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Ultrafast radiographic imaging and tracking: An overview of instruments, methods, data, and applications

Ultrafast radiographic imaging and tracking (U-RadIT) use state-of-the-art ionizing particle and light sources to experimentally study sub-nanosecond transients or dynamic processes in physics, chemistry, biology, geology, materials science and other fields. These processes are fundamental to modern technologies and applications, such as nuclear fusion energy, advanced manufacturing, communication, and green transportation, which often involve one mole or more atoms and elementary particles, and thus are challenging to compute by using the first principles of quantum physics or other forward models. One of the central problems in U-RadIT is to optimize information yield through, e.g. high-luminosity X-ray and particle sources, efficient imaging and tracking detectors, novel methods to collect data, and large-bandwidth online and offline data processing, regulated by the underlying physics, statistics, and computing power. We review and highlight recent progress in: (a.) Detectors such as high-speed complementary metal-oxide semiconductor (CMOS) cameras, hybrid pixelated array detectors integrated with Timepix4 and other application-specific integrated circuits (ASICs), and digital photon detectors; (b.) U-RadIT modalities such as dynamic phase contrast imaging, dynamic diffractive imaging, and four-dimensional (4D) particle tracking; (c.) U-RadIT data and algorithms such as neural networks and machine learning, and (d.) Applications in ultrafast dynamic material science using XFELs, synchrotrons and laser-driven sources. Hardware-centric approaches to U-RadIT optimization are constrained by detector material properties, low signal-to-noise ratio, high cost and long development cycles of critical hardware components such as ASICs. Interpretation of experimental data, including comparisons with forward models, is frequently hindered by sparse measurements, model and measurement uncertainties, and noise. Alternatively, U-RadIT make increasing use of data science and machine learning algorithms, including experimental implementations of compressed sensing. Machine learning and artificial intelligence approaches, refined by physics and materials information, may also contribute significantly to data interpretation, uncertainty quantification and U-RadIT optimization.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Exploring the synergy of kinematics and dynamics for collider physics

In collider experiments, an event is characterized by two distinct yet mutually complementary features: the “global features” and the “local features.” Kinematic information such as the event topology of a hard process, masses, and spins of particles comprises global features spanning the entire phase space. This global feature can be inferred from reconstructed objects. In contrast, representations of particles in gauge groups, such as quantum chromodynamics (QCD), offer localized features revealing the dynamics of an underlying theory. These local features, particularly observed in the patterns of radiation as raw data in various detector components, complement the global kinematic features. We propose a simple but effective neural network architecture that seamlessly integrates information from both kinematics and QCD to enhance the signal sensitivity at colliders. Published by the American Physical Society 2024

Ban, Kayoung (ORCID:000000019691877X)↗

Optical versus radiographic imaging and tomography: introduction to the ROADS feature issue

Optical imaging is an ancient branch of imaging dating back to thousands of years. Radiographic imaging and tomography (RadIT), including the first use of X-rays by Wilhelm Röntgen, and then, $γ$ -rays, energetic charged particles, neutrons, etc. are about 130 years young. The synergies between optical and radiographic imaging can be cast in the framework of these building blocks: Physics, Sources, Detectors, Methods, and Data Science, as described in Appl. Opt. 61, RDS1 (2022). Optical imaging has expanded to include three-dimensional (3D) tomography (including holography), due in to part the invention of optical (including infrared) lasers. RadIT are intrinsically 3D because of the penetrating power of ionizing radiation. Both optical imaging and tomography (OIT) and RadIT are evolving into even higher dimensional regimes, such as time-resolved tomography (4D) and temporarily and spectroscopically resolved tomography (4D + ). Further advances in OIT and RadIT will continue to be driven by desires for higher information yield, higher resolutions, and higher probability models with reduced uncertainties. Synergies in quantum physics, laser-driven sources, low-cost detectors, data-driven methods, automated processing of data, and artificially intelligent data acquisition protocols will be beneficial to both branches of imaging in many applications. These topics, along with an overview of the Radiography, Applied Optics, and Data Science virtual feature issue, are discussed here.

47 OTHER INSTRUMENTATION↗

Parallel database search and prime factorization with magnonic holographic memory devices

In this work, we describe the capabilities of Magnonic Holographic Memory (MHM) for parallel database search and prime factorization. MHM is a type of holographic device, which utilizes spin waves for data transfer and processing. Its operation is based on the correlation between the phases and the amplitudes of the input spin waves and the output inductive voltage. The input of MHM is provided by the phased array of spin wave generating elements allowing the producing of phase patterns of an arbitrary form. The latter makes it possible to code logic states into the phases of propagating waves and exploit wave superposition for parallel data processing. We present the results of numerical modeling illustrating parallel database search and prime factorization. The results of numerical simulations on the database search are in agreement with the available experimental data. The use of classical wave interference may results in a significant speedup over the conventional digital logic circuits in special task data processing (e.g., √n in database search). Potentially, magnonic holographic devices can be implemented as complementary logic units to digital processors. Physical limitations and technological constrains of the spin wave approach are also discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Repeatability of measurements: Non-Hermitian observables and quantum Coriolis force

A noncommuting measurement transfers, via the apparatus, information encoded in a system's state to the external “observer.” Classical measurements determine properties of physical objects. In the quantum realm, the very same notion restricts the recording process to orthogonal states as only those are distinguishable by measurements. Thus, even a possibility to describe physical reality by means of non-Hermitian operators should volens nolens be excluded as their eigenstates are not orthogonal. We show that non-Hermitian operators with real spectra can be treated within the standard framework of quantum mechanics. Further, we propose a quantum canonical transformation that maps Hermitian systems onto non-Hermitian ones. Similar to classical inertial forces this map is accompanied by an energetic cost, pinning the system on the unitary path.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Study of direct photon production with heavy flavor jets in $p\overline{p}$ collisions at $\sqrt{s}=1.96$ TeV with DZero detector

In hadronic collisions, photons ($\gamma$) with high energies emerge unaltered from the hard parton-parton interaction and therefore provide a clean probe of the underlying hard-scattering dynamics. Photons produced in these interactions (called direct or prompt) in association with one or more bottom ($b$)-quark jets provide an important test of perturbative Quantum Chromodynamics (QCD) predictions at large hard-scattering scales $Q$ and over a wide range of parton momentum fractions. In addition, the study of these processes also provides information about the parton density functions of $b$ quarks and gluons ($g$), which still have substantial uncertainties. In $p\bar{p}$ collisions, \gb-jet events are produced primarily through the Compton process $gb\to \gamma b$, which dominates for low and moderate photon transverse momenta ($\Ptg$), and through quark-antiquark anni hilation followed by $g \to b\bar{b}$ gluon splitting $q\bar{q}\to \gamma g \to \gamma b\bar{b}$, which dominates at high $\Ptg$. The final state with $b$-quark pair production, $p\bar{p} \rightarrow \gamma+b\bar{b}$, is mainly produced via $q\bar{q}\to \gamma b\bar{b}$ and $gg\to \gamma b\bar{b}$ scatterings. The $\gamma+2~b$-jet process is a crucial component of background in measurements of, for example, $t\bar{t} \gamma$ coupling and in some searches for new phenomena.\\ This thesis presents the first measurements of the differential cross section ${\rm d}\sigma/{\rm d}\Ptg$ for the production of an isolated photon in association with at least two $b$-quark jets. The ratio of differential production cross sections for $\gamma+2~b$-jets to $\gamma+b$-jet as a function of \ptg is also presented. The measurement of the ratio of cross sections leads to cancellation of various experimental and theoretical uncertainties, allowing a more precise comparison with the theoretical predictions. The results are based on the proton-antiproton ! collision data corresponding to an integrated luminosity of $8.7$~fb$^{-1}$ at $\sqrt{s}=$1.96~\TeV collected with the \DO detector at the Fermilab Tevatron Collider. %In this measurement, we follow an inclusive approach by allowing the final state with any additional jet(s) on top of the studied $b$-quark jets. Inclusive $\gamma+2~b$-jet production may also originate from partonic subprocesses involving parton fragmentation into a photon. However, photon isolation requirements significantly reduces the contributions from such processes. The large data sample and use of advanced photon and $b$-jet identification tools enable us to measure the $\gamma+2~b$-jet production cross section differentially as a function of $\Ptg$. This allows for probing the dynamics of the production process over a wide kinematic range not studied before in other measurements of a vector boson + $b$-jet final state. The measured cross sections and their ratios are compared to the NLO perturbative Q CD calculations as well as predictions based on the $k_{\rm T}$-factorization approach and those from the {\sc sherpa} and {\sc pythia} Monte Carlo event generators. We also measure the ratio of cross sections, $\sigma(p\bar{p}\rightarrow Z+2~b~\text{jets})$/$\sigma(p\bar{p}\rightarrow Z+\text{2~jets})$, for associated production of a $Z$ boson with at least two jets. This measurement uses data corresponding to an integrated luminosity of 9.7 fb$^{-1}$ collected by the \DO experiment. The measured integrated ratio is in agreement with predictions from NLO perturbative QCD and the Monte Carlo event generators {\sc alpgen} and {\sc pythia}. A good theoretical description of this process is essential since it forms a major background for a variety of physics processes, including standard model Higgs boson production in association with a $Z$ boson, $ZH(H\rightarrow b\bar{b})$, and searches for supersymmetric partners of the $b$ quark. These results will improve our theoretical understanding as we search for phenomena beyond the standard! model us! ing the data from similar collider experiments in the case where the final states of the interaction involved the production of vector bosons in association with two $b$-quark jets.\\ This work has been done in collaboration with \DO experiment but the analyses and results presented in this thesis are my contribution.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Observation of emission process in hydrogen-like nitrogen Z-pinch discharge with time integrated soft X-ray spectrum pinhole image

The emission spectra of hydrogen-like nitrogen Balmer at the wavelength of 13.4 nm in capillary Z-pinch discharge plasma are experimentally examined. Ionization to fully strip nitrogen at the pinch maximum, and subsequent rapid expansion cooling are required to establish the population inversion between the principal quantum number of n = 2 and n = 3. The ionization and recombination processes with estimated plasma parameters are evaluated by utilizing a time integrated spectrum pinhole image containing radial spatial information. A cylindrical capillary plasma is pinched by a triangular pulsed current with peak amplitude of 50 kA and pulse width of 50 ns.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Volumetric 3D Display System with Static Screen

Current display technology has relied on flat, 2D screens that cannot truly convey the third dimension of visual information: depth. In contrast to conventional visualization that is primarily based on 2D flat screens, the volumetric 3D display possesses a true 3D display volume, and places physically each 3D voxel in displayed 3D images at the true 3D (x,y,z) spatial position. Each voxel, analogous to a pixel in a 2D image, emits light from that position to form a real 3D image in the eyes of the viewers. Such true volumetric 3D display technology provides both physiological (accommodation, convergence, binocular disparity, and motion parallax) and psychological (image size, linear perspective, shading, brightness, etc.) depth cues to human visual systems to help in the perception of 3D objects. In a volumetric 3D display, viewers can watch the displayed 3D images from a completely 360 view without using any special eyewear. The volumetric 3D display techniques may lead to a quantum leap in information display technology and can dramatically change the ways humans interact with computers, which can lead to significant improvements in the efficiency of learning and knowledge management processes. Within a block of glass, a large amount of tiny dots of voxels are created by using a recently available machining technique called laser subsurface engraving (LSE). The LSE is able to produce tiny physical crack points (as small as 0.05 mm in diameter) at any (x,y,z) location within the cube of transparent material. The crack dots, when illuminated by a light source, scatter the light around and form visible voxels within the 3D volume. The locations of these tiny voxels are strategically determined such that each can be illuminated by a light ray from a high-resolution digital mirror device (DMD) light engine. The distribution of these voxels occupies the full display volume within the static 3D glass screen. This design eliminates any moving screen seen in previous approaches, so there is no image jitter, and has an inherent parallel mechanism for 3D voxel addressing. High spatial resolution is possible with a full color display being easy to implement. The system is low-cost and low-maintenance.

Geng, Jason↗

Programmable simulations of molecules and materials with reconfigurable quantum processors

Simulations of quantum chemistry and quantum materials are believed to be among the most important applications of quantum information processors. However, realizing practical quantum advantage for such problems is challenging because of the prohibitive computational cost of programming typical problems into quantum hardware. Here we introduce a simulation framework for strongly correlated quantum systems represented by model spin Hamiltonians that uses reconfigurable qubit architectures to simulate real-time dynamics in a programmable way. Our approach also introduces an algorithm for extracting chemically relevant spectral properties via classical co-processing of quantum measurement results. We develop a digital–analogue simulation toolbox for efficient Hamiltonian time evolution using digital Floquet engineering and hardware-optimized multi-qubit operations to accurately realize complex spin–spin interactions. As an example, we propose an implementation based on Rydberg atom arrays. In addition, we show how detailed spectral information can be extracted from the dynamics through snapshot measurements and single-ancilla control, enabling the evaluation of excitation energies and finite-temperature susceptibilities from a single dataset. To illustrate the approach, we show how to use the method to compute key properties of a polynuclear transition-metal catalyst and two-dimensional magnetic materials.

74 ATOMIC AND MOLECULAR PHYSICS↗

Formation and ultraslow propagation of infrared solitons in graphene under an external magnetic field

Unusual dispersion relation of graphene nanoribbons for electrons can lead to an exceptionally strong optical response in the infrared regime and exhibits a very good tunable frequency. According to quantum optics and solid-material scientific principles, here we show the possibility to generate ultraslow infrared bright and dark solitons in graphene under the action of strong magnetic and infrared laser fields. By means of quantum-mechanical density-matrix formalism, we derive the equations of motion that govern the nonlinear evolution of the probe-pulse envelope in this scheme. It is found that, by properly choosing the parameters of the system, the formation and ultraslow propagation of infrared spatial solitons originate from the balance between nonlinear effects and the dispersion properties of the graphene under infrared excitation. Moreover, the unique electronic properties and selection rules near the Dirac point provide more freedom for us to study the linear and nonlinear dynamical responses of the photonics and graphene system. These results may have potential applications in telecommunication and optical information processing.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Laboratory study of nitrate photolysis in Antarctic snow. II. Isotopic effects and wavelength dependence

Atmospheric nitrate is preserved in Antarctic snow firn and ice. However, at low snow accumulation sites, post-depositional processes induced by sunlight obscure its interpretation. The goal of these studies (see also Paper I by Meusinger et al. [“Laboratory study of nitrate photolysis in Antarctic snow. I. Observed quantum yield, domain of photolysis, and secondary chemistry,” J. Chem. Phys. 140, 244305 (2014)]) is to characterize nitrate photochemistry and improve the interpretation of the nitrate ice core record. Naturally occurring stable isotopes in nitrate ({sup 15}N, {sup 17}O, and {sup 18}O) provide additional information concerning post-depositional processes. Here, we present results from studies of the wavelength-dependent isotope effects from photolysis of nitrate in a matrix of natural snow. Snow from Dome C, Antarctica was irradiated in selected wavelength regions using a Xe UV lamp and filters. The irradiated snow was sampled and analyzed for nitrate concentration and isotopic composition (δ{sup 15}N, δ{sup 18}O, and Δ{sup 17}O). From these measurements an average photolytic isotopic fractionation of {sup 15}ε = (−15 ± 1.2)‰ was found for broadband Xe lamp photolysis. These results are due in part to excitation of the intense absorption band of nitrate around 200 nm in addition to the weaker band centered at 305 nm followed by photodissociation. An experiment with a filter blocking wavelengths shorter than 320 nm, approximating the actinic flux spectrum at Dome C, yielded a photolytic isotopic fractionation of {sup 15}ε = (−47.9 ± 6.8)‰, in good agreement with fractionations determined by previous studies for the East Antarctic Plateau which range from −40 to −74.3‰. We describe a new semi-empirical zero point energy shift model used to derive the absorption cross sections of {sup 14}NO{sub 3}{sup −} and {sup 15}NO{sub 3}{sup −} in snow at a chosen temperature. The nitrogen isotopic fractionations obtained by applying this model under the experimental temperature as well as considering the shift in width and center well reproduced the values obtained in the laboratory study. These cross sections can be used in isotopic models to reproduce the stable isotopic composition of nitrate found in Antarctic snow profiles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Void formation in operator growth, entanglement, and unitarity

The structure of the Heisenberg evolution of operators plays a key role in explaining diverse processes in quantum many-body systems. In this paper, we discuss a new universal feature of operator evolution: an operator can develop a void during its evolution, where its nontrivial parts become separated by a region of identity operators. Such processes are present in both integrable and chaotic systems, and are required by unitarity. We show that void formation has important implications for unitarity of entanglement growth and generation of mutual information and multipartite entanglement. We study explicitly the probability distributions of void formation in a number of unitary circuit models, and conjecture that in a quantum chaotic system the distribution is given by the one we find in random unitary circuits, which we refer to as the random void distribution. We also show that random unitary circuits lead to the same pattern of entanglement growth for multiple intervals as in (1 + 1)-dimensional holographic CFTs after a global quench, which can be used to argue that the random void distribution leads to maximal entanglement growth.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Modular invariant inflation

Modular invariance is a striking symmetry in string theory, which may keep stringy corrections under control. In this paper, we investigate a phenomenological consequence of the modular invariance, assuming that this symmetry is preserved as well as in a four dimensional (4D) low energy effective field theory. As a concrete setup, we consider a modulus field T whose contribution in the 4D effective field theory remains invariant under the modular transformation and study inflation drived by T. The modular invariance restricts a possible form of the scalar potenntial. As a result, large field models of inflation are hardly realized. Meanwhile, a small field model of inflation can be still accomodated in this restricted setup. The scalar potential traced during the slow-roll inflation mimics the hilltop potential V{sub ht}, but it also has a non-negligible deviation from V{sub ht}. Detecting the primordial gravitational waves predicted in this model is rather challenging. Yet, we argue that it may be still possible to falsify this model by combining the information in the reheating process which can be determined self-completely in this setup.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantum Critical Higgs

In this paper, the appearance of the light Higgs boson at the LHC is difficult to explain, particularly in light of naturalness arguments in quantum field theory. However, light scalars can appear in condensed matter systems when parameters (like the amount of doping) are tuned to a critical point. At zero temperature these quantum critical points are directly analogous to the finely tuned standard model. In this paper, we explore a class of models with a Higgs near a quantum critical point that exhibits non-mean-field behavior. We discuss the parametrization of the effects of a Higgs emerging from such a critical point in terms of form factors, and present two simple realistic scenarios based on either generalized free fields or a 5D dual in anti–de Sitter space. For both of these models, we consider the processes gg→ZZ and gg→hh, which can be used to gain information about the Higgs scaling dimension and IR transition scale from the experimental data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantum machine learning with differential privacy

Abstract Quantum machine learning (QML) can complement the growing trend of using learned models for a myriad of classification tasks, from image recognition to natural speech processing. There exists the potential for a quantum advantage due to the intractability of quantum operations on a classical computer. Many datasets used in machine learning are crowd sourced or contain some private information, but to the best of our knowledge, no current QML models are equipped with privacy-preserving features. This raises concerns as it is paramount that models do not expose sensitive information. Thus, privacy-preserving algorithms need to be implemented with QML. One solution is to make the machine learning algorithm differentially private, meaning the effect of a single data point on the training dataset is minimized. Differentially private machine learning models have been investigated, but differential privacy has not been thoroughly studied in the context of QML. In this study, we develop a hybrid quantum-classical model that is trained to preserve privacy using differentially private optimization algorithm. This marks the first proof-of-principle demonstration of privacy-preserving QML. The experiments demonstrate that differentially private QML can protect user-sensitive information without signficiantly diminishing model accuracy. Although the quantum model is simulated and tested on a classical computer, it demonstrates potential to be efficiently implemented on near-term quantum devices [noisy intermediate-scale quantum (NISQ)]. The approach’s success is illustrated via the classification of spatially classed two-dimensional datasets and a binary MNIST classification. This implementation of privacy-preserving QML will ensure confidentiality and accurate learning on NISQ technology.

97 MATHEMATICS AND COMPUTING↗

Basic Energy Sciences Roundtable: Opportunities for Quantum Computing in Chemical and Materials Sciences

Fundamental transformations in the basic logic of computing are few and far between. Since the invention of digital computers in the early 1940s, the logic underlying computation has remained the same, even as computing hardware evolved from vacuum tubes to silicon transistors. With the advent of quantum computation, a fundamental transformation is near. Quantum computation is based on a different type of logic: rather than being in one of the two states of a classical bit, a quantum bit or qubit can be in a superposition of two states simultaneously. Operations and measurements on these qubits obey the constraints of quantum mechanics. It is now understood that quantum computers have great power in principle to go beyond classical computers, but that not every application is well suited to implementation on quantum computers. For reasons explained in more detail in the Introduction, scientific problems in chemical and materials sciences are uniquely suited to take advantage of quantum computing in the relatively near future. Indeed, quantum computing offers the best hope to solve many of the most important and difficult problems in this field. For example, quantum materials, such as superconductors and complex magnetic materials, show novel kinds of ordered phases that are natural from the point of view of quantum mechanics but difficult to access via computation on classical computers. Quantum sensors based on solid materials are already widely used but could be greatly improved with insight from quantum computations, as could materials for information technologies. Quantum chemical dynamics is another example of a problem that is intrinsically well suited to studies on quantum computers. Applications of quantum chemical dynamics include catalysis, artificial photosynthesis, and other industrially important processes. Quantum computers exist in the laboratory and are beginning to exceed 50 qubits, which is roughly the size beyond which their behavior cannot be predicted or emulated on present-day classical supercomputers. While a quantum computer of 50 qubits is almost certainly not powerful enough to tackle the major scientific challenges in chemical and materials sciences, some of these major challenges start to become accessible with a few hundred qubits if error rates can be kept small. This roundtable was convened to ask how emerging quantum computers can be applied to major scientific problems in chemical and materials sciences, in light of Basic Energy Sciences’s leading role in these fields and the Department of Energy’s leading role in high-performance scientific computation more generally. The main outcome of the roundtable was a consensus that there are scientific problems of great importance on which emerging quantum computers have the potential for disruptive impact, and where comparable progress is unlikely to occur by other means.

36 MATERIALS SCIENCE↗

Field programmable gate array-assigned complex-valued computation and its limits

We discuss how leveraging Field Programmable Gate Array (FPGA) technology as part of a high performance computing platform reduces latency to meet the demanding real time constraints of a quantum optics simulation. Implementations of complex-valued operations using fixed point numeric on a Virtex-5 FPGA compare favorably to more conventional solutions on a central processing unit. Our investigation explores the performance of multiple fixed point options along with a traditional 64 bits floating point version. With this information, the lowest execution times can be estimated. Relative error is examined to ensure simulation accuracy is maintained.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Probing transverse momentum dependent structures with azimuthal dependence of energy correlators

We study the azimuthal angle dependence of the energy-energy correlators $\langle \mathcal{E}\left({\widehat{n}}_{1}\right)\mathcal{E}\left({\widehat{n}}_{2}\right)\rangle $ in the back-to-back region for e + e - annihilation and deep inelastic scattering (DIS) processes with general polarization of the proton beam. We demonstrate that the polarization information of the beam and the underlying partons from the hard scattering is propagated into the azimuthal angle dependence of the energy-energy correlators. In the process, we define the Collins-type EEC jet functions and introduce a new EEC observable using the lab-frame angles in the DIS process. Furthermore, we extend our formalism to explore the two-point energy correlation between hadrons with different quantum numbers ${\mathbb{S}}_{i}$ in the back-to-back limit $\langle {\mathcal{E}}_{{\mathbb{S}}_{1}}\left({\widehat{n}}_{1}\right){\mathcal{E}}_{{\mathbb{S}}_{2}}\left({\widehat{n}}_{2}\right)\rangle $. We find that in the Operator Product Expansion (OPE) region the nonperturbative information is entirely encapsulated by a single number. Using our formalism, we present several phenomenological studies that showcase how energy correlators can be used to probe transverse momentum dependent structures.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗