Search NASA⌕ Search

SEARCH · Search NASA

Results for “Small x”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4

Polarized dipole scattering amplitudes meet the valence quark model

The recently revised small- x helicity evolution [], resumming the double-logarithmic factor, α s ln 2 ( 1 / x ) , allows for the study of helicity distributions of quarks and gluons at small Bjorken x , corresponding to high center-of-mass energy. In this work, we calculate the moderate- x initial conditions in the regime, α s ln 2 ( 1 / x ) ∼ 1 , for the small- x helicity evolution using a light-front valence quark model of the proton, which provides additional physical information about the target. The perturbative emission and absorption of a gluon by the valence quarks are also included. The results, given in Eqs. (35), provide a new set of initial conditions with a significantly reduced number of free parameters than conventional models []. Consequently, the predictive power of small- x helicity evolution is expected to improve once the initial conditions from this work are incorporated. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Back-to-back dijet production in DIS at arbitrary Bjorken x: TMD gluon distributions to twist-3 accuracy

We derive the gluon transverse-momentum-dependent (TMD) operator structure of back-to-back\\\\r\\\\nquark–antiquark dijet production in deep inelastic scattering at arbitrary Bjorken-x to twist-3 ac\\\\r\\\\ncuracy. Working at leading order in the strong coupling and in the kinematic regime where the\\\\r\\\\ntransverse momentum imbalance of the jets is much smaller than their individual transverse mo\\\\r\\\\nmenta, we perform a systematic gradient expansion of the quark propagator in a background gluon\\\\r\\\\nfield. This expansion organizes multiple interactions with the target in terms of longitudinal Wilson\\\\r\\\\nlines and gauge-invariant field-strength insertions, yielding a TMD description valid beyond the\\\\r\\\\nstrict high-energy eikonal (x → 0) approximation. We obtain explicit cross sections for longitudi\\\\r\\\\nnally and transversely polarized virtual photons, identifying all contributing gluon TMD operators\\\\r\\\\nup to twist-3, including structures involving F+−, Fij, and three-gluon correlators. The full lon\\\\r\\\\ngitudinal phase eixP+z− associated with Bjorken-x is retained throughout. In the small-x limit,\\\\r\\\\nour results reproduce the known sub-eikonal expressions obtained in the Color Glass Condensate\\\\r\\\\nframework, establishing a direct connection between the general-x TMD expansion and high-energy\\\\r\\\\nfactorization. We further reduce the operator basis using equations of motion, minimizing the num\\\\r\\\\nber of independent nonperturbative matrix elements entering the cross section. This work provides\\\\r\\\\na systematic foundation for extending TMD analyses of dijet production beyond leading twist, es\\\\r\\\\ntablishing a unified operator framework valid at arbitrary Bjorken-x that smoothly interpolates\\\\r\\\\nbetween moderate- and small-x descriptions of gluon TMDs.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Examining polymer‐protein biophysical interactions with small‐angle x‐ray scattering and quartz crystal microbalance with dissipation

Abstract Polymer‐protein hybrids can be deployed to improve protein solubility and stability in denaturing environments. While previous work used robotics and active machine learning to inform new designs, further biophysical information is required to ascertain structure–function behavior. Here, we show the value of tandem small‐angle x‐ray scattering (SAXS) and quartz crystal microbalance with dissipation (QCMD) experiments to reveal detailed polymer‐protein interactions with horseradish peroxidase (HRP) as a test case. Of particular interest was the process of polymer‐protein complex formation under thermal stress whereby SAXS monitors formation in solution while QCMD follows these dynamics at an interface. The radius of gyration ( R g ) of the protein as measured by SAXS does not change significantly in the presence of polymer under denaturing conditions, but thickness and dissipation changes were observed in QCMD data. SAXS data with and without thermal stress were utilized to create bead models of the potential complexes and denatured enzyme, and each model fit provided insight into the degree of interactions. Additionally, QCMD data demonstrated that HRP deforms by spreading upon surface adsorption at low concentration as shown by longer adsorption times and smaller frequency shifts. In contrast, thermally stressed and highly inactive HRP had faster adsorption kinetics. The combination of SAXS and QCMD serves as a framework for biophysical characterization of interactions between proteins and polymers which could be useful in designing polymer‐protein hybrids.

60 APPLIED LIFE SCIENCES↗

Semi-inclusive single-jet production in DIS at next-to-leading order in the Color Glass Condensate

Within the Color Glass Condensate (CGC) effective field theory, we derive the next-to-leading order (NLO) cross-section for the single-jet semi-inclusive cross-section in deep inelastic scattering (DIS) at small x, for both longitudinally and transversely polarized virtual photons. We provide analytic expressions, valid at finite N c and suitable for numerical evaluation, for both the cross-section differential in rapidity and transverse momentum and the cross-section differential in rapidity only. Our NLO formulae demonstrate that the very forward rapidity regime is plagued by large double logarithmic corrections coming from phase space constraints on soft gluons close to the kinematic threshold for jet production. A joint resummation of small-x and threshold logarithms at single logarithmic accuracy is proposed to remedy the instability of the cross-section in this regime. By integrating over the single-jet phase space, we recover known results for the NLO DIS structure functions at small x, previously obtained using the optical theorem.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Gluon double-spin asymmetry in the longitudinally polarized p + p collisions

We derive the first-ever small-x expression for the inclusive gluon production cross section in the central rapidity region of the longitudinally polarized proton-proton collisions. The cross section depends on the polarizations of both protons, therefore comprising the numerator of the longitudinal double-spin asymmetry ALL for the produced gluons. The cross section is calculated in the shock wave formalism and is expressed in terms of the polarized dipole scattering amplitudes on the projectile and target protons. We show that the small-x evolution corrections are included into our cross section expression if one evolves these polarized dipole amplitudes using the double-logarithmic helicity evolution derived in [1–4]. Our calculation is performed for the gluon sector only, with the quark contribution left for future work. When that work is complete, the resulting formula will be applicable to longitudinally polarized proton-proton and proton-nucleus collisions, as well as to polarized semi-inclusive deep inelastic scattering (SIDIS) on a proton or a nucleus. Our results should allow one to extend the small-x helicity phenomenology analysis of [5] to the jet/hadron production data reported for the longitudinally polarized proton-proton collisions at RHIC and to polarized SIDIS measurements at central rapidities to be performed at the EIC.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Resolving domain positions of cellobiose dehydrogenase by small angle X–ray scattering

The interdomain electron transfer (IET) between the catalytic flavodehydrogenase domain and the electron-transferring cytochrome domain of cellobiose dehydrogenase (CDH) plays an essential role in biocatalysis, biosensors and biofuel cells, as well as in its natural function as an auxiliary enzyme of lytic polysaccharide monooxygenase. We investigated the mobility of the cytochrome and dehydrogenase domains of CDH, which is hypothesised to limit IET in solution by small angle X-ray scattering (SAXS). CDH from Myriococcum thermophilum (syn. Crassicarpon hotsonii, syn. Thermothelomyces myriococcoides) was probed by SAXS to study the CDH mobility at different pH and in the presence of divalent cations. By comparison of the experimental SAXS data, using pair-distance distribution functions and Kratky plots, we show an increase in CDH mobility at higher pH, indicating alterations of domain mobility. To further visualise CDH movement in solution, we performed SAXS-based multistate modelling. Glycan structures present on CDH partially masked the resulting SAXS shapes, we diminished these effects by deglycosylation and studied the effect of glycoforms by modelling. The modelling shows that with increasing pH, the cytochrome domain adopts a more flexible state with significant separation from the dehydrogenase domain. On the contrary, the presence of calcium ions decreases the mobility of the cytochrome domain. Experimental SAXS data, multistate modelling and previously reported kinetic data show how pH and divalent ions impact the closed state necessary for the IET governed by the movement of the CDH cytochrome domain.

59 BASIC BIOLOGICAL SCIENCES↗

Gluon distributions and their applications to Ioffe-time distributions

We investigate unpolarized and polarized gluon distributions and their applications to the Ioffe-time distributions, which are related to lattice QCD calculations of parton distribution functions. Guided by the counting rules based on the perturbative QCD at large momentum fraction x and the color coherence of gluon couplings at small x, we parametrize gluon distributions in the helicity basis. By fitting the unpolarized gluon distribution, the inferred polarized gluon distribution from our parametrization agrees with the one from global analysis. A simultaneous fit to both unpolarized and polarized gluon distributions is also performed to explore the model uncertainty. The agreement with the global analysis supports the (1 - x) power suppression of the helicity-antialigned distribution relative to the helicity-aligned distribution. The corresponding Ioffe-time distributions and their asymptotic expansions are calculated from the gluon distributions. Our results of the Ioffe-time distributions can provide guidance to the extrapolation of lattice QCD data to the region lacking precise gluonic matrix elements. Therefore, they can help regulate the ill-posed inverse problem associated with extracting the gluon distributions from discrete data from first-principle calculations, which are available in a limited range of the nucleon momentum and the spatial separation between the gluonic currents. Given various limitations in obtaining lattice QCD data at large Ioffe time, phenomenological approaches can provide important complementary information to extract the gluon distributions in the entire momentum fraction region, especially at small x. The possibility of investigating higher-twist effects and other systematic uncertainties in the contemporary first-principle calculations of parton distributions from phenomenologically well-determined Ioffe-time distributions in the large Ioffe-time region is also discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Novel cross section ratios as possible signals of saturation in ultraperipheral collisions

We propose new cross section ratios in ultraperipheral A + A and p + A collisions (UPCs) as a potential experimental signal of saturation physics. We consider the ratio R 1 of elastic vector meson photoproduction cross section to the inclusive hadron or jet photoproduction cross section. The ratio can be measured in the γ + A and γ + p collisions taking place in the UPCs. We label the ratios R 1 ( A ) and R 1 ( p ) , respectively. Constructing the double ratio R UPC ( A ) = R 1 ( A ) / R 1 ( p ) , and performing a small- x calculation both in the quasiclassical approximation and by including small- x evolution, we observe that R UPC ( A ) exhibits a markedly different dependence on the nuclear atomic number inside and outside the saturation region. This result indicates that R UPC ( A ) and R 1 ( A ) measurements in UPCs may help in the experimental searches for the evidence of saturation physics. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Quantifications of growth rate and particle size of magnesium silicate hydrate cement using small‐angle X‐ray scattering

The focus of recent research on cement binders has shifted to alternatives such as magnesium silicate hydrate (M-S-H) to mitigate the environmental impact of conventional concrete production. However, a detailed understanding of the morphology and growth rate of M-S-H, which informs its applicability as a cementing agent, is lacking. These properties are important as they influence cement hydration and consequently the development of macroscopic properties. Here, in this study, the particle size distribution and growth rate of M-S-H synthesized by mixing aqueous stock solutions were analyzed using synchrotron-based small-angle X-ray scattering. The reaction solutions contained dissolved magnesium and silicon with concentrations ranging from 2 to 500 mM, corresponding to saturation indices with respect to M-S-H endmembers, M 0.75 -S-H and M 1.50 -S-H, between 5.8 and 10.3. The precipitation rates of M-S-H align with affinity-based kinetic models and can be described by the following equations: For M 0.75 -S-H: 𝑟 M 0.75 −S−H =10 −9.54±0.70 ⁢(Ω$^{0.59±0.08}_{M_{0.75}⁢\textrm{SH}}$−1), and for M 1.50 -S-H: 𝑟 M 1.50 −S−H =10 −7.56±0.37 ⁢(Ω$^{0.34±0.04}_{M_{1.50}⁢\textrm{SH}}$−1), where 𝑟 is the rate in mol/L/s, and Ω represents the saturation ratio with respect to M-S-H. Moreover, we observed that changing the [Mg]/[Si] ratio affects particle size, a trend that cannot be fully explained by changes in the saturation index alone. These insights are critical for improving the predictability and control of cementation in concrete that utilizes M-S-H-based binders.

M-S-H↗

Robotic sample changers for macromolecular X-ray crystallography and biological small-angle X-ray scattering at the National Synchrotron Light Source II

In this work, we present two robotic sample changers integrated into the experimental stations for the macromolecular crystallography (MX) beamlines AMX and FMX, and the biological small-angle scattering (bioSAXS) beamline LiX. They enable fully automated unattended data collection and remote access to the beamlines. The system designs incorporate high-throughput, versatility, high-capacity, resource sharing and robustness. All systems are centered around a six-axis industrial robotic arm coupled with a force torque sensor and in-house end effectors (grippers). They have the same software architecture and the facility standard EPICS-based BEAST alarm system. The MX system is compatible with SPINE bases and Unipucks. It comprises a liquid nitrogen dewar holding 384 samples (24 Unipucks) and a stay-cold gripper, and utilizes machine vision software to track the sample during operations and to calculate the final mount position on the goniometer. The bioSAXS system has an in-house engineered sample storage unit that can hold up to 360 samples (20 sample holders) which keeps samples at a user-set temperature (277 K to 300 K). The MX systems were deployed in early 2017 and the bioSAXS system in early 2019.

36 MATERIALS SCIENCE↗

Impact of QCD energy evolution on observables in heavy-ion collisions

Here, we study how the inclusion of energy dependence as dictated by quantum chromodynamic (QCD) small-x evolution equations affects key observables in ultra-relativistic heavy-ion collisions. Specifically, we incorporate JIMWLK evolution into the IP-Glasma framework, which serves as the initial condition for a simulation pipeline that includes viscous relativistic hydrodynamics and a hadronic afterburner. This approach enables a consistent modeling of highly energetic nuclei across varying Bjorken-x values, which are relevant for different collision energies and rapidity regions. In comparison to the standard IP-Glasma setup without small-x evolution, we observe pronounced changes in particle multiplicities and spectral distributions, especially in smaller systems and at the highest available energies. We further explore effects on anisotropic flow observables and correlations between mean transverse momentum and elliptic flow. Our findings underscore the critical role of nonlinear QCD evolution in accurately modeling the early stages of heavy-ion collisions, as well as its implications for extracting transport properties of the quark-gluon plasma.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Material Design Strategy for Halide Solid Electrolytes Li 3 MX 6 (X = Cl, Br, and I) for All-Solid-State High-Voltage Li-Ion Batteries

Although several solid electrolyte (SE) candidates have been explored, achieving the necessary combination of performance, stability, and processability has been challenging. Recently, several lithium ternary halides have attracted increasing attention for SEs because of their favorable combination of high ionic conductivity and wide electrochemical window. This study aims to provide a material design strategy for lithium halides Li 3 MX 6 (X = Cl, Br, and I) for high-voltage all-solid-state Li-ion batteries, achieved by the systematic investigation of crystal structures, phase and electrochemical stabilities, electronic and mechanical properties, and ionic conductivities. Calculation results reveal that the electronegativity difference between M and X affects structural properties and stabilities. Weak Coulomb interactions in Li 3 MX 6 result in the preference of the monoclinic phase, and the oxidation potential and chemical stability against the cathode materials of Li 3 MX 6 increase for relatively small X. Chlorides exhibit the highest oxidation potential (~4.3 V) among Li 3 MX 6 , suggesting that chlorides are appropriate SEs for high-voltage cathodes. The band gap and elastic moduli increase for relatively small X, suggesting the relatively low electronic conductivity and elastic deformability of chlorides. Chlorides with transition metals typically exhibit trigonal phases, a wider electrochemical stability window, a larger band gap, and higher elastic moduli compared to other types of halides. Additionally, chloride Li 3 MCl 6 is expected to have relatively high ionic conductivities with the aliovalent substitution of M 3+ to Zr 4+ and the anion mixing of Cl with Br. The findings of this study will provide fundamental guidelines for the development of lithium halide SEs for high-voltage all-solid-state Li-ion batteries.

25 ENERGY STORAGE↗

Probing gluon saturation with forward di-hadron correlations in proton-nucleus collisions

We present a detailed numerical investigation of semi-inclusive forward di-hadron production in proton–nucleus collisions employing the Color Glass Condensate effective theory. We focus on the regime where di-hadrons are produced nearly back-to-back in the transverse plane, thereby justifying a transverse-momentum-dependent factorization approach in terms of small-x gluon distributions. Our computation integrates several key elements: i) non-linear rapidity evolution via the Balitsky–Kovchegov equation with running coupling, ii) both perturbative and non-perturbative Sudakov resummation, and iii) a phenomenologically constrained model for the initial conditions for small-x gluon distributions. We compare this phenomenological framework to experimental data from the STAR Collaboration on azimuthal correlations in forward di-pion production in both proton–proton and proton–gold collisions. We analyze the systematic theoretical uncertainties associated with the saturation scales of nuclei at the initial scale for rapidity evolution and with those associated with the hadronization process. Finally, we make predictions for the kinematics anticipated to be covered by the ALICE Forward Calorimeter (FoCal) upgrade at the Large Hadron Collider.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

2025 EIC-France Workshop: Physics Highlights and Perspectives

This document presents a synthesis of the theory contributions and discussions from the 2nd EIC-France Workshop, held at IJCLab (Orsay) on 1-3 December 2025. The workshop brought together members of the French hadron-physics community to review recent theoretical developments relevant to the future Electron-Ion Collider (EIC) and to coordinate national efforts in preparation for its early physics program. The report first summarizes the collider's initial running conditions and luminosity performance, as outlined in the EIC Early Science Matrix. It then provides concise overviews of the theoretical presentations on inclusive, semi-inclusive, exclusive, heavy-flavor, and small-x physics. Based on these discussions, two measurements emerged as especially well suited for early EIC operation and strongly aligned with areas of established French expertise: inclusive diffraction and inclusive quarkonium production. These channels offer clean signatures, robust theoretical interpretability, and direct sensitivity to fundamental QCD phenomena such as gluon saturation, heavy-quark dynamics, and the small-x structure of hadrons and nuclei. In addition, the workshop identified longer-term physics opportunities that will benefit from the full capabilities of the EIC after its ramp-up phase. These include accessing the three-dimensional structure of the pion through the Sullivan process and a broader program of exclusive three-body final states, both of which represent high-impact avenues for exploring hadronic structure and non-perturbative QCD. Together, the elements summarized in this report provide a coherent overview of the strategic priorities and scientific ambitions shaping the French community's contribution to the EIC physics program.

FOS: Physical sciences↗

Spatial imaging of polarized deuterons at the Electron-Ion Collider

We study diffractive vector meson production at small-x in the collision of electrons and polarized deuterons e + d $\uparrow$ . We consider the polarization dependence of the nuclear wave function of the deuteron, which results in an azimuthal angular dependence of the produced vector meson when the deuteron is transversely polarized. The Fourier coefficients extracted from the azimuthal angular dependence of the vector meson differential cross-section exhibit notable differences between longitudinally and transversely polarized deuterons. The angular dependence of the extracted effective deuteron radius provides direct insight into the structure of the polarized deuteron wave function. Furthermore, we observe slightly increased gluon saturation effects when the deuteron is longitudinally polarized compared to the transversely polarized case. The small-x observables studied in this work will be accessible at the future Electron-Ion Collider.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Mining for Gluon Saturation at Colliders

Quantum chromodynamics (QCD) is the theory of strong interactions of quarks and gluons collectively called partons, the basic constituents of all nuclear matter. Its non-abelian character manifests in nature in the form of two remarkable properties: color confinement and asymptotic freedom. At high energies, perturbation theory can result in the growth and dominance of very gluon densities at small-x. If left uncontrolled, this growth can result in gluons eternally growing violating a number of mathematical bounds. The resolution to this problem lies by balancing gluon emissions by recombinating gluons at high energies: phenomena of gluon saturation. High energy nuclear and particle physics experiments have spent the past decades quantifying the structure of protons and nuclei in terms of their fundamental constituents confirming predicted extraordinary behavior of matter at extreme density and pressure conditions. In the process they have also measured seemingly unexpected phenomena. We will give a state of the art review of the underlying theoretical and experimental tools and measurements pertinent to gluon saturation physics. We will argue for the need of high energy electron-proton/ion colliders such as the proposed EIC (USA) and LHeC (Europe) to consolidate our knowledge of QCD knowledge in the small x kinematic domains.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Impact of LHC vector boson production in heavy ion collisions on strange PDFs

Abstract The extraction of the strange quark parton distribution function (PDF) poses a long-standing puzzle. Measurements from neutrino-nucleus deep inelastic scattering (DIS) experiments suggest the strange quark is suppressed compared to the light sea quarks, while recent studies of $$W^\pm /Z$$ W ± / Z boson production at the LHC imply a larger strange component at small x values. As the parton flavor determination in the proton depends on nuclear corrections, e.g. from heavy-target DIS, LHC heavy ion measurements can provide a distinct perspective to help clarify this situation. In this investigation we extend the nCTEQ15 nPDFs to study the impact of the LHC proton-lead $$W^\pm /Z$$ W ± / Z production data on both the flavor differentiation and nuclear corrections. This complementary data set provides new insights on both the LHC $$W^\pm /Z$$ W ± / Z proton analyses and the neutrino-nucleus DIS data. We identify these new nPDFs as nCTEQ15WZ . Our calculations are performed using a new implementation of the nCTEQ code ( nCTEQ++ ) based on C++ which enables us to easily interface to external programs such as HOPPET, APPLgrid and MCFM. Our results indicate that, as suggested by the proton data, the small x nuclear strange sea appears larger than previously expected, even when the normalization of the $$W^{\pm }/Z$$ W ± / Z data is accommodated in the fit. Extending the nCTEQ15 analysis to include LHC $$W^\pm /Z$$ W ± / Z data represents an important step as we advance toward the next generation of nPDFs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Millisecond Phase Transition Kinetics of Lyotropic Liquid Crystalline Nanoparticles Observed by Time‐Resolved Small Angle X‐ray Solution Scattering

This study investigates the dynamic behavior of lyotropic liquid crystal nanoparticles (LCNPs), which are widely recognized for their applications in drug delivery. By employing nanosecond near‐infrared laser pulse‐induced temperature jump (T‐jump) and time‐resolved X‐ray solution scattering, the structural dynamics of phase transitions in phytantriol‐based cubosomes and hexosomes are revealed. Both cubosome and hexosome LCNPs undergo phase transitions into noncrystalline phases at high temperatures. Their phase transition kinetics, occurring within milliseconds (ms) and involving one intermediate structure, are captured. Additionally, the reverse self‐assembly processes of LCNPs were observed, occurring on the timescale of a few hundred ms. To our knowledge, this is the first observation of LCNP T‐jump induced phase transitions on the ms timescale and their reverse self‐assembly. These findings provide valuable insights into the LCNP phase transition processes, with potential implications for drug delivery applications.

Chemistry↗