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Explicit Form for the Most General Lorentz Transformation Revisited

Explicit formulae for the 4×4 Lorentz transformation matrices corresponding to a pure boost and a pure three-dimensional rotation are very well known. Significantly less well known is the explicit formula for a general Lorentz transformation with arbitrary non-zero boost and rotation parameters. We revisit this more general formula by presenting two different derivations. The first derivation (which is somewhat simpler than previous ones appearing in the literature) evaluates the exponential of a 4×4 real matrix A, where A is a product of the diagonal matrix diag(+1,−1,−1,−1) and an arbitrary 4×4 real antisymmetric matrix. The formula for expA depends only on the eigenvalues of A and makes use of the Lagrange interpolating polynomial. The second derivation exploits the observation that the spinor product η†σ¯μχ transforms as a Lorentz four-vector, where χ and η are two-component spinors. The advantage of the latter derivation is that the corresponding formula for a general Lorentz transformation Λ reduces to the computation of the trace of a product of 2×2 matrices. Both computations are shown to yield equivalent expressions for Λ.

Science & Technology - Other Topics

Electromagnetic observables of open-shell nuclei from coupled-cluster theory

Here we develop a new method to describe electromagnetic observables of open-shell nuclei with two nucleons outside a closed shell. This approach combines the equation-of-motion coupled-cluster method for such systems and the Lorentz integral transform technique, expanding the applicability of coupled-cluster theory for electromagnetic observables beyond closed-(sub)shell nuclei. To validate this new approach, we compute the non-energy-weighted dipole sum rule and the dipole polarizability of 16,24 ⁢O in both the closed-(sub)shell and the new equation-of-motion coupled-cluster frameworks, finding agreement within error bars. We then analyze the evolution of the dipole polarizability along the oxygen and calcium isotopic chains. Our predictions agree well with available experimental data and other available theoretical calculations for the closed-(sub)shell 16,22 ⁢O and the open-shell 18 O. In the calcium isotopes, we observe that our dipole polarizability predictions for open-shell nuclei are lower than those of closed-(sub)shell nuclei. We expect that our predictions for 24 O and 54,56 ⁢Ca will motivate future experimental studies at the drip line.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

16 O Electroweak Response Functions from First Principles

We present calculations of various electroweak response functions for the 16 O nucleus obtained using coupled-cluster theory in conjunction with the Lorentz integral transform method. We employ nuclear forces derived at next-to-leading order and next-to-next-to-leading order in chiral effective field theory and perform a Bayesian analysis to assess uncertainties. Our results are in good agreement with available electron-scattering data at |𝐪|≈326 MeV/c. Additionally, we provide several predictions for the weak response functions in the quasielastic peak region at |𝐪| =300 and 400 MeV/c, which are critical for long-baseline neutrino experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Nuclear Responses with Neural-Network Quantum States

We introduce a variational Monte Carlo framework that combines neural-network quantum states with the Lorentz integral transform technique to compute the dynamical properties of self-bound quantum many-body systems in continuous Hilbert spaces. While broadly applicable to various quantum systems, including atoms and molecules, in this initial application we focus on the photoabsorption cross section of light nuclei, where benchmarks against numerically exact techniques are available. Our accurate theoretical predictions are complemented by robust uncertainty quantification, enabling meaningful comparisons with experiments. Here, we demonstrate that a relatively simple nuclear Hamiltonian—based on a leading-order pionless EFT expansion and known to accurately reproduce ground-state energies of nuclei with 𝐴 ≤ 40—also provides a reliable description of the photoabsorption cross section.

Ab initio calculations

Structure and dynamics of open-shell nuclei from spherical coupled-cluster theory

We extend the spherical coupled-cluster ab initio method for open-shell nuclei where two nucleons are removed from a shell subclosure. Following the recent implementation of the two-particle-attached approach [Phys. Rev. C 110, 044306 (2024)], we focus on the two-particle-removed method. Using the equations-of-motion framework, we address both nuclear structure and dipole response functions by coupling coupled-cluster theory with the Lorentz integral transform technique. We perform calculations using chiral interactions, including three-nucleon forces, and estimate many-body uncertainties by comparing different coupled-cluster truncation schemes. Here, we validate our approach by studying ground-state energies, excited states, and electric dipole polarizabilities in the oxygen and calcium isotopic chains. For binding energies and selected low-lying excited states, we achieve an accuracy comparable to that of the established closed-shell coupled-cluster theory and generally agree with experiment. Finally, we underestimate experimental data for electric dipole polarizabilities, particularly in calcium isotopes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Nuclear responses with neural-network quantum states

We introduce a variational Monte Carlo framework that combines neural-network quantum states with the Lorentz integral transform technique to compute the dynamical properties of self-bound quantum many-body systems in continuous Hilbert spaces. While broadly applicable to various quantum systems, including atoms and molecules, in this initial application we focus on the photoabsorption cross section of light nuclei, where benchmarks against numerically exact techniques are available. Our accurate theoretical predictions are complemented by robust uncertainty quantification, enabling meaningful comparisons with experiments. We demonstrate that a simple nuclear Hamiltonian, based on a leading-order pionless effective field theory expansion and known to accurately reproduce the ground-state energies of nuclei with $A\leq 20$ nucleons also provides a reliable description of the photoabsorption cross section.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Quantitative phase retrieval and characterization of magnetic nanostructures via Lorentz (scanning) transmission electron microscopy

Magnetic materials phase reconstruction using Lorentz transmission electron microscopy (LTEM) measurements have traditionally been achieved using longstanding methods such as off-axis holography (OAH) fast-Fourier transform technique and the transport-of-intensity equation (TIE). The increase in access to processing power alongside the development of advanced algorithms have allowed for phase retrieval of nanoscale magnetic materials with greater efficacy and resolution. Specifically, reverse-mode automatic differentiation (RMAD) and the extended electron ptychography iterative engine (ePIE) are two recent developments of phase retrieval that can be applied to analyzing micro-to-nano- scale magnetic materials. This work evaluates phase retrieval using TIE, RMAD, and ePIE in simulations of Permalloy (Ni 80 Fe 20 ) nanoscale islands, or nanomagnets. Extending beyond simulations, we demonstrate total phase retrieval and image reconstructions of a NiFe nanowire using OAH and RMAD in LTEM and ePIE in Lorentz-mode-4D scanning transmission electron microscopy experiments and determine the saturation magnetization through corroborations with micromagnetic modeling. Finally, we demonstrate the efficacy of these methods in retrieving the total phase and highlight its use in characterizing and analyzing the proximity effect of the magnetic nanostructures.

Lorentz transmission electron microscopy

Ultralow-temperature cryogenic transmission electron microscopy using a new helium flow cryostat stage

Advances in cryogenic electron microscopy have opened new avenues for probing quantum phenomena in correlated materials. This study reports the installation and performance of a new side-entry condenZero cryogenic cooling system for JEOL (Scanning) Transmission Electron Microscopes (S/TEM), utilizing compressed liquid helium (LHe) and designed for imaging and spectroscopy at ultra-low temperatures. The system includes an external dewar mounted on a vibration-damping stage and a pressurized, low-noise helium transfer line with a remotely controllable needle valve, ensuring stable and efficient LHe flow with minimal thermal and mechanical noise. Performance evaluation demonstrates a stable base temperature of 4.37 K measured using a Cernox bare chip sensor on the holder with temperature fluctuations within ±0.004 K. Complementary in-situ electron energy-loss spectroscopy (EELS) via aluminum bulk plasmon analysis was used to measure the local specimen temperature and validate cryogenic operation during experiments. The integration of cryogenic cooling with other microscopy techniques, including electron diffraction and Lorentz TEM, was demonstrated by resolving charge density wave (CDW) transitions in NbSe2 using electron diffraction, and imaging nanometric magnetic skyrmions in MnSi via Lorentz TEM. In conclusion, this platform provides reliable cryogenic operation below 7 K, establishing a low-drift route for direct visualization of electronic and magnetic phase transformations in quantum materials.

Charge density wave

In-situ L-TEM observations of dynamics of nanometric skyrmions and antiskyrmions

Nanometer-scale magnetic skyrmions and antiskyrmions exhibit unique dynamical behaviors in response to external stimuli, which are critical for their applications in low-power-consumption spintronic devices. This review discusses recent advancements in in-situ Lorentz transmission electron microscopy (L-TEM) observations of skyrmion and antiskyrmion dynamics, and demonstrates the manipulation and evolution of these textures in various magnetic materials under electric, magnetic, and thermal stimuli. Specifically, the motion tracking of single skyrmions and their clusters, and the deformation and transformation of skyrmions has been demonstrated in chiral helimagnets FeGe, Co 9 Zn 9 Mn 2 , and Co 10 Zn 10 with precise application of electric currents. Skyrmions can undergo dynamic transitions in current-driven skyrmion motions, from pinned states to linear flows, and even exhibit deformation into elliptical shapes, underscoring their topological robustness and dynamic flexibility. In addition, the manipulation of single antiskyrmions and antiskyrmion-lattice phases in (Fe 0.63 Ni 0.3 Pd 0.07 ) 3 P with S 4 symmetry is discussed, highlighting their high mobility and unique sliding capabilities along stripe domains at room temperature, facilitated by nanosecond pulsed electric currents. Finally, the temperature gradient-driven motion and topological transformation of elliptical skyrmions and antiskyrmions in this same material are investigated. In conclusion, the comprehensive insights gained from the L-TEM imaging technique are pivotal in advancing the design and functionality of next-generation skyrmion/antiskyrmion-based spintronic devices.

(Anti)skyrmion

Automated imaging of the annihilation of a transverse domain wall in patterned magnetic thin films

Imaging the magnetic domain wall behavior in patterned thin films under external stimuli can enable understanding the underlying energy landscape and the role of local microstructure and defects. We present an automated workflow for in situ Lorentz transmission electron microscopy to image magnetic domain walls at the nanometer length scale and at a time resolution in the sub-millisecond regime—the latter of which is limited by the speed of the available camera. Our workflow is modular and can be broadly applied to various types of in situ experiments, taking us a step closer to the future of autonomous imaging of nanomagnetic films with electron microscopy. Using our workflow, we show the transformation of a transverse domain wall with sub-millisecond time resolution under the application of an in situ transverse magnetic field, a study of whose dynamics are essential in the design of future domain wall mediated spintronic device applications.

Algebraic topology

Five-point functions and the permutation group 𝑆 5

Five-point functions and five-body wave functions play an important role in many areas of nuclear and particle physics, e.g., in 2 →3 scattering processes, in the five-gluon vertex, or in the study of pentaquarks. In this work we consider the permutation group 𝑆 5 to facilitate the description of such objects. We work out the multiplets transforming under irreducible representations of 𝑆 5 and provide compact formulas allowing one to cast the permutations of an object 𝑓 12345 into combinations with definite permutation symmetry. We also give the explicit expressions for the irreducible multiplet products. We consider several practical applications as examples: We arrange the four-momenta and Lorentz invariants of a five-point function into the multiplet structure, we work out the color tensors of the five-gluon vertex in the multiplet notation, and we discuss applications for five-body wave functions like those of pentaquarks.

Bethe-Salpeter equation

Three-dimensional imaging of pion using lattice QCD: generalized parton distributions

In this work, we report a lattice calculation of x-dependent valence pion generalized parton distributions (GPDs) at zero skewness with multiple values of the momentum transfer −t. The calculations are based on an N f = 2 + 1 gauge ensemble of highly improved staggered quarks with Wilson-Clover valence fermion. The lattice spacing is 0.04 fm, and the pion valence mass is tuned to be 300 MeV. We determine the Lorentz-invariant amplitudes of the quasi-GPD matrix elements for both symmetric and asymmetric momenta transfers with similar values and show the equivalence of both frames. Then, focusing on the asymmetric frame, we utilize a hybrid scheme to renormalize the quasi-GPD matrix elements obtained from the lattice calculations. After the Fourier transforms, the quasi-GPDs are then matched to the light-cone GPDs within the framework of large momentum effective theory with improved matching, including the next-to-next-to-leading order perturbative corrections, and leading renormalon and renormalization group resummations. We also present the 3-dimensional image of the pion in impact-parameter space through the Fourier transform of the momentum transfer −t.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Search for heavy scalar resonances decaying to Lorentz-boosted Higgs and Higgs-like bosons in the $\mathrm{b}\overline{\mathrm{b}}4\mathrm{q}$ final state at $\sqrt{s}=13$ TeV

A search is performed for a heavy scalar resonance X decaying to a Higgs boson (H) and a Higgs-like scalar boson (Y) in the two bottom quark (H → $b\bar{b}$) and four quark (Y → VV → 4q) final state, where V denotes a W or Z boson. Masses of the X between 900 and 4000 GeV and the Y between 60 and 2800 GeV are considered. The search is performed in data collected by the CMS experiment at the CERN LHC from proton-proton collisions at 13 TeV center-of-mass energy, with a data set corresponding to a total integrated luminosity of 138 fb −1 . It targets the Lorentz-boosted regime, in which the products of the H → $b\bar{b}$ decay can be reconstructed as a single large-area jet, and those from the Y → VV → 4q decay as either one Y → 4q or two jets V → H → $q\bar{q}$. Jet identification and mass reconstruction exploit machine-learning tools, including a novel attention-based “particle transformer” for Y → 4q identification. No significant excess is observed in the data above the standard model background expectation. Upper limits on the product of production cross section and branching fraction as low as 0.2 fb are derived at 95% confidence level for various mass hypotheses. This is the first search at the LHC for scalar resonances in the all-hadronic H → $b\bar{b}$VV decay channel.

Beyond Standard Model

Search for Higgs boson production at high transverse momentum in the WW decay channel in proton-proton collisions at $\sqrt{s}=13$ TeV

A search for Higgs boson (H) production at high transverse momentum (p T ) in the WW decay channel is presented. The analysis uses proton-proton collisions at $\sqrt{s}=13$ TeV recorded by the CMS experiment in 2016–2018, corresponding to an integrated luminosity of 138 fb −1 . The visible decay products of the Higgs boson are reconstructed as a single large-radius jet with one isolated lepton or none (1ℓ and 0ℓ, respectively; ℓ = e, μ). The H-candidate jets are identified using an advanced transformer-based algorithm and are calibrated with the Lund jet plane reweighting technique. The 1ℓ channel is further split into gluon fusion, vector boson fusion, and associated production with hadronically decaying vector boson categories, while the 0ℓ channel considers all production processes inclusively. The measured cross section times the H → WW branching fraction relative to the standard model expectation is $\mu =-{0.19}_{-0.46}^{+0.48}$, indicating no evidence of a signal above the background. This measurement represents the first dedicated study of highly Lorentz-boosted H → WW decays, complementing earlier searches for high-p T Higgs boson in other decay channels.

Hadron-Hadron Scattering

Proton isovector helicity PDF at NNLO and the twist-3 moment $\tilde{d}$ 2 from lattice QCD at physical quark masses

We present a lattice quantum chromodynamics calculation of the 𝑥-dependent isovector quark helicity parton distribution function (PDF) of the proton in the large momentum effective theory (LaMET) framework. Through operator product expansion (OPE) we also extract the $\tilde{d}$ 2 moment of the twist-3 PDF 𝑔 𝑇 ⁡(𝑥) for the first time in the $\overline{MS}$ scheme, which is proportional to the average color Lorentz force experienced by the quark in the proton. This calculation is performed on a lattice of spacing 𝑎 =0.076 fm at physical quark masses. The quasi-PDF matrix elements are measured in proton states boosted to momenta 𝑃 𝑧 ={0,0.25,1.02,1.53} GeV. We first extract the lowest few helicity PDF moments from the renormalization-group (RG) invariant ratios of the matrix elements with OPE. Combined with the matrix elements relevant for 𝑔 𝑇 ⁡(𝑥), we obtain $\tilde{d}$$^{u-d}_2$⁡(2 GeV) =0.0024⁢(46) at next-to-leading order in $\overline{MS}$. Then, the helicity quasi-PDF matrix elements are renormalized in the hybrid scheme with linear renormalon resummation and Fourier transformed to the 𝑥-space after an asymptotic extrapolation. The quasi-PDF is perturbatively matched to the $\overline{MS}$ PDF with RG and threshold resummations at next-to-leading power and next-to-next-to-leading logarithmic accuracies. After resummations, we determine the PDF in the region 𝑥 ∈[0.25,0.75]. The end-point regions are then parametrized, combined with the LaMET prediction at moderate 𝑥, and fitted to the short-distance matrix elements in coordinate space.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Artificial Intelligence for Event Reconstruction and Higgs Physics at CMS and Future Colliders

This dissertation charts a trajectory in which advances in artificial intelligence (AI) play a central role in pushing the high-energy physics frontier, complementing progress driven by higher collision energies and larger colliders. The discovery potential of the LHC and future colliders relies on accurate reconstruction of increasingly complex particle collision events. In the CMS experiment, this task is performed by the particle-flow (PF) algorithm. This dissertation presents the first implementation of a machine-learning-based particle-flow (MLPF) reconstruction in the CMS detector based on transformer architectures. In simulated top quark--antiquark pair (ttbar) events under LHC Run~3 (2023--2024) conditions, MLPF improves jet energy resolution by 10--20\% compared to standard PF for jets with transverse momentum between 30--100\GeV. Runtime performance is evaluated using simulated multijet events, with a median inference time of 20\unit{ms} per event on an NVIDIA L4 GPU, compa red to approximately 110\unit{ms} for standard PF. The MLPF algorithm is also validated on Run~3 collision data, representing the first data-validated ML-based reconstruction pipeline at any LHC experiment. We then extend MLPF toward future electron--positron colliders and introduce the first full-simulation cross-detector transfer learning workflow for PF reconstruction. The model is pre-trained on simulated events from the Compact Linear Collider detector (CLICdet) and fine-tuned on the CLIC-like detector (CLD) proposed for the Future Circular Collider (FCC). This approach achieves up to a 40\% improvement in jet energy resolution over rule-based reconstruction while reducing the required training dataset size by an order of magnitude, demonstrating the potential of AI to accelerate detector development and optimization. This dissertation also demonstrates how modern AI techniques enhance the sensitivity of LHC physics analyses. A CMS search for highly Lorentz-boosted Higgs bosons decaying to \textrm{W} boson pairs is presented, focusing on the single-lepton final state. A dedicated fine-tuning strategy for \ParT yields an approximately 70\% increase in expected sensitivity relative to the baseline model. The analysis uses proton--proton collision data at a center-of-mass energy of \ensuremath{\sqrt{s}=13\TeV} collected by CMS between 2016 and 2018, corresponding to an integrated luminosity of 138\ensuremath{\ \mathrm{fb}^{-1}}. The expected significance of the search is $1.86\sigma$, with an observed signal strength of $-0.19^{+0.48}_{-0.46}$. Finally, explainable AI techniques are applied to the MLPF and \ParticleNet algorithms using layerwise relevance propagation, showing that both models base their predictions on physically meaningful features consistent with our physics intuition. Together, these results demonstrate how advanced AI methods can enhance reconstruction, analysis sensitivity, and interpretability, shaping the next era of experimental parti cle physics.

Mokhtar, Farouk [UC, San Diego]