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Given the unique role played by the gravitational form factors (GFFs) in unraveling the internal mechanics of hadrons, we examine the GFFs of ground state pseudoscalar mesons $\pi$, $\eta_c$, $\eta_b$ and the hypothetical {\em strangeonium} $\eta_s(s\bar{s})$. We adopt the coupled framework of Dyson-Schwinger and Bethe-Salpeter equations within a contact interaction, and employ a novel approach to the dressed amputated meson-meson scattering amplitude which makes connection with the energy-momentum tensor and with the GFFs. The resulting GFFs fulfill the anticipated symmetry constraints. The corresponding charge and mass radii and the $D-$term are also computed. We show that the $D-$term for the pseudoscalar mesons is bounded within the $(-1, -1/3)$ range; these bounds correspond to the massless (chiral limit) and infinitely massive cases, respectively. Considering the current interest in the GFFs, understanding the \textit{D}-term of pseudoscalar mesons and their GFFs can provide an important first step for future endeavors in the field., Comment: 10 pages, 5 figures

We propose an efficacious approach to derive the generalized parton distributions for the pion and proton, based upon prior knowledge of their respective parton distribution functions (PDFs). Our method leverages on integral representations of the electromagnetic form factors derived from the light-front holographic QCD (LFHQCD) formalism, coupled with PDFs computed from continuum Schwinger functional methods at the hadronic scale. Using these techniques, we calculate gravitational form factors and associated mass distributions for each hadron. Remarkably, our calculations yield results that closely match recent lattice QCD simulations conducted near the physical pion mass. This work not only deepens our understanding of hadronic structure but also highlights the efficacy of the LFHQCD approach in modeling fundamental properties of hadrons., Comment: 6 pages, 5 figures

A recent study by Wang {\it et al.}(arXiv:2309.01417) proposed a novel connection between the nature of the parton distribution function (PDF) and the characteristics of its moments. In this study, we apply these findings to analyze the evolution of the pion valence quark PDF, garnering valuable qualitative insights. Firstly, we validate the non-negativity and continuity of the PDF across a wide range of scales, indicating the logical consistency of our chosen evolution scheme. Subsequently, we examine the unimodality of both the PDF and its transformed counterpart, the xPDF, i.e., the parton distribution function multiplied by the momentum fraction. We observe a smooth evolution of the peak position of the xPDF towards the small-$x$ region with increasing scale, while intriguingly, the PDF undergoes a phase of bimodal competition as the energy scale evolves., Comment: The judgment made based on finite-order moments information about the distribution function (DF) is insufficient

In this work, the $\gamma\to3\pi$ form factor is calculated within the Dyson-Schwinger equations framework using a contact interaction model within the so-called modified rainbow ladder truncation. The present calculation takes into account the pseudovector component in the pion Bethe-Salpeter amplitude (BSA) and $\pi-\pi$ scattering effects, producing a $\gamma\to3\pi$ anomaly which is $1+6\mathcal{R}_\pi^2$ larger than the low energy prediction. Here $\mathcal{R_\pi}$ is the relative ratio of the pseudovector and pseudoscalar components in the pion BSA; with our parameters input, this correction raises the $\gamma\to3\pi$ anomaly by around $10\%$. The main outcome of this work is the unveiling of the origin of such correction, which could be a possible explanation of the discrepancy between the existing experimental data and the low energy prediction. Moreover, it is highlighted how the magnitude of the anomaly is affected in effective theories that require an irremovable ultraviolet cutoff. We find that for both the anomalous processes $\pi\to2\gamma$ and $\gamma\to 3\pi$, the missing contribution to the anomaly can be compensated by the additional structures related with the quark anomalous magnetic moment., Comment: 10 pages, 3 figures, references added

A new method based on the maximum entropy principle for reconstructing the parton distribution function (PDF) from moments is proposed. Unlike traditional methods, the new method no longer needs to introduce any artificial assumptions. For the case of moments with errors, we introduce Gaussian functions to soften the constraints of moments. Through a series of tests, the effectiveness and reconstruction efficiency of this new method are evaluated comprehensively. And these tests indicate that this method is reasonable and can achieve high-quality reconstruction with at least the first six moments as input. Finally, we select a set of lattice QCD results regarding moments as input and provide reasonable reconstruction results for the pion., Comment: 6 pages, 8 figures

We apply a classical mathematical problem, the moment problem, with its related mathematical achievements, to the study of the parton distribution function (PDF) in hadron physics, and propose a strategy to sieve the moments of the PDF by exploiting its properties such as continuity, unimodality, and symmetry. Through an error-inclusive sifting process, we refine three sets of PDF moments from Lattice QCD. This refinement significantly reduces the errors, particularly for higher order moments, and locates the peak of PDF simultaneously. As our strategy is universally applicable to PDF moments from any method, we strongly advocate its integration into all PDF moment calculations., Comment: 6 pages, 2 figures

This document presents the initial scientific case for upgrading the Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab (JLab) to 22 GeV. It is the result of a community effort, incorporating insights from a series of workshops conducted between March 2022 and April 2023. With a track record of over 25 years in delivering the world's most intense and precise multi-GeV electron beams, CEBAF's potential for a higher energy upgrade presents a unique opportunity for an innovative nuclear physics program, which seamlessly integrates a rich historical background with a promising future. The proposed physics program encompass a diverse range of investigations centered around the nonperturbative dynamics inherent in hadron structure and the exploration of strongly interacting systems. It builds upon the exceptional capabilities of CEBAF in high-luminosity operations, the availability of existing or planned Hall equipment, and recent advancements in accelerator technology. The proposed program cover various scientific topics, including Hadron Spectroscopy, Partonic Structure and Spin, Hadronization and Transverse Momentum, Spatial Structure, Mechanical Properties, Form Factors and Emergent Hadron Mass, Hadron-Quark Transition, and Nuclear Dynamics at Extreme Conditions, as well as QCD Confinement and Fundamental Symmetries. Each topic highlights the key measurements achievable at a 22 GeV CEBAF accelerator. Furthermore, this document outlines the significant physics outcomes and unique aspects of these programs that distinguish them from other existing or planned facilities. In summary, this document provides an exciting rationale for the energy upgrade of CEBAF to 22 GeV, outlining the transformative scientific potential that lies within reach, and the remarkable opportunities it offers for advancing our understanding of hadron physics and related fundamental phenomena., Comment: Updates to the list of authors; Preprint number changed from theory to experiment; Updates to sections 4 and 6, including additional figures

In the presence of a momentum cutoff, effective theories seem unable to faithfully reproduce the so called chiral anomaly in the Standard Model. A novel prospect to overcome this related issue is discussed herein via the calculation of the $\gamma^{*}\pi^0\gamma$ transition form factor, $G^{\gamma^* \pi^0 \gamma}(Q^2)$, whose normalization is intimately connected with the chiral anomaly and dynamical chiral symmetry breaking (DCSB). To compute such transition, we employ contact interaction model of Quantum Chromodynamics (QCD) under a modified rainbow ladder truncation, which automatically generates a quark anomalous magnetic moment term, weighted by a strenght parameter $\xi$. This term, whose origin is also connected with DCSB, is interpreted as an additional interaction that mimics the complex dynamics beyond the cutoff. By fixing $\xi$ to produce the value of $G^{\gamma^* \pi^0 \gamma}(0)$ dictated by the chiral anomaly, the computed transition form factor, as well as the interaction radius and neutral pion decay width, turn out to be comparable with QCD-based studies and experimental data., Comment: 9 pages, 2 figures

We present a symmetry-preserving scheme to derive the pion and kaon generalized parton distributions (GPDs) in Euclidean space. The key to maintaining crucial symmetries under this approach is the treatment of the scattering amplitude, such that it contains both the traditional leading-order contributions and the scalar/vector pole contribution automatically, the latter being necessary to ensure the soft-pion theorem. The GPD is extracted analytically via the uniqueness and definition of the Mellin moments and we find that it naturally matches the double distribution; consequently, the polynomiality condition and sum rules are satisfied. The present scheme thus paves the way for the extraction of the GPD in Euclidean space using the Dyson-Schwinger equation framework or similar continuum approaches., Comment: 5 pages, 2 figures, references added

We provide a novel approach to calculate the gravitational form factor of pion under the ladder approximation of the Bethe-Salpeter equation, with contact interactions. Central to this approach is a symmetry-preserving treatment of the dressed $\pi\pi$ amplitude, which shows explicitly the contributions from intrinsic quarks and bound states, the latter being necessary to produce the $D$-term of pion in the soft-pion limit. The approach we provide in this work can be applied to many processes of physical significance., Comment: 7 pages, 3 figures

We propose a novel method to construct the Landau thermodynamic potential directly from the fluctuations measured in heavy-ion collisions. The potential is capable of revealing the signal of the critical end-point (CEP) and the first order phase transition (FOPT) of QCD in the system even away from the phase transition region. With the available experimental data, we show that the criterion of the FOPT is negative for most of the collision energies which indicates no signal of FOPT. The data at $\sqrt{s_\mathrm{NN}}=7.7$ GeV with 0-5% centrality shows a different behavior and the mean value of the data satisfies the criterion. However, the uncertainty is still too large to make a certain conclusion. The higher order fluctuations are also required for confirming the signal. We emphasize therefore that new measurements with higher precision for the $C_{1,...,6}$ within 0-5% centrality in the vicinity of $\sqrt{s_\mathrm{NN}}=7.7$ GeV are in demand which may finally reveal the signal of QCD phase transition., Comment: 7 pages, 4 figures

A symmetry-preserving regularization procedure for dealing with the contact interaction model is proposed in this work. This regularization procedure follows a series of consistency conditions which are necessary to maintain gauge symmetry. Under this regularization, proofs for the preservation of the Ward-Takahashi identities are given and the loop integrals in the contact interaction model are systematically computed. As an application example, the kaon electromagnetic form factor and $K_{l3}$ transition form factor are computed and self-consistent results are obtained. Since the proposed regularization properly handles the divergence, one is freed from the inconsistencies caused by the regularization and can concentrate more on the physical discussion., Comment: 10 pages, 3 figures

The pion scalar, vector and tensor form factors are calculated within a symmetry-preserving contact interaction model (CI) of quantum chromodynamics (QCD), encompassed within a Dyson-Schwinger and Bethe-Salpeter equations approach. In addition to the traditional rainbow-ladder truncation, a modified interaction kernel for the Bethe-Salpeter equation is adopted. The implemented kernel preserves the vector and axial-vector Ward-Takahashi identities, while also providing additional freedom. Consequently, new tensor structures are generated in the corresponding interaction vertices, shifting the location of the mass poles appearing in the quark-photon and quark tensor vertex and yielding a notorious improvement in the final results. Despite the simplicity of the CI, the computed form factors and radii are compatible with recent lattice QCD simulations., Comment: 11 pages, 8 figures

The wave propagation and power deposition in blue-core helicon plasma are computed referring to recent experiments. It is found that the radial profile of wave electric field peaks off-axis during the blue-core formation, and the location of this peak is very close to that of particle transport barrier observed in experiment; the radial profile of wave magnetic field shows multiple radial modes inside the blue-core column, which is consistent with the experimental observation of coherent high $m$ modes through Bessel function. The axial profiles of wave field indicate that, once the blue-core mode has been achieved, waves can only propagate inside the formed column with distinct phase compared to that outside. The wave energy distribution shows a clear and sharp boundary at the edge of blue-core column, besides which periodic structures are observed and the axial periodicity inside is nearly twice that outside. The dispersion relation inside the blue-core column exhibits multiple modes, a feature of resonant cavity that selects different modes during frequency variation, while the dispersion relation outside gives constant wave number with changed frequency. The power deposition appears to be off-axis in the radial direction and periodic in the axial direction, and mostly inside the blue-core column. Analyses based on step-like function theory and introduced blue-core constant provide consistent results. The equivalence of blue-core column to optical fiber for electromagnetic communication is also explored and inspires a novel application of helicon plasma, which may be one of the most interesting findings of present work.

Working with proton and pion valence distribution functions (DFs) determined consistently at the same, unique hadron scale and exploiting the possibility that there is an effective charge which defines an evolution scheme for DFs that is all-orders exact, we obtain a unified body of predictions for all proton and pion DFs - valence, glue, and four-flavour-separated sea. Whilst the hadron light-front momentum fractions carried by identifiable parton classes are the same for the proton and pion at any scale, the pointwise behaviour of the DFs is strongly hadron-dependent. All calculated distributions comply with quantum chromodynamics constraints on low- and high-$x$ scaling behaviour and, owing to emergent hadron mass, pion DFs are the most dilated. These results aid in elucidating the sources of similarities and differences between proton and pion structure., Comment: 8 pages, 4 figures, 2 tables

An algebraic Ansatz for the proton's Poincar\'e-covariant wave function, which includes both scalar and pseudovector diquark correlations, is used to calculate proton valence, sea, and glue distribution functions (DFs). Regarding contemporary data, a material pseudovector diquark component in the proton is necessary for an explanation of the neutron-proton structure function ratio; and a modest Pauli blocking effect in the gluon splitting function is sufficient to explain the proton's light-quark antimatter asymmetry. In comparison with pion DFs, the light-front momentum fractions carried by all identifiable parton classes are the same; on the other hand, the higher moments are different. Understanding these features may provide insights that explain distinctions between Nambu-Goldstone bosons and seemingly less complex hadrons., Comment: 8 pages, 2 figures, 1 table

Based on the recently precise measurements of the electron-positron annihilation reactions into a neutron and anti-neutron pair by BESIII collaboration, the effective form factor of neutron was determined in the time like region, and it was found that the effective form factor of neutron is smaller than the ones of proton. The effective form factors of neutron shows a periodic behaviour, similar to the case of proton. Here, a compared analysis for $\Lambda$, $\Sigma^0$ and $\Xi^0$ is performed. Fits of the available data on the effective form factors of $\Lambda$, $\Sigma^0$ and $\Xi^0$ with charge zero, allow to show a universal phenomenon of the oscillation behavior in their effective form factors. However, this needs to be confirmed by future precise experiments. Both theoretical and experimental investigations of this phenomenon can shed light on the reaction mechanisms of the electron-positron annihilation process., Comment: 4 figures, 5 pages. Experimental data on $\Xi^0$ are included, title is slightly modified

The static properties, masses and decay constants, of pseudoscalar meson triplet in a strongly magnetized medium are studied through the Dyson-Schwinger equation approach treatment of a contact interaction. Complementary to the usual vector-vector form, a symmetry-preserving formulation of couplings has been proposed in this work, without modifying the quark propagator, to control the strength of the $p$-wave component of Bethe-Salpeter amplitude. It is found that, with the help of flexible auxiliary interaction, our simple model is able to reproduce the observation in the lattice QCD simulation, where the spectra of the charged pseudo-scalar meson shows a non-monotonic behavior as the magnetic field grows. The discovery of this work implies the strong magnetic field affects the inner structure of mesons dramatically., Comment: 17 pages, 8 figures

Clear windows onto emergent hadron mass (EHM) and modulations thereof by Higgs boson interactions are provided by observable measures of pion and kaon structure, many of which are accessible via generalised parton distributions (GPDs). Beginning with algebraic GPD Ansaetze, constrained entirely by hadron-scale $\pi$ and $K$ valence-parton distribution functions (DFs), in whose forms both EHM and Higgs boson influences are manifest, numerous illustrations are provided. They include the properties of electromagnetic form factors, impact parameter space GPDs, gravitational form factors and associated pressure profiles, and the character and consequences of all-orders evolution. The analyses predict that mass-squared gravitational form factors are stiffer than electromagnetic form factors; reveal that $K$ pressure profiles are tighter than $\pi$ profiles, with both mesons sustaining near-core pressures at magnitudes similar to that expected at the core of neutron stars; deliver parameter-free predictions for $\pi$ and $K$ valence, glue, and sea GPDs at the resolving scale $\zeta=2$GeV; and predict that at this scale the fraction of meson mass-squared carried by glue and sea combined matches that lodged with the valence degrees-of-freedom, with a similar statement holding for mass-squared radii., Comment: 22 pages, 19 figures, 2 tables

Beginning with precise data on the ratio of structure functions in deep inelastic scattering (DIS) from $^3$He and $^3$H, collected on the domain $0.19 \leq x_B \leq 0.83$, where $x_B$ is the Bjorken scaling variable, we employ a robust method for extrapolating such data to arrive at a model-independent result for the $x_B=1$ value of the ratio of neutron and proton structure functions. Combining this with information obtained in analyses of DIS from nuclei, corrected for target-structure dependence, we arrive at a prediction for the proton's valence-quark ratio: $\left. d_v/u_v \right|_{x_B\to 1} = 0.230 (57)$. Requiring consistency with this result presents a challenge to many descriptions of proton structure., Comment: 6 pages, 3 figures

The $\gamma^{(\ast)}+p \to N(1535) \tfrac{1}{2}^-$ transition is studied using a symmetry-preserving regularisation of a vector$\,\otimes\,$vector contact interaction (SCI). The framework employs a Poincar\'e-covariant Faddeev equation to describe the initial and final state baryons as quark+di\-quark composites, wherein the diquark correlations are fully dynamical, interacting with the photon as allowed by their quantum numbers and continually engaging in breakup and recombination as required by the Faddeev kernel. The presence of such correlations owes largely to the mechanisms responsible for the emergence of hadron mass; and whereas the nucleon Faddeev amplitude is dominated by scalar and axial-vector diquark correlations, the amplitude of its parity partner, the $N(1535) \tfrac{1}{2}^-$, also contains sizeable pseudoscalar and vector diquark components. It is found that the $\gamma^{(\ast)}+p \to N(1535) \tfrac{1}{2}^-$ helicity amplitudes and related Dirac and Pauli form factors are keenly sensitive to the relative strengths of these diquark components in the baryon amplitudes, indicating that such resonance electrocouplings possess great sensitivity to baryon structural details. Whilst SCI analyses have their limitations, they also have the virtue of algebraic simplicity and a proven ability to reveal insights that can be used to inform more sophisticated studies in frameworks with closer ties to quantum chromodynamics., Comment: 16 pages, 14 figures, 4 tables

A symmetry-preserving treatment of mesons, within a Dyson-Schwinger and Bethe-Salpeter equations approach, demands an interconnection between the kernels of the quark gap equation and meson Bethe-Salpeter equation. Appealing to those symmetries expressed by the vector and axial-vector Ward-Green-Takahashi identitiges (WGTI), we construct a two-body Bethe-Salpeter kernel and study its implications in the vector channel; particularly, we analyze the structure of the quark-photon vertex, which explicitly develops a vector meson pole in the timelike axis and the quark anomlaous magnetic moment term, as well as a variety of $\rho$ meson properties: mass and decay constants, electromagnetic form factors, and valence-quark distribution amplitudes., Comment: 12 pages, 5 figures