Center for Theoretical Physics Publications

Scale separation is an important physical principle that has previously enabled algorithmic advances such as multigrid solvers. Previous work on normalizing flows has been able to utilize scale separation in the context of scalar field theories, but the principle has been largely unexploited in the context of gauge theories. This work gives an overview of a new method for generating gauge fields using hierarchical normalizing flow models. This method builds gauge fields from the outside in, allowing different parts of the model to focus on different scales of the problem. Numerical results are presented for \(U(1)\) and \(SU(3)\) gauge theories in 2, 3, and 4 spacetime dimensions.

We study the general framework of effective theories obtained via exact path integration of a complete theory over some sector of its degrees of freedom. Theories constructed this way contain multi-integrals which couple fields arbitrarily far apart, and in certain settings even on path-disconnected components of the space. These are not just entanglement, but genuine non-local interactions that we dub quantum wormholes. Any state the path integral of such an effective theory prepares is shown to be a partial trace of a state of the complete theory over the integrated-out sector. The resulting reduced density operator is generally mixed due to bra-ket wormholes. An infinite family of ensembles of pure states of the complete theory giving the same effective state is identified. These allow one to equivalently interpret any effective state as being prepared by an ensemble of theories. When computing entropic quantities, bra-ket wormholes give rise to replica wormholes. This causes replica path integrals for the effective theory to not factorize even when the underlying manifold does, as expected from mixing. In contrast, effective theories obtained by derivative expansions have no quantum wormholes and prepare pure states. There exist operators in the algebra of effective theories which can distinguish mixed from pure states, implying a breakdown of non-exact effective theories for sufficiently complex observables. This framework unifies and provides new insights into much of the phenomena observed in quantum gravity, including the interplay between wormholes and unitarity, the breakdown of bulk effective theory, the factorization puzzle, state ensembles, theory ensembles, quantum error correction, and baby universes. Some interesting lessons are drawn accounting also for characteristic aspects of gravity concerning IR/UV mixing and Kaluza-Klein reductions.

The transverse momentum-dependent fragmentation functions (TMD FFs) of heavy (bottom and charm) quarks, which we recently introduced, are universal building blocks that enter predictions for a large number of observables involving final-state heavy quarks or hadrons. They enable the extension of fixed-order subtraction schemes to quasi-collinear limits, and are of particular interest in their own right as probes of the nonperturbative dynamics of hadronization. In this paper we calculate all TMD FFs involving heavy quarks and the associated TMD matrix element in heavy-quark effective theory (HQET) to next-to-leading order in the strong interaction. Our results confirm the renormalization properties, large-mass, and small-mass consistency relations predicted in our earlier work. We also derive and confirm a prediction for the large-\(z\) behavior of the heavy-quark TMD FF by extending, for the first time, the formalism of joint resummation to capture quark mass effects in heavy-quark fragmentation. Our final results in position space agree with those of a recent calculation by another group that used a highly orthogonal organization of singularities in the intermediate momentum-space steps, providing a strong independent cross check. As an immediate application, we present the complete quark mass dependence of the energy-energy correlator (EEC) in the back-to-back limit at \(\mathcal{O}(\alpha_s)\).

We study future lepton collider prospects for testing predictive models of leptophilic dark matter candidates with a thermal origin. We calculate experimental milestones for testing the parameter space compatible with freeze-out and the associated collider signals at past, present, and future facilities. This analysis places new limits on such models by leveraging the utility of lepton colliders. At \(e^+e^-\) machines, we make projections using precision \(Z\)-pole observables from \(e^+e^-\to l^+l^- + \) missing energy signatures at LEP and future projections for FCC-ee in these channels. Additionally, a muon collider could also probe new thermal relic parameter space in this scenario via \(\mu^+\mu^- \to X + \) missing energy where \(X\) is any easy identifiable SM object. Collectively, these processes can probe much all of the parameter space for which DM direct annihilation to \(l^+l^-\) yields the observed relic density in Higgs-like models with mass-proportional couplings to charged leptons.

Massive particles leave imprints on primordial non-Gaussianity via couplings to the inflaton, even despite their exponential dilution during inflation: practically, the Universe acts as a Cosmological Collider. We present the first dedicated search for spin-zero particles using BOSS redshift-space galaxy power spectrum and bispectrum multipoles, as well as Planck CMB non-Gaussianity data. We demonstrate that some Cosmological Collider models are well approximated by the standard equilateral and orthogonal parametrization; assuming negligible inflaton self-interactions, this facilitates us translating Planck non-Gaussianity constraints into bounds on Collider models. Many models have signatures that are not degenerate with equilateral and orthogonal non-Gaussianity and thus require dedicated searches. Here, we constrain such models using BOSS three-dimensional redshift-space galaxy clustering data, focusing on spin-zero particles in the principal series and constraining their couplings to the inflaton at varying speed and mass, marginalizing over the unknown inflaton self-interactions. This is made possible through an improvement in Cosmological Bootstrap techniques and the combination of perturbation theory and halo occupation distribution models for galaxy clustering. Our work sets the standard for inflationary spectroscopy with cosmological observations, providing the ultimate link between physics on the largest and smallest scales.

Superconducting detectors are a promising technology for probing dark matter at extremely low masses, where dark matter interactions are currently unconstrained. Realizing the potential of such detectors requires new readout technologies to achieve the lowest possible thresholds for deposited energy. Here we perform a prototype search for dark matter--electron interactions with kinetic inductance detectors (KIDs), a class of superconducting detector originally designed for infrared astronomy applications. We demonstrate that existing KIDs can achieve effective thresholds as low as 0.2 eV, and we use existing data to set new dark matter constraints. The relative maturity of the technology underlying KIDs means that this platform can be scaled significantly with existing tools, enabling powerful new searches in the coming years.

The Unruh effect can be formulated as the statement that the Minkowski vacuum in a Rindler wedge has a boost as its modular flow. In recent years, other examples of states with geometrically local modular flow have played important roles in understanding energy and entropy in quantum field theory and quantum gravity. Here I initiate a general study of the settings in which geometric modular flow can arise, showing (i) that any geometric modular flow must be a conformal symmetry of the background spacetime, and (ii) that in a well behaved class of "weakly analytic" states, geometric modular flow must be future-directed. I further argue that if a geometric transformation is conformal but not isometric, then it can only be realized as modular flow in a conformal field theory. Finally, I discuss a few settings in which converse results can be shown -- i.e., settings in which a state can be constructed whose modular flow reproduces a given vector field.

This work summarizes recent results, both theoretical and experimental, in \(B\)-meson leptonic and semileptonic decays and metrology of \(V_{ub}\) and \(V_{cb}\), which were presented at the CKM 2023 workshop. We place these results in context and discuss future prospects in the field.

We expand the concept of two-dimensional topological insulators to encompass a novel category known as topological dipole insulators (TDIs), characterized by conserved dipole moments along the \(x\)-direction in addition to charge conservation. By generalizing Laughlin's flux insertion argument, we prove a no-go theorem and predict possible edge patterns and anomalies in a TDI with both charge \(U^e(1)\) and dipole \(U^d(1)\) symmetries. The edge of a TDI is characterized as a quadrupolar channel that displays a dipole \(U^d(1)\) anomaly. A quantized amount of dipole gets transferred between the edges under the dipolar flux insertion, manifesting as `quantized quadrupolar Hall effect' in TDIs. A microscopic coupled-wire Hamiltonian realizing the TDI is constructed by introducing a mutually commuting pair-hopping terms between wires to gap out all the bulk modes while preserving the dipole moment. The effective action at the quadrupolar edge can be derived from the wire model, with the corresponding bulk dipolar Chern-Simons response theory delineating the topological electromagnetic response in TDIs. Finally, we enrich our exploration of topological dipole insulators to the spinful case and construct a dipolar version of the quantum spin Hall effect, whose boundary evidences a mixed anomaly between spin and dipole symmetry. Effective bulk and the edge action for the dipolar quantum spin Hall insulator are constructed as well.

We report universal statistical properties displayed by ensembles of pure states that naturally emerge in quantum many-body systems. Specifically, two classes of state ensembles are considered: those formed by i) the temporal trajectory of a quantum state under unitary evolution or ii) the quantum states of small subsystems obtained by partial, local projective measurements performed on their complements. These cases respectively exemplify the phenomena of "Hilbert-space ergodicity" and "deep thermalization." In both cases, the resultant ensembles are defined by a simple principle: the distributions of pure states have maximum entropy, subject to constraints such as energy conservation, and effective constraints imposed by thermalization. We present and numerically verify quantifiable signatures of this principle by deriving explicit formulae for all statistical moments of the ensembles; proving the necessary and sufficient conditions for such universality under widely-accepted assumptions; and describing their measurable consequences in experiments. We further discuss information-theoretic implications of the universality: our ensembles have maximal information content while being maximally difficult to interrogate, establishing that generic quantum state ensembles that occur in nature hide (scramble) information as strongly as possible. Our results generalize the notions of Hilbert-space ergodicity to time-independent Hamiltonian dynamics and deep thermalization from infinite to finite effective temperature. Our work presents new perspectives to characterize and understand universal behaviors of quantum dynamics using statistical and information theoretic tools.

Systems reaching thermal equilibrium are ubiquitous. For classical systems, this phenomenon is typically understood statistically through ergodicity in phase space, but translating this to quantum systems is a long-standing problem of interest. Recently a quantum notion of ergodicity has been proposed, namely that isolated, global quantum states uniformly explore their available state space, dubbed Hilbert-space ergodicity. Here we observe signatures of this process with an experimental Rydberg quantum simulator and various numerical models, before generalizing to the case of a local quantum system interacting with its environment. For a closed system, where the environment is a complementary subsystem, we predict and observe a smooth quantum-to-classical transition in that observables progress from large, quantum fluctuations to small, Gaussian fluctuations as the bath size grows. This transition is universal on a quantitative level amongst a wide range of systems, including those at finite temperature, those with itinerant particles, and random circuits. Then, we consider the case of an open system interacting noisily with an external environment. We predict the statistics of observables under largely arbitrary noise channels including those with correlated errors, allowing us to discriminate candidate error models both for continuous Hamiltonian time evolution and for digital random circuits. Ultimately our results clarify the role of ergodicity in quantum dynamics, with fundamental and practical consequences.

Many machine learning applications involve learning a latent representation of data, which is often high-dimensional and difficult to directly interpret. In this work, we propose "Moment Pooling", a natural extension of Deep Sets networks which drastically decrease latent space dimensionality of these networks while maintaining or even improving performance. Moment Pooling generalizes the summation in Deep Sets to arbitrary multivariate moments, which enables the model to achieve a much higher effective latent dimensionality for a fixed latent dimension. We demonstrate Moment Pooling on the collider physics task of quark/gluon jet classification by extending Energy Flow Networks (EFNs) to Moment EFNs. We find that Moment EFNs with latent dimensions as small as 1 perform similarly to ordinary EFNs with higher latent dimension. This small latent dimension allows for the internal representation to be directly visualized and interpreted, which in turn enables the learned internal jet representation to be extracted in closed form.

We investigate the hypothesis that sexaquarks, hypothetical stable six-quark states, could be a significant component of the dark matter. We expand on previous studies of sexaquark cosmology, accounting for the possibility that some relevant interaction cross sections might be strongly suppressed below expectations based on dimensional analysis. We update direct-detection constraints on stable sexaquarks comprising a subdominant fraction of the dark matter, as well as limits on the annihilation of an antisexaquark component from Super-Kamiokande. We argue that the scenario where sexaquarks comprise a \(O(1)\) fraction of the dark matter would require either a suppression of \(O(10^{-19})\) in sexaquark interactions with baryons, combined with a very high yield of net sexaquark number from the quark-hadron transition, or else a very strong suppression of the cross section for antisexaquark annihilation on nucleons (24+ orders of magnitude below the QCD scale). Independently, we find that a sexaquark component comprising more than \(O(10^{-3})\) of the dark matter can be excluded from direct-detection bounds, unless its scattering cross section is severely suppressed compared to the expected scale of strong and even electromagnetic interactions.

In this paper, we present a general framework for quantum many-body simulations called the operator learning renormalization group (OLRG). Inspired by machine learning perspectives, OLRG is a generalization of Wilson's numerical renormalization group and White's density matrix renormalization group, which recursively builds a simulatable system to approximate a target system of the same number of sites via operator maps. OLRG uses a loss function to minimize the error of a target property directly by learning the operator map in lieu of a state ansatz. This loss function is designed by a scaling consistency condition that also provides a provable bound for real-time evolution. We implement two versions of the operator maps for classical and quantum simulations. The former, which we call the Operator Matrix Map, can be implemented via neural networks on classical computers. The latter, which we call the Hamiltonian Expression Map, generates device pulse sequences to leverage the capabilities of quantum computing hardware. We illustrate the performance of both maps for calculating time-dependent quantities in the quantum Ising model Hamiltonian.

The entanglement wedge reconstruction paradigm in AdS/CFT states that for a bulk qudit within the entanglement wedge of a boundary subregion \(\bar{A}\), operators acting on the bulk qudit can be reconstructed as CFT operators on \(\bar{A}\). This naturally fits within the framework of quantum error correction, with the CFT states containing the bulk qudit forming a code protected against the erasure of the boundary subregion \(A\). In this paper, we set up and study a framework for relational bulk reconstruction in holography: given two code subspaces both protected against erasure of the boundary region \(A\), the goal is to relate the operator reconstructions between the two spaces. To accomplish this, we assume that the two code subspaces are smoothly connected by a one-parameter family of codes all protected against the erasure of \(A\), and that the maximally-entangled states on these codes are all full-rank. We argue that such code subspaces can naturally be constructed in holography in a "measurement-based" setting. In this setting, we derive a flow equation for the operator reconstruction of a fixed code subspace operator using modular theory which can, in principle, be integrated to relate the reconstructed operators all along the flow. We observe a striking resemblance between our formulas for relational bulk reconstruction and the infinite-time limit of Connes cocycle flow, and take some steps towards making this connection more rigorous. We also provide alternative derivations of our reconstruction formulas in terms of a canonical reconstruction map we call the modular reflection operator.

Numerical studies of lattice quantum field theories are conducted in finite spatial volumes, typically with cubic symmetry in the spatial coordinates. Motivated by these studies, this work presents a general algorithm to construct multi-particle interpolating operators for quantum field theories with cubic symmetry. The algorithm automates the block diagonalization required to combine multiple operators of definite linear momentum into irreducible representations of the appropriate little group. Examples are given for distinguishable and indistinguishable particles including cases with both zero and non-zero spin. An implementation of the algorithm is publicly available at https://github.com/latticeqcdtools/mhi.

Jet energy calibration is an important aspect of many measurements and searches at the LHC. Currently, these calibrations are performed on a per-jet basis, i.e. agnostic to the properties of other jets in the same event. In this work, we propose taking advantage of the correlations induced by momentum conservation between jets in order to improve their jet energy calibration. By fitting the \(p_T\) asymmetry of dijet events in simulation, while remaining agnostic to the \(p_T\) spectra themselves, we are able to obtain correlation-improved maximum likelihood estimates. This approach is demonstrated with simulated jets from the CMS Detector, yielding a \(3\)-\(5\%\) relative improvement in the jet energy resolution, corresponding to a quadrature improvement of approximately 35%.

We present an efficient approach to set informative physically motivated priors for EFT-based full-shape analyses of galaxy survey data. We extract these priors from simulated galaxy catalogs based on halo occupation distribution (HOD) models. As a first step, we build a joint distribution between EFT galaxy bias and HOD parameters from a set of 10,500 HOD mock catalogs. We make use of the field level EFT technique that allows for cosmic variance cancellation, enabling a precision calibration of EFT parameters from computationally inexpensive small-volume simulations. As a second step, we use neural density estimators -- normalizing flows -- to model the marginal probability density of the EFT parameters, which can be used as a prior distribution in full shape analyses. As a first application, we use our HOD-based prior distribution in a new analysis of galaxy power spectra and bispectra from the BOSS survey in the context of single field primordial non-Gaussianity. We find that our approach leads to a reduction of the posterior volume of bias parameters by an order of magnitude. We also find \(f_{\rm NL}^{\rm equil} = 650\pm 310\) and \(f_{\rm NL}^{\rm ortho} = 42\pm 130\) (at 68% CL) in a combined two-template analysis, representing a \(\approx 40\%\) improvement in constraints on single field primordial non-Gaussianity, equivalent to doubling the survey volume.

Recently, formalism has been derived for studying electroweak transition amplitudes for three-body systems both in infinite and finite volumes. The formalism provides exact relations that the infinite-volume amplitudes must satisfy, as well as a relationship between physical amplitudes and finite-volume matrix elements, which can be constrained from lattice QCD calculations. This formalism poses additional challenges when compared with the analogous well-studied two-body equivalent one, including the necessary step of solving integral equations of singular functions. In this work, we provide some non-trivial analytical and numerical tests on the aforementioned formalism. In particular, we consider a case where the three-particle system can have three-body bound states as well as bound states in the two-body subsystem. For kinematics below the three-body threshold, we demonstrate that the scattering amplitudes satisfy unitarity. We also check that for these kinematics the finite-volume matrix elements are accurately described by the formalism for two-body systems up to exponentially suppressed corrections. Finally, we verify that in the case of the three-body bound state, the finite-volume matrix element is equal to the infinite-volume coupling of the bound state, up to exponentially suppressed errors.

We present an update for results on \(B\)-meson semileptonic decays using the highly improved staggered quark (HISQ) action for both valence and 2+1+1 sea quarks. The use of the highly improved action, combined with the MILC collaboration's gauge ensembles with lattice spacings down to \(\sim\)0.03 fm, allows the \(b\) quark to be treated with the same discretization as the lighter quarks. The talk will focus on updated results for \(B_{(s)} \to D_{(s)}\), \(B_{(s)} \to K\) scalar and vector form factors.