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The maximum likelihood estimation is a general estimation procedure. It is often compared to estimation procedures like the ordinary least squares regression or generalized method of moments, to name a few. We discuss some basics about the maximum likelihood estimation, its advantages and disadvantages, and provide an example application to a gamma distribution function.
The experimental study of the angle-resolved hemispherical light scattering by V 4 O 7 film within a broad temperature range across metal–insulator transition reveals complex structural reorganization of the film deposited on the c-cut sapphire crystal. The bidirectional scattering distribution function and the surface autocorrelation function were obtained from scattering data to visualize statistics of the spatially resolved contributions of optical inhomogeneities in normal and lateral directions to the surface. The measurements reveal an anisotropic surface roughness distribution due to the twinned domain structure, with significant anisotropy changes across the phase transition. The V 4 O 7 film deposited on sapphire leads to a polydomain structure, minimizing elastic strain energy with distinct multiscale distributions of surface domains. Near T c , the material shows the lowest roughness but the highest lateral disorder of the surface.
Here, we compute the suppression of ϒ(1𝑆), ϒ(2𝑆), and ϒ(3𝑆) states in 𝑝-Pb collisions relative to 𝑝𝑝 collisions, including nuclear parton distribution function (nPDF) effects, coherent energy loss, momentum broadening, and final-state interactions in the quark-gluon plasma. We employ the EPPS21 nPDFs and calculate the uncertainty resulting from variation over the associated error sets. To compute coherent energy loss and momentum broadening, we follow the approach of Arleo, Peigne, and collaborators. The 3+1D viscous hydrodynamical background evolution of the quark-gluon plasma is generated by anisotropic hydrodynamics. The in-medium suppression of bottomonium in the quark-gluon plasma is computed using a next-to-leading-order open quantum system framework formulated within potential nonrelativistic quantum chromodynamics. We find that inclusion of all these effects provides a reasonable description of experimental data from the ALICE, ATLAS, CMS, and LHCb Collaborations for the suppression of ϒ(1𝑆), ϒ(2𝑆), and ϒ(3𝑆) as a function of both transverse momentum and rapidity.
The maximum likelihood estimation is a general estimation procedure. It is often compared to estimation procedures like the ordinary least squares regression or generalized method of moments, to name a few. We discuss some basics about the maximum likelihood estimation, its advantages and disadvantages, and provide an example application to a gamma distribution function.
We analyze the quasiparton distributions of the lightest 𝜂′ meson in massive two-dimensional quantum electrodynamics (QED2) by exact diagonalization. The Hamiltonian and boost operators are mapped onto spin qubits in a spatial lattice with open boundary conditions. The lowest excited state in the exact diagonalization is shown to interpolate continuously between an anomalous 𝜂′ state at strong coupling, and a nonanomalous heavy meson at weak coupling, with a cusp at the critical point. The boosted 𝜂′ state follows relativistic kinematics but with large deviations in the luminal limit. The spatial quasiparton distribution function and amplitude for the 𝜂′ state are computed numerically for increasing rapidity both at strong and weak coupling, and compared to the exact light front results. The numerical results from the boosted form of the spatial parton distributions, compare fairly with the inverse Fourier transformation of the luminal parton distributions, derived in the lowest Fock space approximation. Our analysis points out some of the limitations facing the current lattice program for the parton distributions.
This paper presents the primary charged-particle multiplicity distributions in proton–lead collisions at a centre-of-mass energy per nucleon–nucleon collision of $\sqrt{s_{NN}}$ = 5.02 TeV. The distributions are reported for non-single diffractive collisions in different pseudorapidity ranges. The measurements are performed using the combined information from the Silicon Pixel Detector and the Forward Multiplicity Detector of ALICE. The multiplicity distributions are parametrised with a double negative binomial distribution function which provides satisfactory descriptions of the distributions for all the studied pseudorapidity intervals. The data are compared to models and analyzed quantitatively, evaluating the first four moments (mean, standard deviation, skewness, and kurtosis). The shape evolution of the measured multiplicity distributions is studied in terms of KNO variables and it is found that none of the considered models reproduces the measurements. This paper also reports on the average charged-particle multiplicity, normalised by the average number of participating nucleon pairs, as a function of the collision energy. The multiplicity results are then compared to measurements made in proton–proton and nucleus–nucleus collisions across a wide range of collision energies.
We report the first global extraction of generalized parton distributions, GUMP 1.0, by combining deeply virtual Compton scattering and 𝜌-meson production data from Jefferson Lab and the Hadron-Electron Ring Accelerator with global fits of parton distribution functions, charge form factors, and lattice quantum chromodynamics simulations. Using a conformal moment space parametrization, we achieve a unified description across low- and high-𝑥 regions at next to leading order accuracy in perturbative corrections. The results provide state-of-the-art generalized parton distributions consistent with almost all known facts, enabling three-dimensional nucleon imaging in impact parameter space and, at the same time, establishing a benchmark for future theoretical and experimental studies of the nucleon structure.
In situ high-pressure ultrasonic velocity measurements of CaAl 2 O 4 glass reveal abrupt irreversible discontinuities in the elastic wave velocities at ~8–10 GPa. Total structure factor and pair distribution functions measured by synchrotron x-ray diffraction show a rapid change in the intermediate range structure attributed to a rearrangement of calcium ions over this narrow pressure region. Atomistic models obtained from molecular dynamics simulations reveal that this intermediate range structure is explained by a transition of Ca–O void radius distribution from a bimodal distribution with peaks at ~2.1 and ~2.4 Å to a single distribution centered at ~2.1 Å. Further, these abrupt structural changes involving the rapid increase in elastic wave velocity are markedly different to the continuous transformations observed in conventional network-forming glasses, such as SiO 2 .
This handbook provides a comprehensive review of transverse-momentum-dependent parton distribution functions and fragmentation functions, commonly referred to as transverse momentum distributions (TMDs). TMDs describe the distribution of partons inside the proton and other hadrons with respect to both their longitudinal and transverse momenta. They provide unique insight into the internal momentum and spin structure of hadrons, and are a key ingredient in the description of many collider physics cross sections. Understanding TMDs requires a combination of theoretical techniques from quantum field theory, nonperturbative calculations using lattice QCD, and phenomenological analysis of experimental data. The handbook covers a wide range of topics, from theoretical foundations to experimental analyses, as well as recent developments and future directions. It is intended to provide an essential reference for researchers and graduate students interested in understanding the structure of hadrons and the dynamics of partons in high energy collisions.
While Li-ion batteries (LIBs) are a leading energy storage technology, their energy densities are limited by the low capacity of conventional intercalation cathodes, driving interest in high energy-density Li–S batteries that make use of conversion chemistry. Achieving high capacity, reversibility, and cycle stability, and controlling volume changes in conversion batteries during the charge–discharge process, however, remains challenging. Here, in this study, we present a porous, amorphous, sulfide-based Mn x Mo 3 S 13 chalcogel, which concurrently offers high capacity and cycle stability. The solution-processable room temperature synthesized Mn x Mo 3 S 13 (x = 0.25) chalcogel exhibits a local structure that resembles the Mo 3 S 13 cluster with Mn 2+ distributed across the Mo 3 S 13 matrix, as determined by synchrotron X-ray pair distribution function (PDF) and extended X-ray absorption fine structure (EXAFS). Ab initio molecular dynamics (AIMD) simulations reveal that Mn 2+ incorporation shortens the polysulfide chain in the gel matrix compared to the Mo 3 S 13 chalcogel, while forming a coordination environment with disulfide groups, analogous to the experimental findings. A Li/Mn 0.25 Mo 3 S 13 half-cell delivers 897 mAh g –1 capacity during the first discharge and retains 571 mAh g –1 capacity after 100 cycles at a C/3 rate. Distribution of relaxation time (DRT) unveils a stable solid–electrolyte interphase (SEI) formation upon cycling that enables charge–discharge reversibility. Here, the enhanced capacity retention and cycle stability compared to those of the Li/Mo 3 S 13 cell are attributed to the reduced dissolution of active mass into the electrolyte, facilitated by the formation of shorter polysulfide chains within the Mn 0.25 Mo 3 S 13 structure and the strong affinity of Lewis-acidic Mn 2+ for polysulfide anions generated during the charge–discharge process of the Li/Mn 0.25 Mo 3 S 13 cell. Thus, this work illustrates a design principle of material for high-capacity and cycle-stable Li-metal sulfide batteries.
We compute the inclusive 𝐷 0 production cross section in ultraperipheral Pb-Pb collisions at the LHC as a function of the 𝐷 0 transverse momentum and rapidity. These calculations are carried out within the new generalized photon-nucleus FONLL (G𝛾A−FONLL) framework, which can predict photonuclear cross sections for charm and beauty hadrons in electron-proton, electron-nucleus, and ultraperipheral heavy-ion collisions. The framework relies on fixed-order next-to-leading logarithm (FONLL) to model heavy-quark production in photonuclear collisions and employs a photon-flux reweighting procedure to describe the production cross sections in ultraperipheral heavy-ion collisions. The G𝛾A calculations are first validated against the photoproduction cross sections of 𝐷* in electron-proton collisions at HERA. The predictions for the 𝐷 0 production cross section in ultraperipheral Pb-Pb collisions at the LHC are then presented and compared to the first experimental results obtained by CMS at $\sqrt{s_{NN}}$ = 5.36 TeV. The predictions are benchmarked against different choices of nuclear parton distribution functions, fragmentation functions, and renormalization and factorization scales.
Measurements of exclusive J/ψ, ψ(2s), and electron-positron (e + e - ) pair photoproduction in Au+Au ultraperipheral collisions are reported by the STAR experiment at $\sqrt{s_{NN}}$ = 200GeV. Here, we report several first measurements at the BNL Relativistic Heavy Ion Collider, which are (i) J/ψ photoproduction with large momentum transfer up to 2.2(GeV/c) 2 , (ii) coherent J/ψ photoproduction associated with neutron emissions from nuclear breakup, (iii) the rapidity dependence of incoherent J/ψ photoproduction, (iv) the ψ(2s) photoproduction cross section at midrapidity, and (v) e + e - pair photoproduction up to high invariant mass of 6GeV/c 2 . For measurement (ii), the coherent J/ψ total cross section of γ + Au → J/ψ + Au as a function of the center-of-mass energy W γN has been obtained without photon energy ambiguities. The data are quantitatively compared with the Monte Carlo models STARlight, Sartre, BeAGLE, and theoretical calculations of gluon saturation with color glass condensate, nuclear shadowing with leading twist approximation, quantum electrodynamics, and the next-to-leading-order perturbative QCD. At the photon-nucleon center-of-mass energy of 25.0 GeV, the coherent and incoherent J/ψ cross sections of Au nuclei are found to be 71% ± 10% and 36% ± 7%, respectively, of that of free protons. These data provide an important experimental constraint for nuclear parton distribution functions and a unique opportunity to advance the understanding of the nuclear modification effect at the top RHIC energy.
Bicarbonate (HCO 3 - ) and sodium (Na + )-containing solutions contain droplets of a separate, bicarbonate-rich liquid condensed phase (LCP) that have higher concentrations of HCO 3 - relative to the bulk solution in which they reside. The existence and composition of the LCP droplets has been investigated by nanoparticle tracking analysis, nuclear magnetic resonance spectroscopy, refractive index measurements and X-ray pair distribution function analysis. The bicarbonate-rich LCP species is a previously unaccounted-for, ionic phenomenon which occurs even in solutions with solely monovalent cations. Its existence requires re-evaluation of models used to describe and model aqueous solution physicochemistry, especially those used to describe and model carbonate mineral formation.
Mn 3 Si 2 Te 6 is a ferrimagnetic topological nodal-line semiconductor that exhibits unconventional colossal magnetoresistance behavior, with short-range spin fluctuations being potentially intimately linked to the emergent properties. Here we determine the short-range magnetic order and anisotropy through total neutron scattering and polarized neutron powder diffraction measurements on polycrystalline Mn 3 Si 2 Te 6 . Strong in-plane anisotropy is quantified on the Mn ions through extraction of the local site susceptibility tensor. Here, the real-space local spin structure is determined through the application of magnetic pair distribution function analysis covering a wide temperature range. Short-range order over a locally frustrated trimer of three nearest neighbors is found to exist well above the long-range ferrimagnetic transition.
Iron (Fe) oxy-hydroxide minerals such as ferrihydrite (Fh) are ubiquitous in Earth-surface environments and important in biogeochemical element cycling. Recent research has suggested that their formation is preceded by the precipitation of ultrasmall (~1 nm) Keggin-like Fe oxy-hydroxide clusters. However, relatively little is understood about the structure of the precursor clusters and the impacts of pH and time on their growth and transformation to more stable phases. Here, we used a new method that involves mixed flow reactors (MFR) to synthesize these Fe oxy-hydroxide precursor clusters at pH 1.0, 1.5, 2.5, and 4.5. In situ and ex situ synchrotron scattering measurements and laboratory small-angle X-ray scattering (SAXS) were used to study the structure and size of Fe oxy-hydroxide clusters and their transformation products, respectively. Results show that with increasing pH, the particle size and structural order of samples increase, forming solids that resemble 2-line Fh at pH 4.5. The experimental data were compared with X-ray pair distribution functions (PDF) calculated for a range of Fe(III) oxyhydroxide clusters, including Fe 13 Keggin isomers computed previously using density functional theory (DFT), which yielded at best only partial agreement at short range (<5 Å). Aging of the clusters synthesized at pH 1.5 and 2.5 results in growth and transformation via Ostwald ripening to mixtures of goethite (Gt) and lepidocrocite (Lp). This process was inhibited by immediately reacting the early-formed clusters with phosphate (PO 4 3– ), suggesting that oxyanion surface complexes can stabilize the initial clusters by preventing growth and crystallization to more stable phases.
We revisit the two-dimensional Fourier transform of generalized parton distributions (GPDs) at nonzero skewness. At 𝜂 = 0 it reduces to the standard impact-parameter density, while at 𝜂 ≠ 0 it is an off-forward amplitude that we interpret as a genuine parton–nucleon correlation. Its overall strength (the transverse-plane integral of the density) is fixed by the GPD at the kinematic point 𝑡 =−𝑐 𝜂 =−4𝜂 2 𝑚$^{2}_{𝑁}$/(1 − 𝜂 2 ) and decreases monotonically with the rapidity gap Δ𝑦 = ln[(1+𝜂)/(1−𝜂)] = 2 artanh(𝜂). This rapidity dependence implies rapidity-modified Ji identities that connect helicity, orbital, and total angular momenta of the correlation in closed form. To quantify these effects, we construct leading-twist quark and gluon GPDs in a string-based conformal framework: conformal moments are parametrized by linear open- and closed-string Regge trajectories with slopes constrained by parton distribution functions (PDFs), hadron/glueball spectroscopy, and form-factor data, and GPDs are reconstructed over the full (𝑥,𝜂,𝑡) domain by Mellin-Barnes inversion with next-to-leading order evolution. We find qualitative agreement (and fair quantitative agreement within quoted uncertainties) for several moments and selected nonsinglet 𝑥-space channels at 𝜇 = 2 GeV when compared with lattice QCD, while we also identify channels with visible tension and discuss likely sources (PDF priors and 𝑡-slope systematics).
Partially ionized plasma physics has attracted increased attention recently due to numerous technological applications made possible by the increased sophistication of computer modelling, the depth of the theoretical analysis, and the technological applications to a vast field of manufacturing for computer components. Partially ionized plasma is characterized by a significant presence of neutral particles in contrast to the fully ionized plasma. The theoretical analysis is based upon solutions of the kinetic Boltzmann equation, yielding the non-Maxwellian electron energy distribution function (EEDF), thereby emphasizing the difference with a fully ionized plasma. The impact of the effect on discharges in inert and molecular gases is described in detail, yielding the complex nonlinear phenomena resulting in plasma selforganization. A few examples of such phenomena are given, including the non-monotonic EEDFs in the discharge afterglow in a mixture of argon with the molecular gas NF3; the explosive generation of cold electron populations in capacitive discharges, hysteresis of EEDF in inductively coupled plasmas. Recently, highly advanced computer codes were developed in order to address the outstanding challenges in plasma technology. These developments are briefly described in general terms.
We propose a new method to calculate parton distribution functions (PDFs) from lattice correlations of boosted quarks and gluons in the Coulomb gauge. Compared to the widely used gauge-invariant Wilson-line operators, these correlations greatly simplify the renormalization thanks to the absence of linear power divergence. Additionally, they enable access to larger off-axis momenta under preserved 3D rotational symmetry, as well as enhanced long-range precision that facilitates the Fourier transform. We verify the factorization formula that relates this new observable to the quark PDF at one-loop order in perturbation theory. Moreover, through a lattice calculation of the pion valence quark PDF, we demonstrate the aforementioned advantage and features of the Coulomb gauge correlation and show that it yields consistent results with the gauge-invariant method. This opens the door to a more efficient way to calculate parton physics on the lattice.