We present a comprehensive analysis of the Landau-Khalatnikov-Fradkin transformations for the charged fermion propagator in reduced quantum electrodynamics (RQED). Starting from the propagator in a reference gauge, we perform a gauge transformation to obtain its analytical expression valid to all orders in an arbitrary covariant gauge and also applicable in a nonperturbative context. This work complements and extends previous studies of quantum electrodynamics in various spacetime dimensions, for both massless and massive fermions. At the perturbative level, we expand the resulting expressions up to two-loop order for both massless and massive cases, and compare our results with those available in the literature wherever possible. We argue that the most suitable choice of the reference covariant gauge in RQED is ξ=1/3, as in this case the leading logarithmic contribution to the massless wave-function renormalization vanishes at one-loop order. This choice provides a direct connection between perturbation theory and the constraints imposed by multiplicative renormalizability on the massless fermion propagator. We also investigate the implications of the Landau-Khalatnikov-Fradkin transformations for the dynamically generated mass function of the fermion propagator. Finally, through numerical computation, we demonstrate that both the chiral fermion condensate and the fermion pole mass are gauge-invariant quantities.

We present a continuum-QCD determination of the leading-order hadronic vacuum-polarization contribution to the anomalous magnetic moment of the muon within the Dyson-Schwinger and Bethe-Salpeter equation framework. The calculation incorporates pion back-reaction, a fully dressed quark-photon vertex with a dynamically generated ρ-resonance structure in the timelike region, and both strong and electromagnetic isospin breaking treated self-consistently at the quark level. We obtain a_μ^HVP,LO(u+d+s+c)|_ISB = 709.7 × 10^-10, in good agreement with recent lattice-QCD determinations, and find an isospin-breaking shift of Δa_μ^HVP,LO = 4.5 × 10^-10 (0.6%), demonstrating that isospin-breaking effects, while quantitatively modest, are not negligible. Including the bottom-quark contribution and an indicative estimate of the systematic uncertainties, we obtain our final result, a_μ^HVP,LO(u+d+s+c+b)|_ISB = (710.0 ± 14.5) × 10^-10.

The standard Feynman rules used for perturbative calculations in quantum chromodynamics (QCD) are derived from a Lagrangian that is first-order in derivatives. It includes a three-point quark-gluon vertex which obscures the precise disentangled manner in which spin and momentum are interchanged during these interactions. An unambiguous understanding of this interchange is insightful for efficiently extracting physically relevant information from various Green's functions. To separate the scalar and spin degrees of freedom and gain physical insight from the outset, we examine the quark-gluon vertex using the less commonly employed second-order formalism of QCD. We compute this off-shell vertex in arbitrary space-time dimensions and covariant gauges by using scalar integrals with shifted dimensions, which include higher powers of the propagators, within a combined first- and second-order formalism. This approach naturally identifies the transverse components of the quark-gluon vertex, even before evaluating the tensor Feynman integrals. We also compute the on-shell version of this vertex using exclusively the second-order formalism, facilitating a precise identification of spin and momentum interchange. Through analyzing the Pauli form factor at k^2=0 (where k represents the momentum of the external gluon), we find that only a specific set of second-order Feynman diagrams are relevant for calculating the electromagnetic and chromomagnetic dipole moments. These diagrams represent quantum processes in which the spin of the incoming quark changes only once due to interactions with the virtual gluons that form the quark-gluon vertex. All other interactions involve only momentum interchange (scalar interactions). Our results are in complete agreement with those obtained from the first-order formalism.

We investigate the properties of the radially excited charged pion, with a specific focus on its electromagnetic form factor (EFF) and its box contribution to the hadronic light-by-light (HLbL) component of the muon's anomalous magnetic moment, .Utilizing a coupled non perturbative framework combining Schwinger-Dysonand a mu Bethe-Salpeter equations, we first compute the mass and weak decay constant of the pion's first radial excitation. Initial results are provided for the Rainbow-Ladder (RL) approximation, followed by an extended beyond RL (BRL) analysis that incorporates meson cloud effects. Building on our previous work, this analysis demonstrates that an accurate description of the first radial excitation can be achieved without the need for a reparametrization of the interaction kernels. Having demonstrated the effectiveness of the truncation scheme, we proceed to calculate the corresponding EFF, from which we derive the contribution of the pion's first radial excitation to the HLbL component of the muon's anomalous magnetic moment, producing a(mu)(pi 1-box) (RL) = -(2.03 +/- 0.12) x 10(-13) a(mu)(pi 1-box) , mu (BRL) = -(2.02 +/- 0.10) x 10(-13). Our computation also sets the groundwork for calculating related pole contributions of excited pseudoscalar mesons to . a mu

We investigate the internal structure of a comprehensive set of pseudoscalar and vector mesons, including both flavor-symmetric and flavor-asymmetric systems, by reconstructing their charge distributions from electromagnetic form factors. To achieve this, we employ a Maximum Entropy Method optimized for charge distributions, utilizing previously published form factor data obtained within the Dyson–Schwingers and Bethe–Salpeter equations framework. Furthermore, we calculate the average distance between the valence quark and antiquark that constitute the meson, interpreting it as an estimate for both the meson’s spatial size and the typical range of quark motion. Our results reveal that this distance for the lightest quarkonia is approximately five times larger than that for the heaviest. Moreover, due to spin effects, vector mesons exhibit sizes that are 5–15 % larger than their pseudoscalar counterparts.

We carry out a comprehensive analysis of the Landau-Khalatnikov-Fradkin transformations for a charged fermion propagator at the two-loop level in quantum electrodynamics (QED). Starting with an arbitrary covariant gauge xi and space-time dimension d, we provide its explicit expressions in three- and four-dimensional QED. We begin with the tree-level fermion propagator in the Landau gauge and gaugetransform it to obtain an analytical expression for an all order result in an arbitrary covariant gauge. We expand it out to two loops both for the massless and massive propagators in three and four space-time dimensions. In addition to comparing with all earlier results in the literature wherever possible, we also study constraints of multiplicative renormalizabilty of our results in four-dimensional QED which are logarithmically divergent. Finally, we analyze representative solutions of the fermion propagator which correspond to dynamical chiral symmetry breaking and mass generation in QED. We study the gauge dependence of these emergent solutions, that of the Euclidean pole mass and the chiral fermion condensate.

We recently reported new results on the $\gamma^{(*)} + N(940)\frac{1}{2}^+ \to \Delta(1700)\frac{3}{2}^{-}$ transition form factors using a symmetry-preserving treatment of a vector$\,\otimes\,$vector contact interaction (SCI) within a coupled formalism based on the Dyson-Schwinger, Bethe-Salpeter, and Faddeev equations. In this work, we extend our investigation to the $\gamma^{(*)} + N(940)\frac{1}{2}^+ \to N(1520)\frac{3}{2}^{-}$ transition. Our computed transition form factors show reasonable agreement with experimental data at large photon virtualities. However, deviations emerge at low $Q^2$, where experimental results exhibit a sharper variation than theoretical predictions. This discrepancy is expected, as these continuum QCD analyses account only for the quark-core of baryons, while low photon virtualities are dominated by meson cloud effects. We anticipate that these analytical predictions, based on the simplified SCI framework, will serve as a valuable benchmark for more refined studies and QCD-based truncations that incorporate quark angular momentum and the contributions of scalar and vector diquarks.

Several aspects of the internal structure of pseudoscalar mesons,accessible through generalized parton distri-butions in their zero-skewness limit,are examined.These include electromagnetic and gravitational form factors related to charge and mass densities;and distributions in the impact parameter space.To this end,we employ an algebraically viable framework that is based upon the valence-quark generalized parton distribution expressed explicitly in terms of the associated distribution function and a profile function that governs the off-forward dynamics.The predominantly analytical nature of this scheme yields several algebraic results and relations while also facilitating the exploration of insightful limiting cases.With a suitable input distribution function,guided either by experiment or theory,and with an appropriate choice of the profile function,it is possible to provide testable predictions for spatial distributions of valence quarks inside pseudoscalar mesons.When comparison is possible,these predictions align well with existing experimental data as well as the findings of reliable theoretical approaches and lattice QCD.

The internal structure of the lowest-lying pseudo-scalar mesons with heavy-light quark content is thoroughly studied using an algebraic model that has been successfully applied to similar physical observables of pseudoscalar and vector mesons with hidden-flavor quark content, ranging from light to heavy quark sectors. This model is based on constructing simple and evidence-based ansätze for the mesons' Bethe-Salpeter amplitude (BSA) and quark propagator, allowing the Bethe-Salpeter wave function (BSWF) to be computed algebraically. Its projection onto the light front yields the corresponding light-front wave function (LFWF), which provides easy access to the valence-quark Parton Distribution Amplitude (PDA) by integrating over the transverse momentum squared. We leverage our current knowledge of the PDAs of the lowest-lying pseudo-scalar heavy-light mesons to compute their Generalized Parton Distributions (GPDs) via the overlap representation of the LFWFs. From this three-dimensional information, various limits and projections allow us to deduce the related Parton Distribution Functions (PDFs), Electromagnetic Form Factors (EFFs), and Impact Parameter Space GPDs (IPS-GPDs). Whenever possible, we make explicit comparisons with available experimental results and previous theoretical predictions.

The internal structure of all lowest-lying pseudo-scalar mesons with heavy-light quark content is studied in detail using an algebraic model that has been applied recently, and successfully, to the same physical observables of pseudo-scalar and vector mesons with hidden-flavor quark content, from light to heavy quark sectors. The algebraic model consists on constructing simple and evidence-based \emph{ans\"atze} of the meson's Bethe-Salpeter amplitude (BSA) and quark's propagator in such a way that the Bethe-Salpeter wave function (BSWF) can then be readily computed algebraically. Its subsequent projection onto the light front yields the light front wave function (LFWF) whose form allows us a simple access to the valence-quark Parton Distribution Amplitude (PDA) by integrating over the transverse momentum squared. We exploit our current knowledge of the PDAs of lowest-lying pseudo-scalar heavy-light mesons to compute their Generalized Parton Distributions (GPDs) through the overlap representation of LFWFs. From these three dimensional knowledge, different limits/projections lead us to deduce the related Parton Distribution functions (PDFs), Electromagnetic Form Factors (EFFs), and Impact parameter space GPDs (IPS-GPDs). When possible, we make explicit comparisons with available experimental results and earlier theoretical predictions.

Based upon a combined formalism of Schwinger-Dyson and Bethe-Salpeter equations in quantum chromodynamics (QCD), we propose a QCD-kindred algebraic model for the dressed quark propagator, for the Bethe-Salpeter amplitude of the pion and the electromagnetic quark-photon interaction vertex. We then compute the gamma*pi(0)gamma. transition form factor G(gamma)*(pi 0 gamma) (Q(2)) for a wide range of photon momentum transfer squared Q(2). The quark propagator is expanded out in its perturbative functional form but with dynamically generated dressed quark mass. It has complex conjugate pole singularities in the complex-momentum plane, which is motivated by the solution of the quark gap equation with rainbow-ladder truncation of the infinite set of Schwinger-Dyson equations. This complex pole singularity structure of the quark propagator can be associated with a signal of confinement, which prevents quarks from becoming stable asymptotic states. The Bethe-Salpeter amplitude is expressed without a spectral density function, which encapsulates its low- and large-momentum behavior. The QCD evolution of the distribution amplitude is also incorporated into our model through the direct implementation of Efremov-Radyushkin-Brodsky-Lepage evolution equations. We include the effects of the quark anomalous magnetic moment in the description of the quark-photon vertex, whose infrared enhancement is known to dictate hadronic properties. Once the QCD-kindred model is constructed, we calculate the form factor G(gamma)*(pi 0 gamma) (Q(2)) and find it consistent with direct QCD-based studies, as well as most available experimental data. It slightly exceeds the conformal limit for large Q(2), which might be attributed to the scaling violations in QCD. The associated interaction radius and neutral pion decay width turn out to be compatible with experimental data.

We compute electromagnetic and two-photon transition form factors of ground-state pseudoscalar mesons: pi, K, eta(c), eta(b). To this end, we employ an algebraic model based upon the coupled formalism of Schwinger-Dyson and Bethe-Salpeter equations. Within this approach, the dressed quark propagator and the relevant Bethe-Salpeter amplitude encode the internal structure of the corresponding meson. Electromagnetic properties of the meson are probed via the quark-photon interaction. The algebraic model employed by us unifies the treatment of all ground-state pseudoscalar mesons. Its parameters are carefully fitted performing a global analysis of existing experimental data including the knowledge of the charge radii of the mesons studied. We then compute and predict electromagnetic and two-photon transition form factors for a wide range of probing photon momentum-squared which is of direct relevance to the experimental observations carried out thus far or planned at different hadron physics facilities such as the Thomas Jefferson National Accelerator Facility (JLab) and the forthcoming Electron-Ion Collider. We also present comparisons with other theoretical models and approaches and lattice quantum chromodynamics.

We present a calculation for the masses of the first radially excited states of 40 mesons and diquarks made up of u, d, s, c, and b quarks, including states that contain one or both heavy quarks. To this end, we employ a combined analysis of the Bethe-Salpeter and Schwinger-Dyson equations within a self-consistent and symmetry-preserving vector-vector contact interaction. The same set of parameters describes ground and excited states of mesons and their diquark partners. The wave function of the first radial excitation contains a zero whose location is correlated with an additional parameter dF which is a function of dressed quark masses. Our results satisfy the equal spacing rules given by the Gell-Mann Okubo mass relations. Wherever possible, we make comparisons of our findings with known experimental observations as well as theoretical predictions of several other models and approaches including lattice quantum chromodynamics, finding a very good agreement. We report predictions for a multitude of radial excitations not yet observed in experiments. Published by the American Physical Society 2024

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 z, rlg, rlb and the hypothetical strangeonium rls(ss). We adopt the coupled framework of Dyson-Schwinger and BetheSalpeter 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 D term of pseudoscalar mesons and their GFFs can provide an important first step for future endeavors in the field.

We present a detailed survey of electric, magnetic, and quadrupole form factors of light and heavy spin-1 vector mesons. It complements our analogous analysis of the electromagnetic form factors of pseudoscalar and scalar mesons reported earlier. Our formalism is based upon the Schwinger-Dyson equations treatment of a vector x vector contact interaction and the Bethe-Salpeter equation description of relativistic two-body bound states. We compute the form factors, associated moments, and charge radii, comparing these quantities to earlier theoretical studies and experimental results if and when possible. We also investigate the quark-mass dependence of the charge radii and find the anticipated hierarchy such that it decreases with increasing dressed quark masses. In addition, our analysis shows that the magnetic moment is independent of the mass of the light and heavy mesons. Our results agree with most measurements reported earlier, finding a negative quadrupole moment, implying the charge distribution is oblate.

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.

Despite its role in the continuing evolution of the Universe, only a small fraction of the mass of visible material can be attributed to the Higgs boson alone. The overwhelmingly dominant share may/should arise from the strong interactions that act in the heart of nuclear matter; namely, those described by quantum chromodynamics. This contribution describes how studying and explaining the attributes of pseudoscalar mesons can open an insightful window onto understanding the origin of mass in the Standard Model and how these insights inform our knowledge of hadron structure. The survey ranges over distribution amplitudes and functions, electromagnetic and gravitational form factors, light-front wave functions, and generalized parton distributions. Advances made using continuum Schwinger function methods and their relevance for experimental efforts are highlighted.

The Electron-Ion Collider, a next generation electron-hadron and electron-nuclei scattering facility, will be built at Brookhaven National Laboratory. The wealth of new data will shape research in hadron physics, from nonperturbative QCD techniques to perturbative QCD improvements and global QCD analyses, for the decades to come. With the present proposal, Latin America based physicists, whose expertise lies on the theory and phenomenology side, make the case for the past and future efforts of a growing community, working hand-in-hand towards developing theoretical tools and predictions to analyze, interpret and optimize the results that will be obtained at the EIC, unveiling the role of the glue that binds us all. This effort is along the lines of various initiatives taken in the U.S., and supported by colleagues worldwide, such as the ones by the EIC User Group which were highlighted during the Snowmass Process and the Particle Physics Project Prioritization Panel (P5).

Inspired by the recent development of an algebraic model which provides an adequate and unified description of the internal structure of the lowest-lying pseudo-scalar mesons, belonging both to the light quarks sector and to the one of heavy quarks, we perform its first extension to the vector-meson case. The algebraic model describes meson's structure in terms of the spectral density function that appears in a Nakanishi integral representation of the covariant quark-antiquark bound-state amplitude, \emph{i.e.}, the Bethe-Salpeter amplitude. We compute the leading-twist light-front wave functions of the $\rho(770)$, $\phi(1020)$, $J/\psi$ and $\Upsilon(1S)$ mesons through their connection with the parton distribution amplitudes. Among the results we present, the following are of particular interest: (i) transverse light-front wave functions can be obtained algebraically from the corresponding parton distribution amplitudes, whereas that is not the case for longitudinal light-front wave functions, which requires an intermediate step where a spectral density function must be derived from the particular parton distribution amplitude; (ii) the derived spectral density functions show marked differences between light and heavy vector mesons, the latter being narrower as compared to the former; these are also non-positive definite, although the integral over the entire curve is larger than zero as expected; and (iii) the longitudinal and transverse light-front wave functions of vector mesons with light quark content exhibit steep $x$- and $p_\perp^2$-dependence, while those of the $J/\psi$ and $\Upsilon(1S)$ mesons are characterized by narrow distributions in the $x$-range but, comparatively, much more gradual fall-offs with respect to the $p_\perp^2$-range depicted.