special case when space is an \(L\times L\times L_z\) cubic lattice, the logarithm of the GSD depends on \(L\) in an erratic way and grows no faster than \(O(L)\). We also discuss another gapped model, the \(\mathbb{Z}_N\) Laplacian model, which can be defined on any graph. It has fractons and a similarly strange GSD.

The quantum-mechanical description of assemblies of particles whose motion is confined to two (or one) spatial dimensions offers many possibilities that are distinct from bosons and fermions. We call such particles anyons. The simplest anyons are parameterized by an angular phase parameter \(\theta\). \(\theta = 0, \pi\) correspond to bosons and fermions respectively; at intermediate values we say that we have fractional statistics. In two dimensions, \(\theta\) describes the phase acquired by the wave function as two anyons wind around one another counterclockwise. It generates a shift in the allowed values for the relative angular momentum. Composites of localized electric charge and magnetic flux associated with an abelian U(1) gauge group realize this behavior. More complex charge-flux constructions can involve non-abelian and product groups acting on a spectrum of allowed charges and fluxes, giving rise to nonabelian and mutual statistics. Interchanges of non-abelian anyons implement unitary transformations of the wave function within an emergent space of internal states. Anyons of all kinds are described by quantum field theories that include Chern--Simons terms. The crossings of one-dimensional anyons on a ring are uni-directional, such that a fractional phase \(\theta\) acquired upon interchange gives rise to fractional shifts in the relative momenta between the anyons. The quasiparticle excitations of fractional quantum Hall states have long been predicted to include anyons. Recently the anyon behavior predicted for quasiparticles in the \(\nu = 1/3\) fractional quantum Hall state has been observed both in scattering and in interferometric experiments. Excitations within designed systems, notably including superconducting circuits, can exhibit anyon behavior. Such systems are being developed for possible use in quantum information processing.

Quantum neural networks have been widely studied in recent years, given their potential practical utility and recent results regarding their ability to efficiently express certain classical data. However, analytic results to date rely on assumptions and arguments from complexity theory. Due to this, there is little intuition as to the source of the expressive power of quantum neural networks or for which classes of classical data any advantage can be reasonably expected to hold. Here, we study the relative expressive power between a broad class of neural network sequence models and a class of recurrent models based on Gaussian operations with non-Gaussian measurements. We explicitly show that quantum contextuality is the source of an unconditional memory separation in the expressivity of the two model classes. Additionally, as we are able to pinpoint quantum contextuality as the source of this separation, we use this intuition to study the relative performance of our introduced model on a standard translation data set exhibiting linguistic contextuality. In doing so, we demonstrate that our introduced quantum models are able to outperform state of the art classical models even in practice.

The exploration of topologically-ordered states of matter is a long-standing goal at the interface of several subfields of the physical sciences. Such states feature intriguing physical properties such as long-range entanglement, emergent gauge fields and non-local correlations, and can aid in realization of scalable fault-tolerant quantum computation. However, these same features also make creation, detection, and characterization of topologically-ordered states particularly challenging. Motivated by recent experimental demonstrations, we introduce a new approach for quantifying topological states -- locally error-corrected decoration (LED) -- by combining methods of error correction with ideas of renormalization-group flow. Our approach allows for efficient and robust identification of topological order, and is applicable in the presence of incoherent noise sources, making it particularly suitable for realistic experiments. We demonstrate the power of LED using numerical simulations of the toric code under a variety of perturbations, and we subsequently apply it to an experimental realization of a quantum spin liquid using a Rydberg-atom quantum simulator. Extensions to the characterization of other exotic states of matter are discussed.

We propose an observable \(q_*\) sensitive to transverse momentum dependence (TMD) in \(e N \to e h X\), with \(q_*/E_N\) defined purely by lab-frame angles. In 3D measurements of confinement and hadronization this resolves the crippling issue of accurately reconstructing small transverse momentum \(P_{hT}\). We prove factorization for \(\mathrm{d} \sigma_h / \mathrm{d}q_*\) for \(q_*\ll Q\) with standard TMD functions, enabling \(q_*\) to substitute for \(P_{hT}\). A double-angle reconstruction method is given which is exact to all orders in QCD for \(q_*\ll Q\). \(q_*\) enables an order-of-magnitude improvement in the expected experimental resolution at the EIC.

In an isolated quantum many-body system undergoing unitary evolution, we study the thermalization of a subsystem, treating the rest of the system as a bath. In this setting, the eigenstate thermalization hypothesis (ETH) was proposed to explain thermalization. Consider a nearly integrable Sachdev-Ye-Kitaev model obtained by adding random all-to-all \(4\)-body interactions as a perturbation to a random free-fermion model. When the subsystem size is larger than the square root of but is still a vanishing fraction of the system size, we prove thermalization if the system is initialized in a random product state, while almost all eigenstates violate the ETH. In this sense, the ETH is not a necessary condition for thermalization.

The 2+1d continuum Lifshitz theory of a free compact scalar field plays a prominent role in a variety of quantum systems in condensed matter physics and high energy physics. It is known that in compact space, it has an infinite ground state degeneracy. In order to understand this theory better, we consider two candidate lattice regularizations of it using the modified Villain formalism. We show that these two lattice theories have significantly different global symmetries (including a dipole global symmetry), anomalies, ground state degeneracies, and dualities. In particular, one of them is self-dual. Given these theories and their global symmetries, we can couple them to corresponding gauge theories. These are two different \(U(1)\) tensor gauge theories. The resulting models have excitations with restricted mobility, i.e., fractons. Finally, we give an exact lattice realization of the fracton/lineon-elasticity dualities for the Lifshitz theory, scalar and vector charge gauge theories.

It has recently been argued that noisy intermediate-scale quantum computers may be used to optimize interpolating operator constructions for lattice quantum field theory (LQFT) calculations on classical computers. Here, two concrete realizations of the method are developed and implemented. The first approach is to maximize the overlap, or fidelity, of the state created by an interpolating operator acting on the vacuum state to the target eigenstate. The second is to instead minimize the energy expectation value of the interpolated state. These approaches are implemented in a proof-of-concept calculation in (1+1)-dimensions for a single-flavor massive Schwinger model to obtain quantum-optimized interpolating operator constructions for a vector meson state in the theory. Although fidelity maximization is preferable in the absence of noise due to quantum gate errors, it is found that energy minimization is more robust to these effects in the proof-of-concept calculation. This work serves as a concrete demonstration of how quantum computers in the intermediate term might be used to accelerate classical LQFT calculations.

We construct initial data violating the AdS Penrose inequality using scalars with various potentials. Since the Penrose inequality can be derived from basic entries in the AdS/CFT dictionary, we argue that it is a new swampland condition, ruling out holographic UV completion for theories that violate it. We produce exclusion plots on scalar couplings violating the inequality, and we find no violations for top-down potentials. In the special case where the dominant energy condition holds, we use GR techniques to prove the AdS Penrose inequality in all dimensions greater than two, assuming spherical, planar, or hyperbolic symmetry. However, our violations show that this result cannot be generically true with only the null energy condition, and we give an analytic sufficient condition for violation of the Penrose inequality, constraining couplings and the exponential behavior of scalar potentials.

Strong gravitational lensing has emerged as a promising approach for probing dark matter models on sub-galactic scales. Recent work has proposed the subhalo effective density slope as a more reliable observable than the commonly used subhalo mass function. The subhalo effective density slope is a measurement independent of assumptions about the underlying density profile and can be inferred for individual subhalos through traditional sampling methods. To go beyond individual subhalo measurements, we leverage recent advances in machine learning and introduce a neural likelihood-ratio estimator to infer an effective density slope for populations of subhalos. We demonstrate that our method is capable of harnessing the statistical power of multiple subhalos (within and across multiple images) to distinguish between characteristics of different subhalo populations. The computational efficiency warranted by the neural likelihood-ratio estimator over traditional sampling enables statistical studies of dark matter perturbers and is particularly useful as we expect an influx of strong lensing systems from upcoming surveys.

Dwarf galaxies are small, dark matter-dominated galaxies, some of which are embedded within the Milky Way. Their lack of baryonic matter (e.g., stars and gas) makes them perfect test beds for probing the properties of dark matter -- understanding the spatial dark matter distribution in these systems can be used to constrain microphysical dark matter interactions that influence the formation and evolution of structures in our Universe. We introduce a new method that leverages simulation-based inference and graph-based machine learning in order to infer the dark matter density profiles of dwarf galaxies from observable kinematics of stars gravitationally bound to these systems. Our approach aims to address some of the limitations of established methods based on dynamical Jeans modeling. We show that this novel method can place stronger constraints on dark matter profiles and, consequently, has the potential to weigh in on some of the ongoing puzzles associated with the small-scale structure of dark matter halos, such as the core-cusp discrepancy.

The quantum chromodynamics axion with a decay constant near the Grand Unification (GUT) scale has an ultralight mass near a neV. We show, however, that axion-like particles with masses near the keV - PeV range with GUT-scale decay constants are also well motivated in that they naturally arise from axiverse theories with dark non-abelian gauge groups. We demonstrate that the correct dark matter abundance may be achieved by the heavy axions in these models through the misalignment mechanism in combination with a period of early matter domination from the long-lived dark glueballs of the same gauge group. Heavy axion dark matter may decay to two photons, yielding mono-energetic electromagnetic signatures that may be detectable by current or next-generation space-based telescopes. We project the sensitivity of next-generation telescopes including \(\textit {Athena,}\) AMEGO, and e-ASTROGAM to such decaying axion dark matter. If the dark sector contains multiple confining gauge groups, then the observed primordial baryon asymmetry may also be achieved in this scenario through spontaneous baryogenesis. We present explicit orbifold constructions where the dark gauge groups unify with the SM at the GUT scale and axions emerge as the fifth components of dark gauge fields with bulk Chern-Simons terms.

This work presents a determination of potential short-distance contributions to the unphysical \(\pi^-\rightarrow\pi^+ e^- e^-\) decay through lattice QCD calculations. The hadronic contributions to the transition amplitude are described by the pion matrix elements of five Standard Model Effective Field Theory operators, which are computed on five ensembles of domain-wall fermions with \(N_f = 2 + 1\) quark flavors with a range of heavier-than-physical values of the light quark masses. The matrix elements are extrapolated to the continuum, physical light-quark mass, and infinite volume limit using a functional form derived in chiral Effective Field Theory (\(\chi\mathrm{EFT}\)). This extrapolation also yields the relevant low-energy constants of \(\chi\mathrm{EFT}\), which are necessary input for \(\chi\mathrm{EFT}\) calculations of neutrinoless double beta decay of nuclei.

In gauge theory, it is commonly stated that time-reversal symmetry only exists at \(\theta=0\) or \(\pi\) for a \(2\pi\)-periodic \(\theta\)-angle. In this paper, we point out that in both the free Maxwell theory and massive QED, there is a non-invertible time-reversal symmetry at every rational \(\theta\)-angle, i.e., \(\theta= \pi p/N\). The non-invertible time-reversal symmetry is implemented by a conserved, anti-linear operator without an inverse. It is a composition of the naive time-reversal transformation and a fractional quantum Hall state. We also find similar non-invertible time-reversal symmetries in non-Abelian gauge theories, including the \(\mathcal{N}=4\)\(SU(2)\) super Yang-Mills theory along the locus \(|\tau|=1\) on the conformal manifold.

Elastic nucleon-pion scattering amplitudes are computed using lattice QCD on a single ensemble of gauge field configurations with \(N_f = 2+1\) dynamical quark flavors and \(m_{\pi}\) = 200 MeV. The \(s\)-wave scattering lengths with both total isospins \(I=1/2\) and \(I=3/2\) are inferred from the finite-volume spectrum below the inelastic threshold together with the \(I=3/2\) \(p\)-wave containing the \(\Delta(1232)\) resonance. The amplitudes are well-described by the effective range expansion with parameters constrained by fits to the finite-volume energy levels enabling a determination of the \(I=3/2\) scattering length with statistical errors below \(5\%\), while the \(I = 1/2\) is somewhat less precise. Systematic errors due to excited states and the influence of higher partial waves are controlled, providing a pathway for future computations down to the physical light quark masses with multiple lattice spacings and physical volumes.

This work develops neural-network--based preconditioners to accelerate solution of the Wilson-Dirac normal equation in lattice quantum field theories. The approach is implemented for the two-flavor lattice Schwinger model near the critical point. In this system, neural-network preconditioners are found to accelerate the convergence of the conjugate gradient solver compared with the solution of unpreconditioned systems or those preconditioned with conventional approaches based on even-odd or incomplete Cholesky decompositions, as measured by reductions in the number of iterations and/or complex operations required for convergence. It is also shown that a preconditioner trained on ensembles with small lattice volumes can be used to construct preconditioners for ensembles with many times larger lattice volumes, with minimal degradation of performance. This volume-transferring technique amortizes the training cost and presents a pathway towards scaling such preconditioners to lattice field theory calculations with larger lattice volumes and in four dimensions.

We consider the partition function for Euclidean \(SU(N)\) super Yang-Mills on a squashed seven-sphere. We show that the localization locus of the partition function has instanton membrane solutions wrapping the six ``fixed" three-spheres on the \(\mathbb{S}^7\). The ADHM variables of these instantons are fields living on the membrane world volume. We compute their contribution by localizing the resulting three-dimensional supersymmetric field theory. In the round-sphere limit the individual instanton contributions are singular, but the singularities cancel when adding the contributions of all six three-spheres. The full partition function on the \({\mathbb S}^7\) is well-defined even when the square of the effective Yang-Mills coupling is negative. We show for an \(SU(2)\) gauge theory in this regime that the bare negative tension of the instanton membranes is canceled off by contributions from the instanton partition function, indicating the existence of tensionless membranes. We provide evidence that the low energy phase in this regime is distinct from the usual weakly coupled super Yang-Mills and, in fact, is gravitational.