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At least 415 records · Page 23

Accurate Force Field for Carbon Dioxide–Silica Interactions Based on Density Functional Theory

Fluid–silica interfaces are ubiquitous in chemistry, occurring in both natural geochemical environments and practical applications ranging from separations to catalysis. Simulations of these interfaces have been, and continue to be, a significant avenue for understanding their behavior. A constraining factor, however, is the availability of accurate force fields. Most simulations use traditional “mixing rules” to determine nonbonded dispersion interactions, an approach that has not been critically examined. Here, in this study, we present Lennard-Jones parameters for the interaction of carbon dioxide with silica interfaces that are optimized to reproduce density functional theory (DFT)-based binding energies. The modeling is based on the recently developed silica-DDEC force field, whose atomic charges are consistent with DFT calculations. Standard mixing rules are found to predict weaker CO 2 binding to silica than that obtained from DFT, an effect corrected by the optimized parameters given here. This behavior extends to other silica force fields (Clayff and Gulmen-Thompson), and the present Lennard-Jones parameters improve their performance as well. The effects of improved Lennard-Jones parameters on the structural and dynamical properties of condensed CO 2 in silica slit pores are also examined.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Transient Symmetry Controls Photo Dynamics near Conical Intersections

Excited-state chemistry lacks generalised symmetry rules. With many femtochemistry studies focused on individual cases, it is hard to build up the same level of chemical intuition for excited-states as exists for ground states. Here, we unravel the degrees of freedom involved in ultrafast internal conversion (IC) by mapping the vibrational coherence of the initial wavepacket, and the dependence on molecular symmetry in various cyclic tertiary amines. Molecular symmetry plays an important role in the preservation of vibrational coherence in the transit from one electronic state to another. We show here that it is sufficient for the molecule to simply have the possibility of a more symmetric structure to achieve the preservation of vibrational coherence. It can be transient and still lead to preservation. Furthermore, this finding provides an additional angle on how symmetry influences electronic transitions and an additional piece to the puzzle of establishing symmetry-based selection rules for excited-state processes.

74 ATOMIC AND MOLECULAR PHYSICS↗

Hybridization of Excited Interlayer Excitons with Intralayer Excitons in Transition-Metal Dichalcogenide Heterostructures: Interplay of Orbital and Structural Symmetry

Hybridization between interlayer exciton (ILX) and intralayer excitons offers a powerful route to engineer light–matter interactions in transition-metal dichalcogenide (TMDC) heterostructures, yet the underlying mechanism and selection rules remain elusive. Here we probe exciton hybridization in MoTe2/MoSe2 heterobilayers under a tunable out-of-plane electric field and observe distinct avoided crossings in the electric-field dependent reflection spectra. We associate them with coupling between excited ILX states, including the 2p and 2s Rydberg states, and MoTe2 intralayer exciton. Supported by ab initio GW plus Bethe-Salpeter equation (GW-BSE) calculations, we identify the hybridizing states and establish optical selection rules based on the effective angular momentum of the exciton states. These findings highlight the role of excitonic binding in the observed hybridization, rather than that of simple band-mixing models, and provide a new pathway for brightening high-energy dark states.

Yao, Helen [Department of Materials Science and En↗

Enhanced Second and Third Harmonic Generations in Metasurfaces Enabled through Point Group Design and Accidental Bound States in the Continuum

Here, we investigate enhanced second‑ and third‑harmonic generation (SHG and THG) in GaAs metasurfaces by combining electromagnetic point‑group designs with accidental bound states in the continuum (BICs). Using group theory, we predict the existence, suppression, and polarization selection rules of SHG and THG for metasurfaces belonging to the D 2h and C 2v point groups. In D 2h metasurfaces, inversion symmetry suppresses SHG while enabling polarization‑selective THG, which is strongly enhanced near accidental BICs with ultrahigh Q‑factors approaching 107. By breaking inversion symmetry to form C 2v metasurfaces through the introduction of nanogaps, SHG is now allowed and is dramatically enhanced near accidental BICs. Importantly, accidental BICs preserve polarization selection rules while providing a robust parameter range for high‑Q resonances, in contrast to quasi‑BICs induced by symmetry breaking. Our results demonstrate that the combination of point‑group theory and accidental‑BIC engineering offers a predictive and robust route toward highly efficient nonlinear metasurfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Impact of 2D–3D Heterointerface on Remote Epitaxial Interaction through Graphene

Remote epitaxy has drawn attention as it offers epitaxy of functional materials that can be released from the substrates with atomic precision, thus enabling production and heterointegration of flexible, transferrable, and stackable freestanding single-crystalline membranes. In addition, the remote interaction of atoms and adatoms through two-dimensional (2D) materials in remote epitaxy allows investigating and utilizing electrical/chemical/physical coupling of bulk (3D) materials via 2D materials (3D-2D-3D coupling). Here, we unveil the respective roles and impacts of the substrate material, graphene, substrate-graphene interface, and epitaxial material for electrostatic coupling of these materials, which governs cohesive ordering and can lead to single-crystal epitaxy in the overlying film. Further, we show that simply coating a graphene layer on wafers does not guarantee successful implementation of remote epitaxy, since atomically precise control of the graphene-coated interface is required, and provide key considerations for maximizing the remote electrostatic interaction between the substrate and adatoms. This was enabled by exploring various material systems and processing conditions, and we demonstrate that the rules of remote epitaxy vary significantly depending on the ionicity of material systems as well as the graphene-substrate interface and the epitaxy environment. The general rule of thumb discovered here enables expanding 3D material libraries that can be stacked in freestanding form.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Engineering Thermal Transport across Layered Graphene–MoS 2 Superlattices

Layering two-dimensional van der Waals materials provides a high degree of control over atomic placement, which could enable tailoring of vibrational spectra and heat flow at the sub-nanometer scale. In this work, using spatially resolved ultrafast thermoreflectance and spectroscopy, we uncover the design rules governing cross-plane heat transport in superlattices assembled from monolayers of graphene (G) and MoS 2 (M). Using a combinatorial experimental approach, we probe nine different stacking sequences, G, GG, MG, GGG, GMG, GGMG, GMGG, GMMG, and GMGMG, and identify the effects of vibrational mismatch, interlayer adhesion, and junction asymmetry on thermal transport. Pure G sequences display evidence of quasi-ballistic transport, whereas adding even a single M layer strongly disrupts heat conduction. The experimental data are described well by molecular dynamics simulations, which include thermal expansion, accounting for the effect of finite temperature on the interlayer spacing. The simulations show that an increase of ~2.4% in the layer separation of GMGMG, relative to its value at 300 K, can lead to a doubling of the thermal resistance. Using these design rules, we experimentally demonstrate a five-layer GMGMG superlattice “thermal metamaterial” with an ultralow effective cross-plane thermal conductivity comparable to that of air.

2D materials↗

Systematic Mapping of Bacterial CRISPRa Systems for Synergistic Gene Activation Reveals Antagonistic Effects

CRISPR gene activation (CRISPRa) tools have shown great promise for bacterial strain engineering but often require customization for each intended application. Our goal is to create generalizable CRISPRa tools that can overcome previous limitations of gene activation in bacteria. In eukaryotic cells, multiple activators can be combined for synergistic gene activation. To identify potential effectors for synergistic activation in bacteria, we systematically characterized bacterial activator proteins with a set of engineered synthetic promoters. We found that optimal target sites for different activators could vary by up to 200 bases in the region upstream of the transcription start site (TSS). These optimal target sites qualitatively matched previous reports for each activator, but the precise targeting rules varied between different promoters. By characterizing targeting rules in the same promoter context, we were able to test activator combinations with each effector positioned at its optimal target site. We did not find any activator combinations that produced synergistic activation, and we found that many combinations were antagonistic. Furthermore, this systematic investigation highlights fundamental mechanistic differences between bacterial and eukaryotic transcriptional activation systems and suggests that alternative strategies will be necessary for strong bacterial gene activation at arbitrary endogenous targets.

CRISPR activation↗

Three-Dimensional Lead Iodide Perovskitoid Hybrids with High X-ray Photoresponse

Large organic A cations cannot stabilize the 3D perovskite AMX 3 structure because they cannot be accommodated in the cubo-octhedral cage (do not follow the Goldschmidt tolerance factor rule), and they generally template low-dimensional structures. In this paper, we report that the large dication aminomethylpyridinium (AMPY) can template novel 3D structures which resemble conventional perovskites. They have the formula (xAMPY)M 2 I 6 (x = 3 or 4, M = Sn 2+ or Pb 2+ ) which is double of the AMX3 formula. However, because of the steric requirement of the Goldschmidt tolerance factor rule, it is impossible for (xAMPY)M 2 I 6 to form proper perovskite structures. Instead, a combination of corner-sharing and edge-sharing connectivity is adopted in these compounds leading to the new 3D structures. DFT calculations reveal that the compounds are indirect band gap semiconductors with direct band gaps presenting at slightly higher energies and dispersive electronic bands. The indirect band gaps of the Sn and Pb compounds are ~1.7 and 2.0 eV, respectively, which is slightly higher than the corresponding AMI 3 3D perovskites. The Raman spectra for the compounds are diffuse, with a broad rising central peak at very low frequencies around 0 cm –1 , a feature that is characteristic of dynamical lattices, high anharmonicity, and dissipative vibrations very similar to the 3D AMX 3 perovskites. Devices of (3AMPY)Pb 2 I 6 crystals exhibit clear photoresponse under ambient light without applied bias, reflecting a high carrier mobility (μ) and long carrier lifetime (τ). The devices also exhibit sizable X-ray generated photocurrent with a high μτ product of ~1.2×10 -4 cm 2 /V and a X-ray sensitivity of 207 μC∙Gy -1 ∙cm -2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Origin of 182 W Anomalies in Ocean Island Basalts

Ocean island basalts (OIB) show variable 182 W deficits that have been attributed to either early differentiation of the mantle or core-mantle interaction. However, 182 W variations may also reflect nucleosynthetic isotope heterogeneity inherited from Earth's building material, which would be evident from correlated 182 W and 183 W anomalies. Some datasets for OIB indeed show hints for such correlated variations, meaning that a nucleosynthetic origin of W isotope anomalies in OIB cannot be excluded. We report high-precision W isotope data for OIB from Samoa and Hawaii, which confirm previously reported 182 W deficits for these samples, but also demonstrate that none of these samples have resolvable 183 W anomalies. These data therefore rule out a nucleosynthetic origin of the 182 W deficits in OIB, which most likely reflect the entrainment of either core material or an overabundance of late-accreted materials within OIB mantle sources. If these processes occurred over Earth's history, they may have also been responsible for shifting the 182 W composition of the bulk mantle to its modern-day value. We also report Mo isotope data for some Hawaiian OIB, which reveal no resolved nucleosynthetic Mo isotopic anomalies. This is consistent with inheritance of 182 W deficits in OIB from the addition of either core or late-accreted material, but only if these materials have a non-carbonaceous (NC) meteorite-like heritage. As such, these data rule out significant contributions of carbonaceous chondrite (CC)-like materials to either Earth's core or late accretion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Phonon-exciton Interactions in WSe 2 under a quantizing magnetic field

Strong many-body interaction in two-dimensional transitional metal dichalcogenides provides a unique platform to study the interplay between different quasiparticles, such as prominent phonon replica emission and modified valley-selection rules. A large out-of-plane magnetic field is expected to modify the exciton-phonon interactions by quantizing excitons into discrete Landau levels, which is largely unexplored. Here, we observe the Landau levels originating from phonon-exciton complexes and directly probe exciton-phonon interaction under a quantizing magnetic field. Phonon-exciton interaction lifts the inter-Landau-level transition selection rules for dark trions, manifested by a distinctively different Landau fan pattern compared to bright trions. This allows us to experimentally extract the effective mass of both holes and electrons. The onset of Landau quantization coincides with a significant increase of the valley-Zeeman shift, suggesting strong many-body effects on the phonon-exciton interaction. Our work demonstrates monolayer WSe 2 as an intriguing playground to study phonon-exciton interactions and their interplay with charge, spin, and valley.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Gaussian-preserved, non-volatile shape morphing in three-dimensional microstructures for dual-functional electronic devices

Motile plant structures such as Mimosa pudica leaves, Impatiens glandulifera seedpods, and Dionaea muscipula leaves exhibit fast nastic movements in a few seconds or less. This motion is stimuli-independent mechanical movement following theorema egregium rules. Artificial analogs of tropistic motion in plants are exemplified by shape-morphing systems, which are characterized by high functional robustness and resilience for creating 3D structures. However, all shape-morphing systems developed so far rely exclusively on continuous external stimuli and result in slow response. Here, we report a Gaussian-preserved shape-morphing system to realize ultrafast shape morphing and non-volatile reconfiguration. Relying on the Gaussian-preserved rules, the transformation can be triggered by mechanical or thermal stimuli within a microsecond. Moreover, as localized energy minima are encountered during shape morphing, non-volatile configuration is preserved by geometrically enhanced rigidity. Using this system, we demonstrate a suite of electronic devices that are reconfigurable, and therefore, expand functional diversification.

36 MATERIALS SCIENCE↗

Bias free multiobjective active learning for materials design and discovery

The design rules for materials are clear for applications with a single objective. For most applications, however, there are often multiple, sometimes competing objectives where there is no single best material and the design rules change to finding the set of Pareto optimal materials. In this work, we leverage an active learning algorithm that directly uses the Pareto dominance relation to compute the set of Pareto optimal materials with desirable accuracy. We apply our algorithm to de novo polymer design with a prohibitively large search space. Using molecular simulations, we compute key descriptors for dispersant applications and drastically reduce the number of materials that need to be evaluated to reconstruct the Pareto front with a desired confidence. This work showcases how simulation and machine learning techniques can be coupled to discover materials within a design space that would be intractable using conventional screening approaches.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Nutrient supply controls the linkage between species abundance and ecological interactions in marine bacterial communities

Nutrient scarcity is pervasive for natural microbial communities, affecting species reproduction and co-existence. However, it remains unclear whether there are general rules of how microbial species abundances are shaped by biotic and abiotic factors. Here we show that the ribosomal RNA gene operon (rrn) copy number, a genomic trait related to bacterial growth rate and nutrient demand, decreases from the abundant to the rare biosphere in the nutrient-rich coastal sediment but exhibits the opposite pattern in the nutrient-scarce pelagic zone of the global ocean. Both patterns are underlain by positive correlations between community-level rrn copy number and nutrients. Furthermore, inter-species co-exclusion inferred by negative network associations is observed more in coastal sediment than in ocean water samples. Nutrient manipulation experiments yield effects of nutrient availability on rrn copy numbers and network associations that are consistent with our field observations. Based on these results, we propose a “hunger games” hypothesis to define microbial species abundance rules using the rrn copy number, ecological interaction, and nutrient availability.

59 BASIC BIOLOGICAL SCIENCES↗

Small-world complex network generation on a digital quantum processor

Abstract Quantum cellular automata (QCA) evolve qubits in a quantum circuit depending only on the states of their neighborhoods and model how rich physical complexity can emerge from a simple set of underlying dynamical rules. The inability of classical computers to simulate large quantum systems hinders the elucidation of quantum cellular automata, but quantum computers offer an ideal simulation platform. Here, we experimentally realize QCA on a digital quantum processor, simulating a one-dimensional Goldilocks rule on chains of up to 23 superconducting qubits. We calculate calibrated and error-mitigated population dynamics and complex network measures, which indicate the formation of small-world mutual information networks. These networks decohere at fixed circuit depth independent of system size, the largest of which corresponding to 1,056 two-qubit gates. Such computations may enable the employment of QCA in applications like the simulation of strongly-correlated matter or beyond-classical computational demonstrations.

97 MATHEMATICS AND COMPUTING↗

Quasi-one-dimensional hydrogen bonding in nanoconfined ice

Abstract The Bernal-Fowler ice rules stipulate that each water molecule in an ice crystal should form four hydrogen bonds. However, in extreme or constrained conditions, the arrangement of water molecules deviates from conventional ice rules, resulting in properties significantly different from bulk water. In this study, we employ machine learning-driven first-principles simulations to identify a new stabilization mechanism in nanoconfined ice phases. Instead of forming four hydrogen bonds, nanoconfined crystalline ice can form a quasi-one-dimensional hydrogen-bonded structure that exhibits only two hydrogen bonds per water molecule. These structures consist of strongly hydrogen-bonded linear chains of water molecules that zig-zag along one dimension, stabilized by van der Waals interactions that stack these chains along the other dimension. The unusual interplay of hydrogen bonding and van der Waals interactions in nanoconfined ice results in atypical proton behavior such as potential ferroelectric behavior, low dielectric response, and long-range proton dynamics.

Science & Technology - Other Topics↗

Author Correction: Genome-guided isolation of the hyperthermophilic aerobe Fervidibacter sacchari reveals conserved polysaccharide metabolism in the Armatimonadota

Correction to: Nature Communicationshttps://doi.org/10.1038/s41467-024-53784-3, published online 4 November 2024 In the version of this article initially published, Table 1 did not include the properties of the taxa being proposed or refer directly to another location in the main manuscript describing the properties. As such, the original manuscript did not comply with Rule 27 (2)(c) of the ICNP. Also, Table 1 listed the order Fervidibacterales as the nomenclatural type for the class Fervidibacteria, which violates latest emended version of Rule 15 stating that the nomenclatural type for a class must be a genus. Below we provide a modification of Table 1 containing protologues with these errors corrected. We have also changed the order of the taxa in the table to meet the most common ordering. (Table presented.) Taxon names proposed under the ICNP Proposed taxon Etymology Description Genus Fervidibacter Fer.vi.di.bac’ter. L. masc. adj. fervidus, hot, steaming; N.L. masc. n. bacter, a rod; N.L. masc. n. Fervidibacter, a hot rod Thermophilic or hyperthermophilic inhabitants of freshwater thermal environments. All members are likely polysaccharide-degrading chemoheterotrophs with numerous carbohydrate-active enzymes encoded in their genomes. Aerobic, with high-affinity and/or low-affinity terminal oxidases present in the genomes. The oxidative pentose phosphate pathway and the tricarboxylic acid cycle are complete in genomes belonging to the genus. Gram-stain-negative and diderm cell envelope structure. Ovoid- to rod-shaped morphology. Spores are not formed. The genus is a distinct phylogenetic lineage in the family Fervidibacteraceae, the order Fervidibacterales, and the class Fervidibacteria in the phylum Armatimonadota. The type species is Fervidibacter sacchariT. Species Fervidibacter sacchari sac’cha.ri. N.L. gen. n. sacchari, of sugar Hyperthermophilic, microaerophilic, facultatively anaerobic, and grows chemoheterotrophically on monosaccharides and polysaccharides. Cells are ovoid- to rod-shaped, Gram-stain negative, and are 0.9–1.3 µm in width and 1.6–3.6 µm in length. Grows between 65 and 87.5 °C and an optimum temperature of 80 °C, and a pH range of 6.5–8.6 with an optimum pH of 7.5. Grows at an optimum O2 concentration of 5–10%. Grows on D-arabinose, D-galactose, D-glucose, D-rhamnose, D-ribose, D-xylose, chondroitin sulfate, colloidal chitin, galactan, gellan gum, guar gum, karaya gum, locust bean gum, xantham gum, xyloglucan, β-glucan, glycogen, starch, AFEX-pretreated corn stover, miscanthus, sugarcane bagasse, acetate and casamino acids. Grows weakly on xyloglucan under fermentation conditions. The major fatty acids (>10%) are C16:0, C18:0 and/or cyclo-C17:0, and iso-C16:0. The major respiratory quinones (>10%) are MK-8 and MK-9. The isolate and genomes of the species have been recovered from geothermal springs in the Great Basin, Nevada, USA. GC content of genomes range between 51–52%. Subunits for both the high-affinity and low-affinity terminal oxidases are encoded in the genomes. Genomes also encode a Group 3d [NiFe] hydrogenase, which produces hydrogen as an electron sink for NAD+ regeneration. The type strain PD1T (= JCM 39283T = DSM 113467T) was isolated from Great Boiling Spring in Nevada, USA. Family Fervidibacteraceae Fer.vi.di.bac.te.ra’ce.ae. N.L. masc. n. Fervidibacter type genus of the family; L. suff. -aceae ending to denote a family; N.L. fem. pl. n. Fervidibacteraceae the family of the genus Fervidibacter Thermophilic or hyperthermophilic inhabitants of freshwater thermal environments. All members are likely polysaccharide-degrading chemoheterotrophs with numerous carbohydrate-active enzymes encoded in their genomes. Aerobic, with high-affinity and/or low-affinity terminal oxidases present in the genomes. The oxidative pentose phosphate pathway and the tricarboxylic acid cycle are complete in genomes belonging to the family. The family is a distinct phylogenetic lineage in the order Fervidibacterales and the class Fervidibacteria in the phylum Armatimonadota. The type genus is Fervidibacter. Order Fervidibacterales Fer.vi.di.bac.te.ra’les. N.L. masc. n. Fervidibacter type genus of the order; L. suff. -ales ending to denote an order; N.L. fem. pl. n. Fervidibacterales the order of the genus Fervidibacter Thermophilic or hyperthermophilic inhabitants of freshwater thermal environments. All members are likely polysaccharide-degrading chemoheterotrophs with numerous carbohydrate-active enzymes encoded in their genomes. Aerobic or strictly anaerobic. Phylogenomic placement of this lineage within the Fervidibacteria and relative evolutionary divergence supports delineation of this lineage as an order within the class Fervidibacteria and phylum Armatimonadota. The type genus is Fervidibacter. Class Fervidibacteria Fer.vi.di.bac.te’ri.a. N.L. masc. n. Fervidibacter type genus of the type order of the class; L. suff. -ia ending to denote a class; N.L. neut. pl. n. Fervidibacteria the class of the order Fervidibacterales Thermophilic or hyperthermophilic inhabitants of freshwater thermal environments. All members are likely polysaccharide-degrading chemoheterotrophs with numerous carbohydrate-active enzymes encoded in their genomes. Aerobic or strictly anaerobic. Phylogenomic placement of this lineage within the Armatimonadota and relative evolutionary divergence supports delineation of this lineage as a class within the Armatimonadota. The type genus is Fervidibacter. The error has not been corrected in the PDF or HTML versions of the Article.

Nou, Nancy O↗

A quantum liquid of magnetic octupoles on the pyrochlore lattice

Spin liquids are highly correlated yet disordered states formed by the entanglement of magnetic dipoles. Theories define such states using gauge fields and deconfined quasiparticle excitations that emerge from a local constraint governing the ground state of a frustrated magnet. For example, the ‘2-in–2-out’ ice rule for dipole moments on a tetrahedron can lead to a quantum spin ice in rare-earth pyrochlores. However, $f$-electron ions often carry multipole degrees of freedom of higher rank than dipoles, leading to intriguing behaviours and ‘hidden’ orders. In this paper we show that the correlated ground state of a Ce 3+ -based pyrochlore, Ce 2 Sn 2 O 7 , is a quantum liquid of magnetic octupoles. Our neutron scattering results are consistent with a fluid-like state where degrees of freedom have a more complex magnetization density than that of magnetic dipoles. The nature and strength of the octupole–octupole couplings, together with the existence of a continuum of excitations attributed to spinons, provides further evidence for a quantum ice of octupoles governed by a ‘2-plus–2-minus’ rule. Our work identifies Ce 2 Sn 2 O 7 as a unique example of frustrated multipoles forming a ‘hidden’ topological order, thus generalizing observations on quantum spin liquids to multipolar phases that can support novel types of emergent fields and excitations.

36 MATERIALS SCIENCE↗

Measurement of the proton spin structure at long distances

Measuring the spin structure of protons and neutrons tests our understanding of how they arise from quarks and gluons, the fundamental building blocks of nuclear matter. At long distances, the coupling constant of the strong interaction becomes large, requiring non-perturbative methods to calculate quantum chromodynamics processes, such as lattice gauge theory or effective field theories. In this work, we report proton spin structure measurements from scattering a polarized electron beam off polarized protons. The spin-dependent cross-sections were measured at large distances, corresponding to the region of low momentum transfer squared between 0.012 and 1.0GeV 2 . This kinematic range provides unique tests of chiral effective field theory predictions. Our results show that a complete description of the nucleon spin remains elusive, and call for further theoretical works, for example, in lattice quantum chromodynamics. Finally, our data extrapolated to the photon point agree with the Gerasimov–Drell–Hearn sum rule, a fundamental prediction of quantum field theory that relates the anomalous magnetic moment of the proton to its integrated spin-dependent cross-sections.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗