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Understanding the interactions between quark-antiquark pairs is essential for elucidating quark confinement within the framework of quantum chromodynamics (QCD). This study investigates the field distribution patterns that arise between these pairs by employing advanced machine learning techniques, namely multilayer perceptrons (MLP) and Kolmogorov-Arnold networks (KAN), to analyze data obtained from lattice QCD simulations. The models developed through this training are then applied to calculate the string tension and width associated with chromo flux tubes, and these results are rigorously compared to those derived from lattice QCD. Moreover, we introduce a preliminary analytical expression that characterizes the field distribution as a function of quark separation, utilizing the KAN methodology. Our comprehensive quantitative analysis underscores the potential of integrating machine learning approaches into conventional QCD research., Comment: 8 pages, 5 figures

Street Scene Semantic Understanding (denoted as TriSU) is a complex task for autonomous driving (AD). However, inference model trained from data in a particular geographical region faces poor generalization when applied in other regions due to inter-city data domain-shift. Hierarchical Federated Learning (HFL) offers a potential solution for improving TriSU model generalization by collaborative privacy-preserving training over distributed datasets from different cities. Unfortunately, it suffers from slow convergence because data from different cities are with disparate statistical properties. Going beyond existing HFL methods, we propose a Gaussian heterogeneous HFL algorithm (FedGau) to address inter-city data heterogeneity so that convergence can be accelerated. In the proposed FedGau algorithm, both single RGB image and RGB dataset are modelled as Gaussian distributions for aggregation weight design. This approach not only differentiates each RGB image by respective statistical distribution, but also exploits the statistics of dataset from each city in addition to the conventionally considered data volume. With the proposed approach, the convergence is accelerated by 35.5\%-40.6\% compared to existing state-of-the-art (SOTA) HFL methods. On the other hand, to reduce the involved communication resource, we further introduce a novel performance-aware adaptive resource scheduling (AdapRS) policy. Unlike the traditional static resource scheduling policy that exchanges a fixed number of models between two adjacent aggregations, AdapRS adjusts the number of model aggregation at different levels of HFL so that unnecessary communications are minimized. Extensive experiments demonstrate that AdapRS saves 29.65\% communication overhead compared to conventional static resource scheduling policy while maintaining almost the same performance., Comment: 16 pages

Various adverse weather conditions pose a significant challenge to autonomous driving (AD) street scene semantic understanding (segmentation). A common strategy is to minimize the disparity between images captured in clear and adverse weather conditions. However, this technique typically relies on utilizing clear image as a reference, which is challenging to obtain in practice. Furthermore, this method typically targets a single adverse condition, and thus perform poorly when confronting a mixture of multiple adverse weather conditions. To address these issues, we introduce a reference-free and Adverse weather-Immune scheme (called AdvImmu) that leverages the invariance of weather conditions over short periods (seconds). Specifically, AdvImmu includes three components: Locally Sequential Mechanism (LSM), Globally Shuffled Mechanism (GSM), and Unfolded Regularizers (URs). LSM leverages temporal correlations between adjacent frames to enhance model performance. GSM is proposed to shuffle LSM segments to prevent overfitting of temporal patterns. URs are the deep unfolding implementation of two proposed regularizers to penalize the model complexity to enhance across-weather generalization. In addition, to overcome the over-reliance on consecutive frame-wise annotations in the training of AdvImmu (typically unavailable in AD scenarios), we incorporate a foundation model named Segment Anything Model (SAM) to assist to annotate frames, and additionally propose a cluster algorithm (denoted as SBICAC) to surmount SAM's category-agnostic issue to generate pseudo-labels. Extensive experiments demonstrate that the proposed AdvImmu outperforms existing state-of-the-art methods by 88.56% in mean Intersection over Union (mIoU)., Comment: 16 Pages

Pareto set learning (PSL) is an emerging approach for acquiring the complete Pareto set of a multi-objective optimization problem. Existing methods primarily rely on the mapping of preference vectors in the objective space to Pareto optimal solutions in the decision space. However, the sampling of preference vectors theoretically requires prior knowledge of the Pareto front shape to ensure high performance of the PSL methods. Designing a sampling strategy of preference vectors is difficult since the Pareto front shape cannot be known in advance. To make Pareto set learning work effectively in any Pareto front shape, we propose a Pareto front shape-agnostic Pareto Set Learning (GPSL) that does not require the prior information about the Pareto front. The fundamental concept behind GPSL is to treat the learning of the Pareto set as a distribution transformation problem. Specifically, GPSL can transform an arbitrary distribution into the Pareto set distribution. We demonstrate that training a neural network by maximizing hypervolume enables the process of distribution transformation. Our proposed method can handle any shape of the Pareto front and learn the Pareto set without requiring prior knowledge. Experimental results show the high performance of our proposed method on diverse test problems compared with recent Pareto set learning algorithms., Comment: 7 pages

Investigation of decay and scattering processes of particles in a vortex state offers a novel and promising approach for probing particle structure. Our study reveals distinct properties of vortex neutron decay, which deviate from those of classical plane-wave neutron decay. We present the energy-angle distributions of the final-state electron and antineutrino in unpolarized vortex neutrons, as well as angle distributions integrated over their energies. Notably, we provide theoretical calculations of the decay behavior of neutrons with varying vortex cone angles and initial energies. We propose that identifying the vortex state of the initial neutron can be achieved by analyzing the angular and energy distributions of the final-state particles, introducing new degrees of freedom for studying weak interactions and neutron decay kinematics that have been previously overlooked in particle physics. This timely investigation takes advantage of recent advancements in vortex neutron preparation and analysis, opening up new avenues for exploring the fundamental properties of matter., Comment: 10 pages, 7 figures

In this study we demonstrate the application of the Maximum Entropy Method (MEM) to determine the valence quark distribution of exotic hadrons. Our investigation yields three key findings. Firstly, we observe a significant shift towards smaller Bjorken scale $x$ in the peak position of the valence quark distribution for hadrons with an increasing number of valence quarks, consistent with previous results by Kawamura and Kumano. Secondly, assuming that the $Z_c(3900)$ initially consists of four valence quarks, we employ MEM to determine its initial valence quark distribution, estimating a radius of $r_c=1.276$ fm at an extremely low resolution scale $Q^2$. Furthermore, we identify a notable discrepancy between our computed charge form factor $G_c(q)$ at leading order and the outcomes of hadron molecular state calculations. We propose that this form factor can be extracted from the QCD counting rule cross-section, which is grounded in Generalized Distribution Amplitudes (GDA) linked to the multi-quark states., Comment: 7 pages, 7 figures

Street Scene Semantic Understanding (denoted as TriSU) is a crucial but complex task for world-wide distributed autonomous driving (AD) vehicles (e.g., Tesla). Its inference model faces poor generalization issue due to inter-city domain-shift. Hierarchical Federated Learning (HFL) offers a potential solution for improving TriSU model generalization, but suffers from slow convergence rate because of vehicles' surrounding heterogeneity across cities. Going beyond existing HFL works that have deficient capabilities in complex tasks, we propose a rapid-converged heterogeneous HFL framework (FedRC) to address the inter-city data heterogeneity and accelerate HFL model convergence rate. In our proposed FedRC framework, both single RGB image and RGB dataset are modelled as Gaussian distributions in HFL aggregation weight design. This approach not only differentiates each RGB sample instead of typically equalizing them, but also considers both data volume and statistical properties rather than simply taking data quantity into consideration. Extensive experiments on the TriSU task using across-city datasets demonstrate that FedRC converges faster than the state-of-the-art benchmark by 38.7%, 37.5%, 35.5%, and 40.6% in terms of mIoU, mPrecision, mRecall, and mF1, respectively. Furthermore, qualitative evaluations in the CARLA simulation environment confirm that the proposed FedRC framework delivers top-tier performance., Comment: This work has been accepted by 2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2024)

The relationship between QCD and the string model offers a valuable perspective for exploring the interaction potential between quarks. In this study, we investigate the restoration of chiral symmetry in connection with the Unruh effect experienced by accelerating observers. Utilizing the Schwinger model, we analyze the critical point at which the string or chromoelectric flux tube between quark-antiquarks breaks with increasing separation between quarks. In this study, the critical distance for quark-antiquark chromoelectric flux tube or string breaking is determined to be $r_c=1.294\pm0.040$ fm. The acceleration and Unruh temperature corresponding to this critical point signify the transition of the system's chiral symmetry from a broken to a restored state. Our estimates for the critical acceleration ($a_c=1.14\times 10^{34}$ cm/s$^{2}$) and Unruh temperature ($T_c=0.038$ GeV) align with previous studies. This analysis illuminates the interplay between chiral symmetry restoration, the Unruh effect, and the breaking of the string or chromoelectric flux tube within the context of quark interactions., Comment: 8 pages, 2 tables, 4 figures, accepted for publication in Physics Letters B

Deep learning-based Autonomous Driving (AD) models often exhibit poor generalization due to data heterogeneity in an ever domain-shifting environment. While Federated Learning (FL) could improve the generalization of an AD model (known as FedAD system), conventional models often struggle with under-fitting as the amount of accumulated training data progressively increases. To address this issue, instead of conventional small models, employing Large Vision Models (LVMs) in FedAD is a viable option for better learning of representations from a vast volume of data. However, implementing LVMs in FedAD introduces three challenges: (I) the extremely high communication overheads associated with transmitting LVMs between participating vehicles and a central server; (II) lack of computing resource to deploy LVMs on each vehicle; (III) the performance drop due to LVM focusing on shared features but overlooking local vehicle characteristics. To overcome these challenges, we propose pFedLVM, a LVM-Driven, Latent Feature-Based Personalized Federated Learning framework. In this approach, the LVM is deployed only on central server, which effectively alleviates the computational burden on individual vehicles. Furthermore, the exchange between central server and vehicles are the learned features rather than the LVM parameters, which significantly reduces communication overhead. In addition, we utilize both shared features from all participating vehicles and individual characteristics from each vehicle to establish a personalized learning mechanism. This enables each vehicle's model to learn features from others while preserving its personalized characteristics, thereby outperforming globally shared models trained in general FL. Extensive experiments demonstrate that pFedLVM outperforms the existing state-of-the-art approaches., Comment: This paper was submitted to CVPR 2024 in Nov. 2023

Fairness in federated learning has emerged as a critical concern, aiming to develop an unbiased model for any special group (e.g., male or female) of sensitive features. However, there is a trade-off between model performance and fairness, i.e., improving model fairness will decrease model performance. Existing approaches have characterized such a trade-off by introducing hyperparameters to quantify client's preferences for model fairness and model performance. Nevertheless, these approaches are limited to scenarios where each client has only a single pre-defined preference, and fail to work in practical systems where each client generally have multiple preferences. The key challenge is to design a method that allows the model to adapt to diverse preferences of each client in real time. To this end, we propose a Preference-aware scheme in Fair Federated Learning paradigm (called PraFFL) to generate preference-wise model in real time. PraFFL can adaptively adjust the model based on each client's preferences to meet their needs. We theoretically prove that PraFFL can offer the optimal model tailored to an arbitrary preference of each client, and show its linear convergence. Experimental results show that our proposed PraFFL outperforms five fair federated learning algorithms in terms of the model's capability of adapting to clients' different preferences., Comment: 14 pages, 10 figures

We propose that the signal of dark photons can be found in the decay channel of $\eta$, and that a certain number of events of dark photon leptonic decay can be observed in the double-photon collision process of heavy-ion ultra-peripheral collisions (UPC). We estimate the total cross-section for producing dark photons in ultra-peripheral $PbPb$ collisions at existing and planned future hadron colliders, as well as the number of signal events. Our results support the search for dark photon signals in ultra-peripheral $PbPb$ collisions. We consider the recent signals of $\eta$ decays produced in LHC $pp$ collisions and estimate the number of dark photon events from the same number of $\eta$ decays from CMS. Based on CMS results, we estimate that there will be at least 1000 signal events of dark photons observed for the mass $m_{A^\prime}$ less than 500 MeV. In this study, we propose a method using $\eta$ meson decay to search for signs of dark photons at heavy-ion colliders, such as LHC and RHIC., Comment: 8 pages, 5 figures

Within the confining color flux tube picture, we assess the color electric field generated by quark-antiquark pairs within the framework of the Schwinger model and estimate its impact on the chiral condensate. We observe differences in the distribution of the color flux tube generated by quark-antiquark pairs at different separation distances, leading to discrepancies in the partial restoration of chiral symmetry. Furthermore, we suggest incorporating the color magnetic field in the calculation of chiral condensate, leading to quantum entanglement effects, and proceed to compute the entanglement entropy. We observe that the entanglement entropy increases with the distance of the color source (the separation distance between quark and anti-quark), and the magnitude of the color electric field and chiral condensate restoration after spatial integration also increases with the distance of the color source. Then, we try to provide a qualitative explanation for the existence of these phenomena., Comment: 8 pages, 3 figures and 1 table, published in Physics letter B

We present the gluon distribution functions of pion and kaon in small-$x$ and large-$x$ regions, and compare them with the results obtained from lattice QCD and continuum Schwinger function methods. Whether in the small-$x$ region or the large-$x$ region, our gluon distribution of pion is consistent with the results of lattice QCD and continuum Schwinger function method. In addition, the first four moments of gluon distributions of pion and kaon at different $Q^{2}$ scales are calculated. Furthermore, we present the mass decompositions of pion and kaon with the dynamical parton distribution functions calculated by the DGLAP equation with parton-parton recombination corrections. The mass structures of pion and kaon are totally different from that of the proton., Comment: 7 figures

The Abelian decomposition of QCD reveals two types of gluons: color-neutral ``neurons" and color-carrying ``chromons". This classification does not alter the overall properties of QCD, but the investigation of different types of gluon dynamics is necessary. By employing the Cho-Duan-Ge decomposition theorem, we have derived dynamic evolution equations for two types of gluons by using the time-ordered perturbation theory. We propose that the new equations are compatible with the DGLAP equations, requiring only the separate contributions of neurons and chromons to be summed. Surprisingly, with the evolution to high $Q^2$, the ratio of the number of chromons to neurons is approximately 3:1 in small-$x$ region regardless of the inputs at evolution starting point. The new gluon dynamic equations reevaluate the gluon distribution functions and allow for a elaborate inverstigation of the distinct contributions of gluons in high-energy collisions., Comment: 19 pages, 6 figures

This study delves into the contribution of the strange quark within the proton, which influences several fundamental proton properties. By establishing a robust relationship between the proton's quantum anomalous energy and the sigma term, we successfully extract the contribution of the strangeness sigma term in the proton, obtaining it from parameterized fits of the differential cross-section using exponential and dipole forms. The extracted sigma term values are estimated to be $455.62\pm64.60$ MeV (exponential fit) and $337.74\pm106.79$ MeV (dipole fit). Additionally, we present novel results for the proton trace anomalous energy, observing values of $0.13\pm0.02$ (exponential fit) and $0.15 \pm 0.03$ (dipole fit). Our analysis integrates the novel data from the $J/\psi-007$ and GlueX collaborations, to some extent providing an experimental phenomenological window into the non-zero strange quark content inside proton, with the statistical significances: $7.1\sigma$ (exponential fit) and $3.2\sigma$ (dipole fit), respectively. Furthermore, we discussed the possibility of scheme-independence in the extraction results and examine the uniformity of sigma terms obtained from the datasets provided by the two collaborations. Our analysis may reveals compatibility between the extracted results of the respective experiments., Comment: 8 pages, 3 figures, 4 tables, accepted by Physical Review D, some spelling mistakes are fixed

The Short-Range Correlations between nucleons in nuclei is regarded as a complex system. We investigate the relationship between the orbital entanglement entropy of SRCs $S_{ij}$ in nuclear structures and Tan contact $c_{ij}$, and find that the orbital entanglement entropies and Tan contacts corresponding to proton-proton SRC pairs and neutron-proton SRC pairs in nuclei demonstrate a scaling relation. More specifically, the proportionality of entanglement entropy between proton-proton pairs and neutron-proton pairs is directly related to the ratio of nuclear contacts within the atomic nucleus, demonstrating an approximate ratio of 2.0. Our research suggests that this scaling relationship should hold true for all symmetric nuclei, furthermore, we offer a possible explanation for this phenomenon., Comment: 8 pages, 5 figures, 1 table, accepted by PLB

While federated learning (FL) improves the generalization of end-to-end autonomous driving by model aggregation, the conventional single-hop FL (SFL) suffers from slow convergence rate due to long-range communications among vehicles and cloud server. Hierarchical federated learning (HFL) overcomes such drawbacks via introduction of mid-point edge servers. However, the orchestration between constrained communication resources and HFL performance becomes an urgent problem. This paper proposes an optimization-based Communication Resource Constrained Hierarchical Federated Learning (CRCHFL) framework to minimize the generalization error of the autonomous driving model using hybrid data and model aggregation. The effectiveness of the proposed CRCHFL is evaluated in the Car Learning to Act (CARLA) simulation platform. Results show that the proposed CRCHFL both accelerates the convergence rate and enhances the generalization of federated learning autonomous driving model. Moreover, under the same communication resource budget, it outperforms the HFL by 10.33% and the SFL by 12.44%.

The study of hadronic structure has been carried out for many years. Generalized parton distribution functions (GPDs) give broad information on the internal structure of hadrons. Combining GPDs and high-energy scattering experiments, we expect yielding three-dimensional physical quantities from experiments. Deeply Virtual Compton Scattering (DVCS) process is a powerful tool to study GPDs. It is one of the important experiments of Electron Ion Collider (EIC) and Electron ion collider at China (EicC) in the future. In the initial stage, the proposed EicC will have $3 \sim 5$ GeV polarized electrons on $12 \sim 25$ GeV polarized protons, with luminosity up to $1 \sim 2 \times 10^{33}$cm$^{-2}$s$^{-1}$. EIC will be constructed in coming years, which will cover the variable c.m. energies from 30 to 50 GeV, with the luminosity about $10^{33} \sim 10^{34}$cm$^{-2}$s$^{-1}$. In this work we present a detailed simulation of DVCS to study the feasibility of experiments at EicC and EIC. Referring the method used by HERMES Collaboration, and comparing the model calculations with pseudo data of asymmetries attributed to the DVCS, we obtained a model-dependent constraint on the total angular momentum of up and down quarks in the proton., Comment: 12 pages, 18 figures, 3 Tables

The structure of the proton remains a significant challenge within the field of Quantum Chromodynamics, with the origin of its spin and mass still lacking a satisfactory explanation. In this study, we utilize the gravitational form factor of the proton as the foundation for constructing the configurational entropy of the proton energy system. In our approach we choose the holographic QCD model for input thus obtaining a holographic version of the proton energy density. Employing this approach, we are able to determine key mechanical quantities such as the proton's mass radius and pressure distribution. Our analysis yields the root-mean-square mass radius of $\sqrt{\langle r_M^2\rangle}=0.720$ fm and scalar radius of $\sqrt{\langle r_S^2\rangle}=1.024$ fm for proton, which are found to be in excellent agreement with recent measurements from the Hall-C collaboration group at Jefferson Lab. Additionally, we examine the radial distribution of pressure and shear force within the proton. We provide a new mode for constraining holographic model parameters in the investigation of proton structures., Comment: 7 pages, 3 figures and 1 table. Accepted by Physics letter B

We calculate the leading twist pion unpolarized transverse momentum distribution $f_1(x,k_T^2)$ and the Boer-Mulders function $h_1^\perp(x,k_T^2)$, using leading Fock-state light front wave functions (LF-LFWFs) based on Dyson-Schwinger and Bethe-Salpeter equations. These DS-BSEs based LF-LFWFs provide dynamically generated s- and p-wave components, which are indispensable in producing chirally odd Boer-Mulders function that has one parton spin flipped. Employing a non-perturbative SU(3) gluon rescattering kernel to treat the gauge link of the Boer-Mulders function, we thus obtain both TMDs at hadronic scale and then evolve them to the scale of $\mu^2=4.0$ GeV$^2$. We finally calculate the generalized Boer-Mulders shift and find it to be in agreement with the lattice prediction., Comment: 20 pages, 5 figures

Low-energy scattering processes of vector meson and nucleon are an important window for studying non-perturbative QCD. The interaction of vector meson with nucleon, vector meson-nucleon scattering length $|\alpha_{VN}|$, is an important component of the study of hadronic interactions. Nowadays many scattering length values $|\alpha_{VN}|$ have been reported using the recent photoproduction experiment data or quasi data. In addition, the study of trace anomalous energy contribution to the proton mass is also a hot topic in non-perturbative QCD and hadron physics. However, it is difficult to measure proton trace anomalous energy experimentally, and the study of the trace anomaly of proton is still inconclusive. In this study, we established the relationship between the scattering length of the vector meson-proton $|\alpha_{Vp}|$ and the trace anomaly contribution of the proton mass $T_{A}$. With the scattering length values extracted by using the Vector Meson Dominance model, we obtained the trace anomaly contribution of the proton mass $T_{A}$ = (22.8$\%$ $\pm$ 1.2$\%$), which is of similar order of magnitude as the 23$\%$ given by Lattice QCD calculation. We conjecture that the trace anomaly contribution of nucleon is independent of the type of vector meson probe. We hope that high precision measurements of vector meson-nucleon scattering length could give us a better chance to explore the origin of the nucleon mass., Comment: 5 pages, 1 figure. arXiv admin note: text overlap with arXiv:2210.11276

In this study, we try to extract $\omega n$, $\omega p$ and $\phi$N scattering lengths from the differential cross-section data of near-threshold $\omega$ and $\phi$ photoproductions not only to the energy at threshold t$_{thr}$, but also in t to t = 0. The incoherent data of $\omega$ and $\phi$ photoproductions on deuterium target for scattering length extractions are provided by CBELSA/TAPS Collaboration and LEPS Collaboration respectively, where the deuteron is usually approximated as a weakly bound state of a quasi-free neutron plus a quasi-free proton. Under the Vector Meson Doninance model and the assumption of energy independence of the differential cross-section, we obtained the $|\alpha_{\omega n^{*}}|$ and $|\alpha_{\omega p^{*}}|$ of loosely bound neutron and proton in the deuteron to be 0.709 $\pm$ 0.078 fm and 0.621 $\pm$ 0.022 fm respectively at threshold t$_{thr}$ (1.258 $\pm$ 0.130 fm and 1.056 $\pm$ 0.032 fm respectively in t to t = 0) for the first time by fitting the near-threshold data of $\gamma$d $\rightarrow$ $\omega$n(p) and $\gamma$d $\rightarrow$ $\omega$p(n). For a comparison study, we also extracted the scattering length $|\alpha_{\omega p}|$ of the free proton from the $\omega$ photoproduction on the hydrogen target by CBELSA/TAPS Collaboration. With the near-threshold and incoherent $\phi$ photoproduction data of $\gamma$d $\rightarrow$ $\phi$pn by LEPS Collaboration, we obtained scattering length $|\alpha_{\phi N}|$ of the bound nucleon inside the deuteron to be 0.109 $\pm$ 0.008 fm at threshold t$_{thr}$ and 0.276 $\pm$ 0.010 fm in t to t = 0, respectively. The obtained $|\alpha_{\omega p}|$ and $|\alpha_{\phi N}|$ are basically in agreement with the experimental indications and the theoretical predictions within the current uncertainties., Comment: 7 pages, 6 figures

In this work, we discuss the production of a tensor glueball in the proton-proton and nuclei-nuclei ultraperipheral collisions (UPCs). The cross section is calculated in the equivalent photon approximation (EPA). The total UPCs cross section is related to the matrix elements of $\gamma \gamma\to \pi^0 G_2$ process, which can be described as in terms of neutral pion and tensor glueball $G_2$'s distribution amplitudes. The predictions for the rapidity distributions of UPCs cross sections and total cross sections are presented. The theoretical uncertainty of the whole calculation is considered. We consider the decay modes of the final-state tensor glueball and estimate the corresponding number of events. We estimate that there are about 10 tensor glueball $G_2\to\phi\phi$ signal events in $PbPb$ collisions at the LHC. We also argue that the lead-lead UPC experiments at future HE-LHC and FCC experiments will provide larger opportunities to measure tensor glueballs., Comment: 16 pages, 5 figures, 2 tables. Accepted by EPJC

The partons model reveals the dynamical structure of nucleons (protons and neutrons). Studies related to thermodynamic quantities of nucleons are interesting and topical questions. In this work, for the first time we apply Page's theory of the studies of black hole to investigate the entropy of proton system. Inspired by the quantum entanglement entropy in black hole information theories, we establish the proton entanglement with the similar way. Based our calculations, the proton entanglement entropy has the approximate form $S = \ln m -1/2$, where $m$ represents the partons density of proton (mainly gluon and sea quark contributions) at small Bjorken $x$. Our calculations using Page's theory are well in agreement with the recent DIS measurements from H1 collaboration., Comment: 6 pages, 2 figures, Accepted by PRD

Exclusive vector meson production is an excellent probe for describing the structure of proton. In this paper, based on dipole model, the differential cross sections, total cross sections and the ratios of the longitudinal to transverse cross sections of $J/\psi$ and $\rho^0$ productions are calculated with the analytical solution of Balitsky-Kovchegov (BK) equation. In addition, we also consider the influences of two meson wave function models on the results. Our predictions, which are little sensitive to meson wave functions, agree with the experimental data. The analytical solution of BK equation is reliable for description of exclusive vector meson production in a certain range of $Q^2$., Comment: 10 pages,8 figures,1 table. Add some references. The paper is to be published in Chinese Physics C

We calculate the valence quark distribution functions of the $\pi$ meson using the non-relativistic chiral constituent quark model. The $\pi$ wave function is obtained by solving the two-body Schr\"odinger equation within the framework of constituent quark model. We transform the $\pi$ wave function from the rest frame to the light cone or infinite momentum frame based on the Lorentz boost. The valence quark distributions at the initial evolution scale are obtained. The QCD evolution are given with the DGLAP equations with parton-parton recombination corrections. With tuning the valence up (down) quark mass to 70 MeV, the calculated valence up quark distributions at $Q^2=20$ GeV$^2$ are in good agreement with the E615 experimental data. The structure functions $\rm{F}_2^\pi(x,Q^2)$ of pion are also calculated which consist with the H1 experimental data. The proposed mechanisms here could be also used to study other hadrons., Comment: 9 pages, 6 figures

As a lot of studies have declared, the proton structure function $F_2$ explicitly satisfies a power-law mathematical formation. We describe the behavior of proton structure function $F_2$ at small-$x$ as well as large $Q^2$ using the analytical solution of the Balitsky-Kovchegov equation. We obtain the effective slope value $\lambda$ of the structure function with $Q^2$. Our results come from fitting the HERA experimental data at low $Q^2$ region and we also give the prediction for the effective slope of $F_2$ at the high $Q^2$ region., Comment: 15 pages,3 figures,3 tables

In this study, we try to extract the mass radii of the neutron and the proton from the differential cross section data of near-threshold $\omega$ and $\phi$ photoproductions on deuterium target, which is often approximated as a quasi-free neutron plus a quasi-free proton. The incoherent data of $\omega$ and $\phi$ photoproductions are provided by CBELSA/TAPS collaboration and LEPS collaboration respectively, where the deuteron is disintegrated in the experiments to measure the properties of individual nucleons. Under the VMD model and the assumption of dipole gravitational form factor, we determined the loosely bound neutron and proton mass radii to be $0.795\pm0.092\rm(stat.)\pm0.073\rm(syst.)$ fm and $0.744\pm0.029\rm(stat.)\pm0.042\rm(syst.)$ fm respectively from the near-threshold data of $\gamma d \rightarrow \omega n (p)$ and $\gamma d \rightarrow \omega p (n)$, for the first time. With the near-threshold and incoherent $\phi$ photoproduction data of $\gamma d \rightarrow \phi p n$, we determined the average mass radius of the bound nucleon (neutron or proton) inside the deuteron to be $0.755\pm0.039\rm(stat.)\pm0.039\rm(syst.)$ fm, for the first time. For a comparison study, we also extracted the mass radius of the free proton from the $\omega$ photoproduction on the hydrogen target by CBELSA/TAPS collaboration. Based on our analysis results under the assumptions of VMD model and a low energy QCD theorem, we find that the neutron mass radius is consistent with the proton mass radius within the current statistical uncertainties, and that the nuclear modification on the nucleon mass radius is small inside the deuteron., Comment: 10 pages, 7 figures

We analyze the exclusive $\phi$-meson photoproduction on both hydrogen and deuterium targets based on the published data of CLAS, SAPHIR and LEPS collaborations. A dipole-form scalar gravitational form factor is applied to describe the $|t|$-dependence of the differential cross section. Based on the average of all the near-threshold data from CLAS, SAPHIR and LEPS, we find that the proton and deuteron mass radii are $0.75 \pm 0.02$ fm and $1.95 \pm 0.19$ fm respectively. The coherent and near-threshold quarkonium photoproduction seems to be sensitive to the radius of the hadronic system. The vector-meson-dominance model together with a low-energy QCD theorem well describe the data of near-threshold $\phi$ photoproduction on the hadronic systems., Comment: 6 pages, 6 figures

We study the internal structure of the proton and propose a shell structure model of the proton. Based on the mass distribution and mass radius of proton we analyze the experiments at different energy scales and conclude that there should be shell structure inside proton, and the quark and gluon shells are energy-scale-dependent. We successfully explain the dip-like structure in the proton-proton elastic scattering cross section distribution from TOTEM Collaboration using the mass decomposition of proton and the proton shell structure at different energy scales., Comment: 16 pages, 6 figures, 1 table

In order to reveal the difference between the latest neutron star observation experiment GW170817 and the existing theory, we mainly consider the effect of the nucleon radius on the neutron star from the existing theory. We believe that the effect of nucleon radius in neutron star is not negligible, and the mass radius of nucleon should be used instead of the charge radius. The nucleon mass radius is set as $r_m = 0.55\pm0.09$ fm from the new measurements. It is considered as an input to the "Excluded Volume Effects" model in the equation of state of nuclear matter. We propose a novel neutron star mass-radius relation by using proton mass radius is consistent with the observation GW170817., Comment: 6 pages, 1 table, 2 figures

We apply a "color" tripole ansatz for describing the $D$-term of the proton. By fitting the experimental data of the vector meson J/$\psi$ and $\phi$ photoproductions near the thresholds, we firstly obtained the gluonic $D$-term of the proton. $D_g(0)$ is estimated to be $-2.16\pm0.42$ for J/$\psi$ and $-1.31\pm0.48$ for $\phi$, and the mechanical root mean square radius of proton is estimated to be $0.61\pm0.29$ fm for $\phi$ and $0.42\pm0.11$ fm for J/$\psi$., Comment: 8 pages, 5 figures, one table, add some references and few corrections

The trace anomalous energy contribution to the proton mass is a very important topic in non-perturbative QCD and hadron physics. In experiments, it is under the hot discussions on how to measure the trace anomalous energy.The QCD interpretation of proton trace anomaly is still not clear.To connect the theory with the experiment,we extract the trace anomaly by analyzing the near-threshold photo-production data of $\phi$ and J/$\psi$ vector mesons. Based on the vector-meson-dominance model and QCD Van der Waals representation, we find that the percentage of trace anomaly in the proton mass ranges from $16\%$ to $24\%$, which is of similar order of magnitude as the 23$\%$ given by Lattice QCD. We also provide the approximate magnitudes of the systematic uncertainties of the extracted results from the model assumptions as well as the data fitting procedures. We give relative statistical uncertainties of 17.2$\%$, 17.7$\%$, 3.6$\%$, and 8.2$\%$, total relative systematic uncertainties of 21.4$\%$, 54.2$\%$, 37.2$\%$, and 25.7$\%$, for the analyses of the GlueX, LEPS, CLAS, and SAPHIR data, respectively. We argue that the near-threshold $\Upsilon$ photo-production experiments are more beneficial for the measurement of trace anomaly in proton mass in the future., Comment: 8 pages, 5 figures, 8 table. This is the version accepted by EPJA

We present an analysis of the proton mass radius by studying the $t$-dependence of the differential cross sections of the vector meson photoproductions near the thresholds. At low energy, the photoproduction of a quarkonium off the proton is connected to the scalar gravitational form factor of the proton, which is sensitive to the proton mass distribution from the QCD trace anomaly. Under an assumption of the scalar form factor of dipole form, the proton mass radius is extracted via the near-threshold photoproduction data of J/$\psi$, $\phi$ and $\omega$ vector mesons. The average value of the proton mass radius is estimated to be $\sqrt{\left} = 0.67\pm0.03$ fm, with the dipole cutoff $m_{\rm s}=1.01\pm0.04$ GeV., Comment: 5 pages, 2 figures, minor modifications

Nonlinear QCD evolution equations are essential tools in understanding the saturation of partons at small Bjorken $x_{\rm B}$, as they are supposed to restore an upper bound of unitarity for the cross section of high energy scattering. In this paper, we present an analytical solution of Balitsky-Kovchegov (BK) equation using the homogeneous balance method. The obtained analytical solution is similar to the solution of a traveling wave. By matching the gluon distribution in the dilute region which is determined from the global analysis of experimental data (CT14 analysis), we get a definitive solution of the dipole-proton forward scattering amplitude in the momentum space. Based on the acquired scattering amplitude and the behavior of geometric scaling, we present also a new estimated saturation scale $Q_s^2(x)$., Comment: 6 pages, 5 figures

In this paper, we use the homogeneous balance(HB) method is used to construct function transformation to solve the nonlinear development equation||Fisher-Kolomogror-Pertrovskii-Piskmov equation (FKPP equation), then the exact solution of FKPP equation is obtained, and the solutionis converted into the form of isolated wave solution. Finally, we have shown the solution of FKPPequation in some picture forms, and the rationality of the solution in this paper can be verified byusing the pictures., Comment: 6 pages,2 figures

The photoproduction of bottomonium-like states $Z_{b}(10610)$ and $Z_{b}(10650)$ via $\gamma p$ scattering is studied within an effectiv Lagrangian approach and the vector-meson-dominance model. The Regge model is employed to calculate the photoproduction of $Z_{b}$ states via $t$-channel with $\pi$ exchange.The numerical results show that the values of the total cross-sections of $Z_{b}(10610)$ and $Z_{b}(10650)$ can reach 0.09 nb and 0.02 nb, respectively, near the center of mass energy of 22 GeV. The experimental measurements and studies on the photoproduction of $Z_{b}$ states near energy region around $W\simeq 22$ GeV is suggested. Moreover, with the help of eSTARlight and STARlight programs, one obtains the cross-sections and event numbers of $Z_{b}(10610)$ production in electron-ion collision (EIC) and Ultraperipheral collisions (UPCs). The results show that a considerable number of events from $Z_{b}(10610)$ can be produced on the relevant experiments of EICs and UPCs. Also, one calculates the rates and kinematic distributions for $\gamma p\rightarrow Z_{b}n$ in $ep$ and $pA$ collisions via EICs and UPCs, and the relevant results will provide an important reference for the RHIC, LHC, EIC-US, LHeC, and FCC experiments to search for the bottomonium-like $Z_{b}$ states., Comment: 9 pages, 5 figures