Dirac Form Research Articles

Malfunction diagnosis based on residence time distribution of radiotracer signals in industrial processes using machine learning techniques

Diagnosing problems in industrial processes has always been a complex challenge, frequently obstructed by the complex structure of these systems. The present study presents a robust methodology integrating nuclear radiotracer data with machine learning approaches to improve diagnosis. Radiotracers are used to measure residence time distribution (RTD) as a crucial diagnostic technology. Experiments utilize a Flow Rig System (FRS) to simulate industrial conditions, where a Tc-99 m radiotracer (1 mCi) is injected in Dirac form and monitored with sodium iodide scintillation detectors integrated with an ALTAIX data acquisition system (DAS). Machine learning algorithms are subsequently employed to categorize four RTD signals: normal RTD, small exchange RTD, recirculation RTD, and parallel flow RTD. Identifying these signal kinds is essential for precise system diagnostics. We utilize deep learning via Convolutional Neural Networks (CNNs) for feature extraction and an Artificial Neural Network (ANN) for classification. Additionally, the Binary Tree Growth Algorithm (BTGA) is employed to refine feature selection, improving model efficacy and decreasing processing demands. The deep learning model attains complete identification accuracy while implementing the HP classifier, which enhances processing time and precision. We simulate RTD signals for two scenarios − Perfect Mixers in Series (PMS) and Perfect Mixers with Exchange (PMSEX). We corroborate our results by comparing them with RTD simulation tools, demonstrating significant correlation and concordance. Our Results highlight the efficacy of combining advanced machine learning approaches with new real-time data modelling to enhance diagnostics efficiency and reliability in industrial operations. This method offers a revolutionary technique to improve process optimization and defect identification.

Nonlocal chiral contributions to generalized parton distributions of the proton at nonzero skewness

We compute the one-loop contributions to spin-averaged generalized parton distributions (GPDs) in the proton from pseudoscalar mesons with intermediate octet and decuplet baryon states at nonzero skewness. Our framework is based on nonlocal covariant chiral effective theory, with ultraviolet divergences regularized by introducing a relativistic regulator derived consistently from the nonlocal Lagrangian. Using the splitting functions calculated from the nonlocal Lagrangian, we find the nonzero skewness GPDs from meson loops by convoluting with the phenomenological pion GPD and the generalized distribution amplitude, and verify that these satisfy the correct polynomiality properties. We also compute the lowest two moments of GPDs to quantify the meson loop effects on the Dirac, Pauli, and gravitational form factors of the proton. Published by the American Physical Society 2024

Inference With Aggregate Data in Probabilistic Graphical Models: An Optimal Transport Approach

We consider inference (filtering) problems over probabilistic graphical models with aggregate data generated by a large population of individuals. We propose a new efficient belief propagation type algorithm over tree graphs with polynomial computational complexity as well as a global convergence guarantee. This is in contrast to previous methods that either exhibit prohibitive complexity as the population grows or do not guarantee convergence. Our method is based on optimal transport, or more specifically, multimarginal optimal transport theory. In particular, we consider an inference problem with aggregate observations, that can be seen as a structured multimarginal optimal transport problem where the cost function decomposes according to the underlying graph. Consequently, the celebrated Sinkhorn/iterative scaling algorithm for multi-marginal optimal transport can be leveraged together with the standard belief propagation algorithm to establish an efficient inference scheme which we call Sinkhorn belief propagation (SBP). We further specialize the SBP algorithm to cases associated with hidden Markov models due to their significance in control and estimation. We demonstrate the performance of our algorithm on applications such as inferring population flow from aggregate observations. We also show that in the special case where the aggregate observations are in Dirac form, our algorithm naturally reduces to the standard belief propagation algorithm.

Onset of Color Transparency in Holographic Light-Front QCD

The color transparency (CT) of a hadron, propagating with reduced absorption in a nucleus, is a fundamental property of QCD (quantum chromodynamics) reflecting its internal structure and effective size when it is produced at high transverse momentum, Q. CT has been confirmed in many experiments, such as semi-exclusive hard electroproduction, eA→e′πX, for mesons produced at Q2>3GeV2. However, a recent JLab (Jefferson Laboratory) measurement for a proton electroproduced in carbon eC→e′pX, where X stands for the inclusive sum of all produced final states, fails to observe CT at Q2 up to 14.2 GeV2. In this paper, the onset of CT is determined by comparing the Q2-dependence of the hadronic cross sections for the initial formation of a small color-singlet configuration using the generalized parton distributions from holographic light-front QCD. A critical dependence on the hadron’s twist, τ, the number of hadron constituents, is found for the onset of CT, with no significant effects from the nuclear medium. This effect can explain the absence of proton CT in the present kinematic range of the JLab experiment. The proton is predicted to have a “two-stage” color transparency with the onset of CT differing for the spin-conserving (twist-3, τ=3) Dirac form factor with a higher onset in Q2 for the spin-flip Pauli (twist-4) form factor. In contrast, the neutron is predicted to have a “one-stage” color transparency with the onset at higher Q2 because of the dominance of its Pauli form factor. The model also predicts a strong dependence at low energies on the flavor of the quark current coupling to the hadron.

Transverse charge density and the radius of the proton

A puzzling discrepancy exists between the values of the proton charge radius obtained using different experimental techniques: elastic electron-proton scattering and spectroscopy of electronic and muonic hydrogen. The proton radius is defined through the slope of the electric form factor, $G_E(Q^2)$, at zero four-momentum transfer, which is inaccessible in scattering experiments. We propose a novel method for extracting the proton radius from scattering data over a broad $Q^2$ range rather than attempting to directly determine the slope of $G_E$ at $Q^2 = 0$. This method relates the radius of the proton to its transverse charge density, which is the two-dimensional Fourier transform of the Dirac form factor, $F_1(Q^2)$. We apply our method to reanalyze the extensive data obtained by the A1 Collaboration [J. C. Bernauer et al., Phys. Rev. Lett. 105, 242001 (2010)] and extract a radius value, $r_E = 0.889(5)_{\text{stat}}(5)_{\text{syst}}(4)_{\text{model}}~\text{fm}$, that is consistent with the original result. We also provide new parametrizations for the Dirac and Pauli form factors and the transverse charge and magnetization densities of the proton. Our reanalysis shows that the proton radius discrepancy cannot be explained by issues with fitting and extrapolating the A1 data to $Q^2 = 0$.

Nucleon electroweak form factors using spin-improved holographic light-front wavefunctions

We construct spin-improved holographic light front wavefunctions for the nucleons (viewed as quark-diquark systems) and use them to successfully predict their electromagnetic Sachs form factors, their electromagnetic charge radii, as well as the axial form factor, charge and radius of the proton. The confinement scale is the universal mass scale of light-front holography, previously extracted from spectroscopic data for light hadrons. With the Dirac and Pauli form factors normalized using the quark counting rules and the measured anomalous magnetic moments respectively, the masses of the quark and diquark are the only remaining adjustable parameters. We fix them using the data set for the proton's Dirac-to-Pauli form factor ratio, and then predict all other data without any further adjustments of parameters. Agreement with data at low momentum-transfer is excellent. Our findings support the idea that light (pseudoscalar and vector) mesons and the nucleons share a nonperturbative universal holographic light-front wavefunction which is modified differently by their spin structures.

Charge radii of the nucleon from its flavor dependent Dirac form factors

We have determined the proton and the neutron charge radii from a global analysis of the proton and the neutron elastic form factors, after first performing a flavor decomposition of these form factors under charge symmetry in the light cone frame formulation. We then extracted the transverse mean-square radii of the flavor dependent quark distributions. In turn, these are related in a model-independent way to the proton and neutron charge radii but allow us to take into account motion effects of the recoiling nucleon for data at finite but high momentum transfer. In the proton case we find $\langle r_p \rangle = 0.852 \pm0.002_{\rm (stat.)} \pm0.009_{\rm (syst.)}~({\rm fm})$, consistent with the proton charge radius obtained from muonic hydrogen spectroscopy \cite{pohl:2010,antog2013}. The current method improves on the precision of the $\langle r_p \rangle$ extraction based on the form factor measurements. Furthermore, we find no discrepancy in the $\langle r_p \rangle$ determination among the different electron scattering measurements, all of which, utilizing the current method of extraction, result in a value that is consistent with the smallest $\langle r_p \rangle$ extraction from the electron scattering measurements \cite{Xiong:2019umf}. Concerning the neutron case, past results relied solely on the neutron-electron scattering length measurements, which suffer from an underestimation of underlying systematic uncertainties inherent to the extraction technique. Utilizing the present method we have performed the first extraction of the neutron charge radius based on nucleon form factor data, and we find $\langle r_n^2 \rangle = -0.122 \pm0.004_{\rm (stat.)} \pm0.010_{\rm (syst.)}~({\rm fm}^2)$.

The Parton Distribution Functions and Calculation of Dirac Neutron Form Factor Considering the EMC and Shadowing Effects

Due to the absence of the free neutron target, the form factors or the structure function of the neutron directly cannot be obtained from the elastic scattering data. Therefore, in this paper, we obtained the neutron structure function using the deep inelastic structure function of the proton and by applying the EMC and the shadowing effects on the structure function of the deuteron. Then, using the quantum chromo dynamics theorem and re-analysis of data from the SLAC experiments E49, E61, E87, and E89 in electron–proton deep inelastic scattering at Q2 = 1–20 GeV2, we have extracted the up and down quark distribution functions, $${{u}_{{v}}}$$ (x), $${{d}_{{v}}}$$ (x), and also, using an appropriate model for the general parton distribution function, we have plotted the Dirac form factor of the neutron. At the end, the curves obtained in this work were compared with the curves obtained in other models.

Nucleon elastic form factors at accessible large spacelike momenta

A Poincar\'e-covariant quark+diquark Faddeev equation is used to compute nucleon elastic form factors on $0\leq Q^2\leq 18 \,m_N^2$ ($m_N$ is the nucleon mass) and elucidate their role as probes of emergent hadronic mass in the Standard Model. The calculations expose features of the form factors that can be tested in new generation experiments at existing facilities, e.g. a zero in $G_E^p/G_M^p$; a maximum in $G_E^n/G_M^n$; and a zero in the proton's $d$-quark Dirac form factor, $F_1^d$. Additionally, examination of the associated light-front-transverse number and anomalous magnetisation densities reveals, inter alia: a marked excess of valence $u$-quarks in the neighbourhood of the proton's centre of transverse momentum; and that the valence $d$-quark is markedly more active magnetically than either of the valence $u$-quarks. The calculations and analysis also reveal other aspects of nucleon structure that could be tested with a high-luminosity accelerator capable of delivering higher beam energies than are currently available.

Covariant model for the Dalitz decay of the N(1535) resonance

We develop a covariant model for the $\gamma^\ast N \to N(1535)$ transition in the timelike kinematical region, the region where the square momentum transfer $q^2$ is positive. Our starting point is the covariant spectator quark model constrained by data in the spacelike kinematical region ($Q^2 = -q^2 >0$). The model is used to estimate the contributions of valence quarks to the transition form factors, and one obtains a fair description of the Dirac form factor at intermediate and large $Q^2$. For the Pauli form factor there is evidence that beyond the quark-core contributions there are also significant contributions of meson cloud effects. Combining the quark-core model with an effective description of the meson cloud effects, we derive a parametrization of the spacelike data that can be extended covariantly to the timelike region. This extension enabled us to estimate the Dalitz decay widths of the $N(1535)$ resonance, among other observables. Our calculations can help in the interpretation of the present experiments at HADES ($pp$ collisions and others).

Basis light-front quantization for a chiral nucleon-pion Lagrangian

We present the first application of the Basis Light-Front Quantization method to a simple chiral model of the nucleon-pion system as a relativistic bound state for the physical proton. The light-front mass-squared matrix of the nucleon-pion system is obtained within a truncated basis. The mass and the corresponding light-front wave function (LFWF) of the proton are computed by numerical diagonalization of the resulting mass-squared matrix. With the boost invariant LFWF, we calculate the probability density distribution of the pion's longitudinal momentum fraction and the Dirac form factor of the proton.

Extended Relativistic Invariance, Quantization of the Kinetic Momentum

The aim of this research is a better understanding of the quantization in physics. The true origin of the quantization is the existence of the quantized kinetic momentum of electrons, neutrinos, protons and neutrons with the value. It is a consequence of the extended relativistic invariance of the wave of fundamental particles with spin 1/2. This logical link is due to properties of the quantum waves of fermions, which are functions of space-time with value into the and End(Cl3) Lie groups. Space-time is a manifold forming the auto-adjoint part of . The Lagrangian densities are the real parts of the waves. The equivalence between the invariant form and the Dirac form of the wave equation takes the form of Lagrange's equations. The momentum-energy tensor linked by Noether's theorem to the invariance under space-time translations has components which are directly linked to the electromagnetic tensor. The invariance under of the kinetic momentum tensor gives eight vectors. One of these vectors has a time component with value . Resulting aspects of the standard model of quantum physics and of the relativistic theory of gravitation are discussed.

The 4-loop slope of the Dirac form factor

The 4-loop contribution to the slope of the Dirac form factor in QED has been evaluated with 1100 digits of precision. The value is $ {m^2}F_1^{(4)'}(0) = {\rm{0}}{\rm{.886545673946443145836821730610315359390424032660064745}} \cdots {\left( {{\alpha \over \pi }} \right)^4} $. We have also obtained a semi-analytical fit to the numerical value. The expression contains harmonic polylogiπ2iπ iπ arithms of argument $ {e^{{{i\pi } \over 3}}},{e^{{{2i\pi } \over 3}}},{e^{{{i\pi } \over 2}}} $, one-dimensional integrals of products of complete elliptic integrals and six finite parts of master integrals, evaluated up to 4800 digits. We show the correction to the energy levels of the hydrogen atom due to the slope.

Field theory of monochromatic optical beams: I. Classical fields

We study monochromatic, scalar solutions of the Helmholtz and paraxial wave equations (PWEs) from a field-theoretic point of view. We introduce appropriate time-independent Lagrangian densities for which the Euler–Lagrange equations reproduces either Helmholtz and PWEs with the z-coordinate, associated with the main direction of propagation of the fields, playing the same role of time in standard Lagrangian theory. For both Helmholtz and paraxial scalar fields, we calculate the canonical energy-momentum tensor and determine the continuity equations relating ‘energy’ and ‘momentum’ of the fields. Eventually, the reduction of the Helmholtz wave equation to a useful first-order Dirac form, is presented. This work sheds some light on the intriguing and not so acknowledged connections between angular spectrum representation of optical wavefields, cosmological models and physics of black holes.

High-precision calculation of the 4-loop QED contribution to the slope of the Dirac form factor

We have evaluated with 1100 digits of precision the contribution of all the 891 mass-independent 4-loop Feynman diagrams contributing to the slope of the Dirac form factor in QED. The total 4-loop contribution ism2F1(4)′(0)=0.886545673946443145836821730610315359390424032660064745…(απ)4. We have fit a semi-analytical expression to the numerical value. The expression contains harmonic polylogarithms of argument eiπ3, e2iπ3, eiπ2, one-dimensional integrals of products of complete elliptic integrals and six finite parts of master integrals, evaluated up to 4800 digits. We show the correction on the shift of the energy levels of the hydrogen atom due to the slope.

Compton scattering in the Endpoint Model

We use the Endpoint Model for exclusive hadronic processes to study experimentally observed scaling behaviour in Compton scattering of the proton. The parameters of the Endpoint Model are fixed using the data for the Dirac form factor F_1 (Q^2) and the ratio of Pauli and Dirac form factors F_2(Q^2)/F_1(Q^2) and then used to obtain numerical predictions for the differential scattering cross section. We study the Compton scattering at fixed theta _{CM} in the s sim |t| gg Lambda _{QCD} regime and at fixed s much larger than |t| regime. We observe that the calculations in the Endpoint Model give a good fit with experimental data in both regions.

Particle-hole mirror symmetries around the half-filled shell: Quantum numbers and algebraic structure of composite fermions

Composite fermions (CFs) of the fractional quantum Hall effect are described as spherical products of electron and vortex spinors, built from underlying L=1/2 ladder operators aligned so that the spinor angular momenta Le and Lv are maximal. We identify the CF's quantum numbers as the angular momentum L in (L_e L_v)L, its magnetic projection m_L, the electron number N, with L_v={N-1)/2, and magnetic \nu-spin, m_\nu=L_e-L_v. Translationally invariant FQHE states are formed by filling p subshells with their respective CFs, in order of ascending L for fixed L_e and L_v, beginning with the lowest allowed value, L=|m_\nu|. We show that this wave function has an exactly equivalent hierarchical form. FQHE states can be grouped into \nu-spin multiplets mirror symmetric around m_\nu=0, with N held constant. Electron particle-hole conjugation with respect to this vacuum is identified as the mirror symmetry relating FQHE states of the same N but distinct fillings \nu = p/(2p+1} and p/( 2p-1). Alternatively, mirror symmetric \nu-spin multiplets can be constructed in which the magnetic field strength is held fixed: the valence states are electron particle-vortex hole excitations. Particle-hole symmetry -- relating the N-particle FQHE state of filling \nu=p/(2p+1} to the $\bar{N}$-particle state of filling {p+1)/(2p+1} -- is shown to be equivalent to electron-vortex exchange. In this construction $\bar{N}$-N CFs of the higher density state occupy an extra zero-mode subshell. We link this structure, familiar from supersymmetric quantum mechanics, to the CF Pauli Hamiltonian, which we show is isospectral, quadratic in the \nu-spin raising and lowering operators, and four-fold degenerate. On linearization, it takes a Dirac form similar to that found in the integer quantum Hall effect (IQHE).

Nucleon Viewed as a Borromean Bound-State

We explain how the emergent phenomenon of dynamical chiral symmetry breaking ensures that Poincar\'e covariant analyses of the three valence-quark scattering problem in continuum quantum field theory yield a picture of the nucleon as a Borromean bound-state, in which binding arises primarily through the sum of two separate contributions. One involves aspects of the non-Abelian character of Quantum Chromodynamics that are expressed in the strong running coupling and generate tight, dynamical color-antitriplet quark-quark correlations in the scalar-isoscalar and pseudovector-isotriplet channels. This attraction is magnified by quark exchange associated with diquark breakup and reformation, which is required in order to ensure that each valence-quark participates in all diquark correlations to the complete extent allowed by its quantum numbers. Combining these effects, we arrive at a properly antisymmetrised Faddeev wave function for the nucleon and calculate, e.g. the flavor-separated versions of the Dirac and Pauli form factors and the proton's leading-twist parton distribution amplitude. We conclude that available data and planned experiments are capable of validating the proposed picture.

Photo- and electroproduction of Λ(1405) via γ(*)p→K+π+Σ−

In this work, we perform a \textit{toy-model} analysis for the unpolarized photo- and electroproduction of $\Lambda(1405)\equiv\Lambda^*$ via $\gamma^{(*)}p\to K^+\pi^+\Sigma^-$ by employing the effective Lagrangian approach at the tree level only. We consider that $\Lambda^*$ consists of the high-mass ($H$) and low-mass ($L$) poles as suggested by the chiral unitary model (ChUM). We determine all the model parameters including coupling constants and cutoff parameters for the phenomenological strong form factors by using the theoretical information from ChUM and available experimental data. The electromagnetic (EM) form factors for the two poles are parameterized appropriately being similar to that for the neutron by employing the ChUM estimates for the EM root-mean-squared (rms) radii for the two poles. We observe from the numerical calculations that, for the photoproduction of $\Lambda^*$, the interference between the two poles turns out to be destructive, resulting in the single-peak line at $M_{\pi^+\Sigma^-}\approx1405$ MeV in the invariant-mass distribution. On the contrary, there appear two peaks in the distribution for the electroproduction as observed in the CLAS/Jlab electroproduction data, due to the constructive interference, which is mainly caused by the Dirac form factors for the two poles. From this observation, we conclude that, in order to explain the photo- and electroproduction data simultaneously, i.e., \textit{single} and \textit{double} peaks, respectively, in the invariant-mass distribution, the interference patterns for the two poles should follow those suggested by ChUM. In turn, it is a strong theoretical and experimental supports for the two-pole structure scenario for $\Lambda^*$.

Unpolarized and polarized densities based on a light-front quark–diquark model

In this paper, we calculate the proton and neutron unpolarized and transversely polarized densities. We use the light-front wave function (LFWF), which at an initial scale is constrained by the soft-wall anti-de Sitter (AdS) QCD model, for calculating the Dirac and Pauli form factors which transverse densities are in terms of these form factors. Also, we use these form factors for calculating the flavor separated results for the proton and neutron electromagnetic form factors and calculate u and d quark unpolarized and transversely polarized densities. Finally, we compare our results with other previous parametrizations.