arXiv subjects

Christopher Leon

Publications and source records attributed to Christopher Leon.

9 recordsLinked to original sources

arXiv2025

Pion Valence Structure at Intermediate x in the Residual Field Approach

We calculate the valence parton distribution function~(PDF) of pion, within the theoretical approach based on spectral function representation of valence quarks in the pion. In this approach we assume that the soft partonic structure of pion is defined by the valence $q\bar q$ cluster, consisting of current quarks, embedded in the residual field of the pion. The valence PDF is calculated using phenomenological Light-Front wave functions for the $q\bar q$ cluster and the residual field. Our result indicates that the peak position of the x weighted valence PDF~(xPDF) depends on parameters characterizing the virtuality of the cluster and the mass of the residual system. Magnitudes of these parameters are obtained by fitting to the height and the peak position of empirical pion xPDF evaluated at starting $Q_0$. They indicate that unlike the nucleon case, very little residual mass is needed to describe existing pion PDFs at intermediate x. They also indicate that the $q\bar q$-cluster is highly virtual and on average the interacting quark carries almost all of the momentum of the $q\bar q$ cluster. This picture is consistent with the dominance of the Feynman mechanism leaving little room for the hard component in the PDF, and practically describing $\sim (1-x)$ behavior observed recently at $x\to 1$ limit. Our non-trivial observation is that the height and the peak position of xPDF define the analytic behavior of valence PDF at $x\to 1$ limit.

hep-ph↗

arXiv2025

Using Convolutional Neural Networks to Accelerate 3D Coherent Synchrotron Radiation Computations

Calculating the effects of Coherent Synchrotron Radiation (CSR) is one of the most computationally expensive tasks in accelerator physics. Here, we use convolutional neural networks (CNN's), along with a latent conditional diffusion (LCD) model, trained on physics-based simulations to speed up calculations. Specifically, we produce the 3D CSR wakefields generated by electron bunches in circular orbit in the steady-state condition. Two datasets are used for training and testing the models: wakefields generated by three-dimensional Gaussian electron distributions and wakefields from a sum of up to 25 three-dimensional Gaussian distributions. The CNN's are able to accurately produce the 3D wakefields $\sim 250-1000$ times faster than the numerical calculations, while the LCD has a gain of a factor of $\sim 34$. We also test the extrapolation and out-of-distribution generalization ability of the models. They generalize well on distributions with larger spreads than what they were trained on, but struggle with smaller spreads.

physics.acc-ph↗

arXiv2024

QP Based Constrained Optimization for Reliable PINN Training

Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for integrating physics-based constraints and data to address forward and inverse problems in machine learning. Despite their potential, the implementation of PINNs are hampered by several challenges, including issues related to convergence, stability, and the design of neural networks and loss functions. In this paper, we introduce a novel training scheme that addresses these challenges by framing the training process as a constrained optimization problem. Utilizing a quadratic program (QP)-based gradient descent law, our approach simplifies the design of loss functions and guarantees convergences to optimal neural network parameters. This methodology enables dynamic balancing, over the course of training, between data-based loss and a partial differential equation (PDE) residual loss, ensuring an acceptable level of accuracy while prioritizing the minimization of PDE-based loss. We demonstrate the formulation of the constrained PINNs approach with noisy data, in the context of solving Laplace's equation in a capacitor with complex geometry. This work not only advances the capabilities of PINNs but also provides a framework for their training.

math.OC↗

arXiv2022

Possible Universal Limit for Valence Parton Distributions

We report the observation of the existence of a possible universal limit for valence parton distributions that should exist once partonic degrees of freedom are relevant for high energy scattering from strongly interacting bound systems like a nucleon, meson or a few nucleon system at very short distances. Our observation is based on the notion that the Bjorken x weighted valence parton distribution function has a peak, $x_p$, that characterizes the average momentum fraction carried out by the valence quarks in the system. Within the residual mean-field model of the valence quark distribution we found that $x_p$ has an upper limit: $x_p \leq {1\over 2(n_V-1)}$, where $n_V$ is the number of valence quarks which can be considered in the cluster embedded in the strongly interacting environment of the bound system. The existence of such a limit imposes a new constraint on choosing the starting resolution scale $Q_0$ for PDFs. Our prediction for the nucleon is that $x_p\mid_{Q\to Q_0}\le{1\over 4}$, which is in agreement with all the available valence PDFs that employ the standard approach for selecting starting $Q_0$. We also demonstrate how the existence of this limit can be used to check the onset of quark-clusters in short range nucleon correlations in nuclei.

hep-ph↗

arXiv2020

Residual Mean Field Model of Valence Quarks in the Nucleon

We develop a non-perturbative model for valence parton distribution functions (PDFs) based on the mean field interactions of valence quarks in the nucleonic interior. The main motivation for the model is to obtain a mean field description of the valence quarks as a baseline to study the short range quark-quark interactions that generate the high $x$ tail of PDFs. The model is based on the separation of the valence three-quark cluster and residual system in the nucleon. Then the nucleon structure function is calculated within the effective light-front diagrammatic approach introducing nonperturbative light-front valence quark and residual wave functions. Within the model a new relation is obtained between the position, $x_p$, of the peak of $xq_V(x)$ distribution of the valence quark and the effective mass of the residual system, $m_R$, in the form: $x_{p} \approx {1\over 4} (1-{m_R\over m_N})$ at starting $Q^2$. This relation explains the difference in the peak positions for d- and u- quarks through the expected difference of residual masses for valence d- and u- quark distributions. The parameters of the model are fixed by fitting the calculated valence quark distributions to the phenomenological PDFs. This allowed us to estimate the overall mean field contribution in baryonic and momentum sum rules for valence d- and u- quarks. Finally, the evaluated parameters of the non-perturbative wave functions of valence 3q-cluster and residual system can be used in calculation of other quantities such as nucleon form factors, generalized partonic and transverse momentum distributions.

hep-ph↗

arXiv2020

The Constituent Counting Rule and Omega Photoproduction

The constituent counting ruling (CCR) has been found to hold for numerous hard, exclusive processes. It predicts the differential cross section at high energies and fixed $\cos \theta_{c.m.}$ should follow $\frac{d \sigma}{dt} \sim \frac{1}{s^{n-2}}$, where $n$ is the minimal number of constituents involved in the reaction. Here we provide an in-depth analysis of the reaction $\gamma p \rightarrow \omega p$ at $\theta_{c.m.}\sim 90^\circ$ using CLAS data with an energy range of $s = 5 - 8$ GeV$^2$, where the CCR has been shown to work in other reactions. We argue for a stringent method to select data to test the CCR and utilize a Taylor-series expansion to take advantage of data from nearby angle bins in our analysis. Na\"{i}vely, this reaction would have $n=9$ (or $n=10$ if the photon is in a $q\bar{q}$ state) and we would expect a scaling of $\sim s^{-7}$ ($s^{-8}$). Instead, a scaling of $s^{-(9.08 \pm 0.11)}$ was observed. Explanations for this apparent failure of the na\"{i}ve CCR assumptions are examined.

hep-ph↗

arXiv2020

A Novel Feature of Valence Quark Distributions in Hadrons

Examining the evolution of the maximum of valence quark distribution weighted by Bjorken x, $h(x,t)\equiv xq_V(x,t)$, we observe that $h(x,t)$ at the peak should become a one parameter function; $h(x_p,t)=\Phi(x_p(t))$, where $x_p$ is the position of the peak and $t= \log{Q^2}$. This observation is used to derive a new model independent relation which connects the partial derivative of the valence parton distribution functions (PDFs) in $x_p$ to the QCD evolution equation through the $x_p$-derivative of the logarithm of the function $\Phi(x_p(t))$. A numerical analysis of this relation using empirical PDFs results in a observation of the exponential form of the $\Phi(x_p(t)) = h(x_p,t) = Ce^{D x_p(t)}$ for leading to next-to-next leading order approximations of PDFs for the all $Q^2$ range covering four orders in magnitude. The exponent, $D$, of the observed "height-position" correlation function converges with the increase of the order of approximation. This result holds for all PDF sets considered. A similar relation is observed also for pion valence quark distribution, indicating that the obtained relation may be universal for any non-singlet partonic distribution. The observed "height - position" correlation is used also to indicate that no finite number exchanges can describe the analytic behavior of the valence quark distribution at the position of the peak at fixed $Q^2$.

hep-ph↗

arXiv2020

Mean Field Quarks on the Light Front

We present a new approach for the calculation of the valence quark distributions in the nucleon based on the scenario in which the spectrum of the valence quarks at x>0.05 is generated through three main mechanisms: interaction of valence quarks with the mean field generated by the residual nucleon system, two and three quark short range interactions through gluon exchanges. In the current report we present the first phase of the project in which we develop a non-perturbative model for valence quark interaction in the mean field of the nucleonic interior to describe their distribution in the moderate x region (0.05 < x < 0.4). The short range quark-quark interaction effects in our approach generate the high x tail of valence quark distributions. The presented non-perturbative model is based on the picture in which three relativistic valence quarks occupy the nucleon core at distances of $\le 0.5$ Fm while interacting in the mean field generated by the residual nucleon system. The calculations are based on the assumption of the a factorization of the internal interaction of short-range three valence quarks with the long-range interaction of these quarks with the residual system. The theoretical approach is based on effective light-front diagrammatic approach which allows us to introduce the valence quark and residual system wave functions in a consistent way The parameters of these wave functions are fixed by the position of the peak of the xf_q(x) distribution of valence quarks at Q_0 corresponding to the charm-quark mass. With few parameters we achieved a very reasonable description of the up and down valence quark distributions in the moderate x region (x < 0.4), where one expects the mean field dynamics to dominate. The model, however, systematically underestimates the high $x$ region where enhanced contributions from partonic short-range correlations are expected.

hep-ph↗

arXiv2018

Photon super-bunching from a generic tunnel junction

Generating correlated photon pairs at the nanoscale is a prerequisite to creating highly integrated optoelectronic circuits that perform quantum computing tasks based on heralded single-photons. Here we demonstrate fulfilling this requirement with a generic tip-surface metal junction. When the junction is luminescing under DC bias, inelastic tunneling events of single electrons produce a photon stream in the visible spectrum whose super-bunching index is 17 when measured with a 53 picosecond instrumental resolution limit. These photon bunches contain true photon pairs of plasmonic origin, distinct from accidental photon coincidences. The effect is electrically rather than optically driven - completely absent are pulsed lasers, down-conversions, and four-wave mixing schemes. This discovery has immediate and profound implications for quantum optics and cryptography, notwithstanding its fundamental importance to basic science and its ushering in of heralded photon experiments on the nanometer scale.

cond-mat.mes-hall↗