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A nonperturbatively-improved, symmetry-preserving approximation to the quantum field equations relevant in calculations of meson masses and interactions is used to deliver predictions for all distribution functions (DFs) of the ground state pion, $\pi_0$, and its first radial excitation, $\pi_1$, viz. valence, glue, and sea. Regarding Mellin moments of the valence DFs, the $m=0,1$ moments in both states are identical; but for each $m\geq 2$, that in the $\pi_0$ is greater than its partner in the $\pi_1$. Working with such information, pointwise reconstructions of the hadron-scale $\pi_{0,1}$ valence DFs are developed. The predicted $\pi_0$ valence DF is consistent with extant results. The $\pi_1$ valence DF is novel: it possesses three-peaks, with the central maximum partnered by secondary peaks on either side, each separated from the centre by a zero: the zeroes lie at $x\approx 0.2,0.8$ and the secondary peaks at $x\approx 0.1,0.9$. Evolution to $\zeta =3.2\,$GeV, a typical scale for nonperturbative calculations, is accomplished using an evolution scheme for parton DFs that is all-orders exact. At this higher scale, differences between the $\pi_{0,1}$ valence DFs remain significant, but analogous differences between glue and sea DFs are far smaller. This analysis shows that, owing to constraints imposed by chiral symmetry and the pattern by which it is broken in Nature, there are noticeable differences between the structural properties of the pion ground state and its radial excitations., Comment: 11 pages, 5 figures, 4 tables

A symmetry-preserving analysis of strong interaction quantum field equations is used to complete a unified treatment of pion, kaon, nucleon electromagnetic and gravitational form factors. Findings include a demonstration that the pion near-core pressure is roughly twice that in the proton, so both are significantly greater than that of a neutron star; parton species separations of the nucleon's three gravitational form factors, in which, inter alia, the glue-to-quark ratio for each form factor is seen to take the same constant value, independent of momentum transfer; and a determination of proton radii orderings, with the mechanical (normal force) radius being less than the mass-energy radius, which is less than the proton charge radius. This body of predictions should prove useful in an era of anticipated experiments that will enable them to be tested., Comment: 11 pages, 8 figures, 1 table

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., Comment: Prepared for the special issue of the Few Body Systems journal: "Advances on the Few-Body Problem in Physics - Selected and refereed papers from the 25th European Conference"

Exploiting crossing symmetry, the hadron scale pion valence quark distribution function is used to predict the kindred elementary valence quark fragmentation function (FF). This function defines the kernel of a quark jet fragmentation equation, which is solved to obtain the full pion FFs. After evolution to a scale typical of FF fits to data, the results for quark FFs are seen to compare favourably with such fits. However, the gluon FF is markedly different. Notably, although FF evolution equations do not themselves guarantee momentum conservation, inclusion of a gluon FF which, for four quark flavours, distributes roughly 11% of the total light-front momentum fraction, is sufficient to restore momentum conservation under evolution. Overall, significant uncertainty is attached to FFs determined via fits to data; hence, the features of the predictions described herein could potentially provide useful guidance for future such studies., Comment: 9 pages, 4 figures

Using a reaction model that incorporates pion bound state effects and continuum results for proton parton distributions and the pion distribution amplitude, $\varphi_\pi$, we deliver parameter-free predictions for the $\mu^+$ angular distributions in $\pi N \to \mu^+ \mu^- X$ reactions on both unpolarised and polarised targets. The analysis indicates that such angular distributions are sensitive to the pointwise form of $\varphi_\pi$ and suggests that unpolarised targets are practically more favourable. The precision of extant data is insufficient for use in charting $\varphi_\pi$; hence, practical tests of this approach to charting $\varphi_\pi$ must await data with improved precision from new-generation experiments. The reaction model yields a nonzero single-spin azimuthal asymmetry, without reference to $T$-odd parton distribution functions (DFs). This may necessitate additional care when attempting to extract such $T$-odd DFs from data., Comment: 8 pages, 7 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

We discuss our present knowledge of $\alpha_s$, the fundamental running coupling or effective charge of Quantum Chromodynamics (QCD). A precise understanding of the running of $\alpha_s(Q^2) $ at high momentum transfer, $Q$, is necessary for any perturbative QCD calculation. Equally important, the behavior of $\alpha_s$ at low $Q^2$ in the nonperturbative QCD domain is critical for understanding strong interaction phenomena, including the emergence of mass and quark confinement. The behavior of $\alpha_s(Q^2)$ at all momentum transfers also provides a connection between perturbative and nonperturbative QCD phenomena, such as hadron spectroscopy and dynamics. We first sketch the origin of the QCD coupling, the reason why its magnitude depends on the scale at which hadronic phenomena are probed, and the resulting consequences for QCD phenomenology. We then summarize latest measurements in both the perturbative and nonperturbative domains. New theory developments include the derivation of the universal nonperturbative behavior of $\alpha_s(Q^2)$ from both the Dyson-Schwinger equations and light-front holography. We also describe theory advances for the calculation of gluon and quark Schwinger functions in the nonperturbative domain and the relation of these quantities to $\alpha_s$. We conclude by highlighting how the nonperturbative knowledge of $\alpha_s$ is now providing a parameter-free determination of hadron spectroscopy and structure, a central and long-sought goal of QCD studies., Comment: Invited review article, Prog Part. Nucl. Phys., in press. (143 pages, 9 figures)

Continuum and lattice analyses have revealed the existence of a mass-scale in the gluon two-point Schwinger function. It has long been conjectured that this expresses the action of a Schwinger mechanism for gauge boson mass generation in quantum chromodynamics (QCD). For such to be true, it is necessary and sufficient that a dynamically-generated, massless, colour-carrying, scalar gluon+gluon correlation emerge as a feature of the dressed three-gluon vertex. Working with results on elementary Schwinger functions obtained via the numerical simulation of lattice-regularised QCD, we establish with an extremely high level of confidence that just such a feature appears; hence, confirm the conjectured origin of the gluon mass scale., Comment: 8 pages, 8 figures

A Symplectic Effective Field Theory that unveils the observed emergence of symplectic symmetry in atomic nuclei is advanced. Specifically, starting from a simple extension of the harmonic-oscillator Lagrangian, an effective field theory applied against symplectic basis states is shown to yield a Hamiltonian system with one fitted parameter. The scale of the system can be determined self consistently as the ratio of the average volume of a nucleus assumed to be spherical to its volume as determined by the average number of oscillator quanta, which is stretched by the fact that the plane-wave solution satisfies the equations of motion at every order without the need for perturbative corrections. As an application of the theory, results for 20Ne, 22Ne and 22Mg are presented that yield energy spectra, B(E2) values, and matter radii in good agreement with experimentally measured results.

In Newtonian mechanics, inertial pseudoforces - or fictitious forces - appear in systems studied in non-Galilean reference frames; e.g., a centrifugal force seems to arise if the dynamics is analyzed in a rotating reference frame. The equivalent of Galilean invariance for relativistic kinematics is Poincar\'e invariance; analogous artificial effects may arise in relativistic quantum field theory (QFT) if a system is studied in a framework violating Poincar\'e invariance. We highlight how such issues complicate the traditional canonical quantization of QFTs and can lead to a subjective description of natural phenomena. In fact, if the system involves the strong interaction, obtaining objective results can become an intractable problem using canonical quantization because the pseudoforces are essentially nonperturbative. In contrast, the treatment of the same problem using light-front (LF) quantization is free of spurious pseudoeffects because Poincar\'e invariance is manifest; thus the treatment of strong interaction problems becomes simpler. These statements are illustrated using several examples: the Gerasimov-Drell-Hearn (GDH) relation, a fundamental feature of QFT; the absence of any measurable impact of Lorentz contraction in high-energy collisions; and the fictitious character of vacuum fluctuation contributions to the cosmological constant., Comment: 21 page, 4 Figure. A version of this document, amended during the peer consultation process, has been accepted for publication in Nature Reviews Physics

Supposing only that there is an effective charge which defines an evolution scheme for parton distribution functions (DFs) that is all-orders exact, strict lower and upper bounds on all Mellin moments of the valence-quark DFs of pion-like systems are derived. Exploiting contemporary results from numerical simulations of lattice-regularised quantum chromodynamics (QCD) that are consistent with these bounds, parameter-free predictions for pion valence, glue, and sea DFs are obtained. The form of the valence-quark DF at large values of the light-front momentum fraction is consistent with predictions derived using the QCD-prescribed behaviour of the pion wave function., Comment: 8 pages, 5 figures, 1 table

Analyses of the pion valence-quark distribution function (DF), ${u}^\pi(x;\zeta)$, which explicitly incorporate the behaviour of the pion wave function prescribed by quantum chromodynamics (QCD), predict ${u}^\pi(x\simeq 1;\zeta) \sim (1-x)^{\beta(\zeta)}$, $\beta(\zeta \gtrsim m_p)>2$, where $m_p$ is the proton mass. Nevertheless, more than forty years after the first experiment to collect data suitable for extracting the $x\simeq 1$ behaviour of ${u}^\pi$, the empirical status remains uncertain because some methods used to fit existing data return a result for ${u}^\pi$ that violates this constraint. Such disagreement entails one of the following conclusions: the analysis concerned is incomplete; not all data being considered are a true expression of qualities intrinsic to the pion; or QCD, as it is currently understood, is not the theory of strong interactions. New, precise data are necessary before a final conclusion is possible. In developing these positions, we exploit a single proposition, viz. there is an effective charge which defines an evolution scheme for parton DFs that is all-orders exact. This proposition has numerous corollaries, which can be used to test the character of any DF, whether fitted or calculated., Comment: 15 pages, 9 figures, 1 table

This report describes the physics case, the resulting detector requirements, and the evolving detector concepts for the experimental program at the Electron-Ion Collider (EIC). The EIC will be a powerful new high-luminosity facility in the United States with the capability to collide high-energy electron beams with high-energy proton and ion beams, providing access to those regions in the nucleon and nuclei where their structure is dominated by gluons. Moreover, polarized beams in the EIC will give unprecedented access to the spatial and spin structure of the proton, neutron, and light ions. The studies leading to this document were commissioned and organized by the EIC User Group with the objective of advancing the state and detail of the physics program and developing detector concepts that meet the emerging requirements in preparation for the realization of the EIC. The effort aims to provide the basis for further development of concepts for experimental equipment best suited for the science needs, including the importance of two complementary detectors and interaction regions. This report consists of three volumes. Volume I is an executive summary of our findings and developed concepts. In Volume II we describe studies of a wide range of physics measurements and the emerging requirements on detector acceptance and performance. Volume III discusses general-purpose detector concepts and the underlying technologies to meet the physics requirements. These considerations will form the basis for a world-class experimental program that aims to increase our understanding of the fundamental structure of all visible matter, Comment: 902 pages, 415 authors, 151 institutions

High precision measurements of the polarized electron beam-spin asymmetry in semi-inclusive deep inelastic scattering (SIDIS) from the proton have been performed using a 10.6~GeV incident electron beam and the CLAS12 spectrometer at Jefferson Lab. We report here a high precision multidimensional study of single $\pi^{+}$ SIDIS data over a large kinematic range in Bjorken x, fractional energy and transverse momentum of the hadron as well as photon virtualities $Q^{2}$ ranging from $1-7\,$GeV$^{2}$. In particular, the structure function ratio $F^{\sin\phi}_{LU}/F_{UU}$ has been determined, where $F^{\sin\phi}_{LU}$ is a twist-3 quantity that can reveal novel aspects of emergent hadron mass and quark-gluon correlations within the nucleon. The data's impact on the evolving understanding of the underlying reaction mechanisms and their kinematic variation is explored using theoretical models for the different contributing transverse momentum dependent parton distribution functions.

The last decade has seen a marked shift in how the internal structure of hadrons is understood. Modern experimental facilities, new theoretical techniques for the continuum bound-state problem and progress with lattice-regularised QCD have provided strong indications that soft quark+quark (diquark) correlations play a crucial role in hadron physics. For example, theory indicates that the appearance of such correlations is a necessary consequence of dynamical chiral symmetry breaking, viz. a corollary of emergent hadronic mass that is responsible for almost all visible mass in the universe; experiment has uncovered signals for such correlations in the flavour-separation of the proton's electromagnetic form factors; and phenomenology suggests that diquark correlations might be critical to the formation of exotic tetra- and penta-quark hadrons. A broad spectrum of such information is evaluated herein, with a view to consolidating the facts and therefrom moving toward a coherent, unified picture of hadron structure and the role that diquark correlations might play., Comment: 113 pages, 41 figures, 8 tables

The topical workshop {\it Strong QCD from Hadron Structure Experiments} took place at Jefferson Lab from Nov. 6-9, 2019. Impressive progress in relating hadron structure observables to the strong QCD mechanisms has been achieved from the {\it ab initio} QCD description of hadron structure in a diverse array of methods in order to expose emergent phenomena via quasi-particle formation. The wealth of experimental data and the advances in hadron structure theory make it possible to gain insight into strong interaction dynamics in the regime of large quark-gluon coupling (the strong QCD regime), which will address the most challenging problems of the Standard Model on the nature of the dominant part of hadron mass, quark-gluon confinement, and the emergence of the ground and excited state hadrons, as well as atomic nuclei, from QCD. This workshop aimed to develop plans and to facilitate the future synergistic efforts between experimentalists, phenomenologists, and theorists working on studies of hadron spectroscopy and structure with the goal to connect the properties of hadrons and atomic nuclei available from data to the strong QCD dynamics underlying their emergence from QCD. These results pave the way for a future breakthrough extension in the studies of QCD with an Electron-Ion Collider in the U.S., Comment: Summary and outlook of the "Strong QCD from Hadron Structure Experiment" topical Workshop at Jefferson Lab, November 4-8, 2019, Newport News, VA, USA, 65 pages, 57 figures

The task of mapping and explaining the spectrum of baryons and the structure of these states in terms of quarks and gluons is a longstanding challenge in hadron physics, which is likely to persist for another decade or more. We review the progress made in this topic using a functional method based on Dyson-Schwinger equations. This framework provides a non-perturbative, Poincar\'e-covariant continuum formulation of Quantum Chromodynamics which is able to extract novel insight on baryon properties since the physics at the hadron level is directly related with the underlying quark-gluon substructure, via convolution of Green functions., Comment: 9 pages, 4 figures; contribution to the proceedings of the XVIII International Conference on Hadron Spectroscopy and Structure, HADRON-2019. August 16-21, Guilin, China

Using a relativized diquark model Hamiltonian, we calculate the masses of $J^{PC}=0^{++}$ ground-state tetraquarks in the following systems: $b s \bar b \bar s$, $bb \bar n \bar n$ ($n=u, d$), $bb \bar s \bar s$, $cc\bar c \bar c$, $b b \bar b \bar b$, $b c\bar b \bar c$ and $b b \bar c \bar c$. We also compute extensive spectra for the fully-heavy quark flavour combinations. Finally, as a test of the diquark model approach, we compute the masses of fully-heavy baryons in the diquark model. Our results may be compared soon to the forthcoming experimental data for fully-heavy three-quark systems., Comment: Accepted on Eur. Phys. J. C

In pure-glue QCD, gluon-gluon scattering in the $J^{PC}=0^{-+}$ channel is described by a very simple equation, especially if one considers just the leading contribution to the scattering kernel. Of all components in this kernel, only the three-gluon vertex, $V_{\mu\nu\rho}$, is poorly constrained by contemporary analyses; hence, calculations of $0^{-+}$ glueball properties serve as a clear window onto the character and form of $V_{\mu\nu\rho}$. This is important given that many modern calculations of $V_{\mu\nu\rho}$ predict the appearance of an infrared suppression in the scalar function which comes to modulate the bare vertex after the nonperturbative resummation of interactions. Such behaviour is a peculiar prediction; but we find that such suppression is essential if one is to achieve agreement with lattice-QCD predictions for the $0^{-+}$ glueball mass. It is likely, therefore, that this novel feature of $V_{\mu\nu\rho}$ is real and has observable implications for the spectrum, decays and interactions of all QCD bound-states., Comment: 6 pages, 4 figures. To appear in Eur. Phys. J. A - Letter

We present a unified description of elastic and transition form factors involving the nucleon and its resonances; in particular, the $N(1440)$, $\Delta(1232)$ and $\Delta(1600)$. We compare predictions made using a framework built upon a Faddeev equation kernel and interaction vertices that possess QCD-kindred momentum dependence with results obtained using a confining, symmetry-preserving treatment of a vector$\,\otimes\,$vector contact-interaction in a widely-used leading-order (rainbow-ladder) truncation of QCD's Dyson-Schwinger equations. This comparison explains that the contact-interaction framework produces hard form factors, curtails some quark orbital angular momentum correlations within a baryon, and suppresses two-loop diagrams in the elastic and transition electromagnetic currents. Such defects are rectified in our QCD-kindred framework and, by contrasting the results obtained for the same observables in both theoretical schemes, shows those objects which are most sensitive to the momentum dependence of elementary quantities in QCD., Comment: 10 pages, 6 figures, contribution to the proceedings of the 15th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon, MENU-2019. June 2-7, Pittsburgh, Pennsylvania, USA. arXiv admin note: text overlap with arXiv:1801.07251, arXiv:1602.02768

Pion valence, glue and sea distributions are calculated using a continuum approach to the two valence-body bound-state problem. Since the framework is symmetry preserving, physical features of the distributions are properly expressed. The analysis reveals that the emergent phenomenon of dynamical chiral symmetry breaking causes a hardening of the valence-quark distribution function, ${q}^\pi(x)$. Nevertheless, this distribution exhibits the $x\simeq 1$ behaviour predicted by quantum chromodynamics (QCD). At the scale $\zeta_2:=2\,$GeV, the following momentum fractions are predicted: $\langle x_{\rm valence} \rangle = 0.48(3)$, $\langle x_{\rm glue} \rangle = 0.41(2)$, $\langle x_{\rm sea} \rangle = 0.11(2)$. Evolving to $\zeta=5.2\,$GeV, the result for ${q}^\pi(x)$ agrees with that computed using lattice QCD. These outcomes should both spur improved analyses of existing experiments and stimulate efforts to obtain new data on the pion distribution functions using available and envisioned facilities., Comment: 13 pages, 7 figures, 2 tables

The $\gamma^\ast \gamma \to \pi^0$ transition form factor, $G(Q^2)$, is computed on the entire domain of spacelike momenta using a continuum approach to the two valence-body bound-state problem in relativistic quantum field theory: the result agrees with data obtained by the CELLO, CLEO and Belle Collaborations. The analysis unifies this prediction with that of the pion's valence-quark parton distribution amplitude (PDA) and elastic electromagnetic form factor, and demonstrates, too, that a fully self-consistent treatment can readily connect a pion PDA that is a broad, concave function at the hadronic scale with the perturbative QCD prediction for the transition form factor in the hard photon limit. The normalisation of that limit is set by the scale of dynamical chiral symmetry breaking, which is a crucial feature of the Standard Model. Understanding of the latter will thus remain incomplete until definitive transition form factor data is available on $Q^2>10\,$GeV$^2$., Comment: 9 pages, 2 figures

We sketch here an approach to the computation of generalised parton distributions (GPDs), based upon a rainbow-ladder (RL) truncation of QCD's Dyson-Schwinger equations and exemplified via the pion's valence dressed-quark GPD, $H_\pi^{\rm v}(x,\xi,t)$. Our analysis focuses on the case of zero skewness, $\xi=0$, and underlines that the impulse-approximation used hitherto to define the pion's valence dressed-quark GPD is generally invalid owing to omission of contributions from the gluons which bind dressed-quarks into the pion. A simple correction enables us to identify a practicable improvement to the approximation for $H_\pi^{\rm v}(x,0,t)$, expressed as the Radon transform of a single amplitude. Therewith we obtain results for $H_\pi^{\rm v}(x,0,t)$ and the associated impact-parameter dependent distribution, $q_\pi^{\rm v}(x,|\vec{b}_\perp|)$, which provide a qualitatively sound picture of the pion's dressed-quark structure at an hadronic scale., Comment: 4th Symposium on Prospects in the Physics of Discrete Symmetries (DISCRETE 2014); CNUM: C14-12-02.1

In order to learn effectively from measurements of generalised parton distributions (GPDs), it is desirable to compute them using a framework that can potentially connect empirical information with basic features of the Standard Model. We sketch an approach to such computations, based upon a rainbow-ladder (RL) truncation of QCD's Dyson-Schwinger equations and exemplified via the pion's valence dressed-quark GPD, $H_\pi^{\rm v}(x,\xi,t)$. Our analysis focuses primarily on $\xi=0$, although we also capitalise on the symmetry-preserving nature of the RL truncation by connecting $H_\pi^{\rm v}(x,\xi=\pm 1,t)$ with the pion's valence-quark parton distribution amplitude. We explain that the impulse-approximation used hitherto to define the pion's valence dressed-quark GPD is generally invalid owing to omission of contributions from the gluons which bind dressed-quarks into the pion. A simple correction enables us to identify a practicable improvement to the approximation for $H_\pi^{\rm v}(x,0,t)$, expressed as the Radon transform of a single amplitude. Therewith we obtain results for $H_\pi^{\rm v}(x,0,t)$ and the associated impact-parameter dependent distribution, $q_\pi^{\rm v}(x,|\vec{b}_\perp|)$, which provide a qualitatively sound picture of the pion's dressed-quark structure at an hadronic scale. We evolve the distributions to a scale $\zeta=2\,$GeV, so as to facilitate comparisons in future with results from experiment or other nonperturbative methods., Comment: 7 pages, 4 figures

A novel method is employed to compute the pion electromagnetic form factor, F_\pi(Q^2), on the entire domain of spacelike momentum transfer using the Dyson-Schwinger equation (DSE) framework in quantum chromodynamics (QCD). The DSE architecture unifies this prediction with that of the pion's valence-quark parton distribution amplitude (PDA). Using this PDA, the leading-order, leading-twist perturbative QCD result for Q^2 F_\pi(Q^2) underestimates the full computation by just 15% on Q^2>~8GeV^2, in stark contrast with the result obtained using the asymptotic PDA. The analysis shows that hard contributions to the pion form factor dominate for Q^2>~8GeV^2 but, even so, the magnitude of Q^2 F_\pi(Q^2) reflects the scale of dynamical chiral symmetry breaking, a pivotal emergent phenomenon in the Standard Model., Comment: 5 pages, 2 figures. To appear in Phys. Rev. Lett

A method is explained through which a pointwise accurate approximation to the pion's valence-quark distribution amplitude (PDA) may be obtained from a limited number of moments. In connection with the single nontrivial moment accessible in contemporary simulations of lattice-regularised quantum chromodynamics (QCD), the method yields a PDA that is a broad concave function whose pointwise form agrees with that predicted by Dyson-Schwinger equation analyses of the pion. Under leading-order evolution, the PDA remains broad to energy scales in excess of 100 GeV, a feature which signals persistence of the influence of dynamical chiral symmetry breaking. Consequently, the asymptotic distribution, \phi_\pi^asy(x), is a poor approximation to the pion's PDA at all such scales that are either currently accessible or foreseeable in experiments on pion elastic and transition form factors. Thus, related expectations based on \phi_\pi^asy(x) should be revised., Comment: 5 pages, 2 figures

Theories that support dynamical generation of a fermion mass gap are of widespread interest. The phenomenon is often studied via the Dyson-Schwinger equation (DSE) for the fermion self energy; i.e., the gap equation. When the rainbow truncation of that equation supports dynamical mass generation, it typically also possesses a countable infinity of simultaneous solutions for the dressed-fermion mass function, solutions which may be ordered by the number of zeros they exhibit. These features can be understood via the theory of nonlinear Hammerstein integral equations. Using QED3 as an example, we demonstrate the existence of a large class of gap equation truncations that possess solutions with damped oscillations. We suggest that there is a larger class, quite probably including the exact theory, which does not. The structure of the dressed-fermion--gauge-boson vertex is an important factor in deciding the issue., Comment: 8 pages, 6 figures. To appear in Phys. Rev. D

We project onto the light-front the pion's Poincare'-covariant Bethe-Salpeter wave-function, obtained using two different approximations to the kernels of QCD's Dyson-Schwinger equations. At an hadronic scale both computed results are concave and significantly broader than the asymptotic distribution amplitude, \phi_\pi^{asy}(x)=6 x(1-x); e.g., the integral of \phi_\pi(x)/\phi_\pi^{asy}(x) is 1.8 using the simplest kernel and 1.5 with the more sophisticated kernel. Independent of the kernels, the emergent phenomenon of dynamical chiral symmetry breaking is responsible for hardening the amplitude., Comment: 5 pages, 2 figures, 1 table

Studies of the structure of excited baryons are key to the N* program at Jefferson Lab. Within the first year of data taking with the Hall B CLAS12 detector following the 12 GeV upgrade, a dedicated experiment will aim to extract the N* electrocouplings at high photon virtualities Q2. This experiment will allow exploration of the structure of N* resonances at the highest photon virtualities ever yet achieved, with a kinematic reach up to Q2 = 12 GeV2. This high-Q2 reach will make it possible to probe the excited nucleon structures at distance scales ranging from where effective degrees of freedom, such as constituent quarks, are dominant through the transition to where nearly massless bare-quark degrees of freedom are relevant. In this document, we present a detailed description of the physics that can be addressed through N* structure studies in exclusive meson electroproduction. The discussion includes recent advances in reaction theory for extracting N* electrocouplings from meson electroproduction off protons, along with QCD-based approaches to the theoretical interpretation of these fundamental quantities. This program will afford access to the dynamics of the non-perturbative strong interaction responsible for resonance formation, and will be crucial in understanding the nature of confinement and dynamical chiral symmetry breaking in baryons, and how excited nucleons emerge from QCD., Comment: 91 pages, 52 figures

We present a workable model for the fermion-photon vertex, which is expressed solely in terms of functions that appear in the fermion propagator and independent of the angle between the relative momenta, and does not explicitly depend on the covariant-gauge parameter. It nevertheless produces a critical coupling for dynamical chiral symmetry breaking that is practically independent of the covariant-gauge parameter and an anomalous magnetic moment distribution for the dressed fermion that agrees in important respects with realistic numerical solutions of the inhomogeneous vector Bethe-Salpeter equation., Comment: 8 pages, 2 figures

We compute nucleon and Roper e.m. elastic and transition form factors using a symmetry-preserving treatment of a contact-interaction. Obtained thereby, the e.m. interactions of baryons are typically described by hard form factors. In contrasting this behaviour with that produced by a momentum-dependent interaction, one achieves comparisons which highlight that elastic scattering and resonance electroproduction experiments probe the infrared evolution of QCD's running masses; e.g., the existence, and location if so, of a zero in the ratio of nucleon Sachs form factors are strongly influenced by the running of the dressed-quark mass. In our description of baryons, diquark correlations are important. These correlations are instrumental in producing a zero in the Dirac form factor of the proton's d-quark; and in determining d_v/u_v(x=1), as we show via a formula that expresses d_v/u_v(x=1) in terms of the nucleon's diquark content. The contact interaction produces a first excitation of the nucleon that is constituted predominantly from axial-vector diquark correlations. This impacts greatly on the gamma*p->P_{11}(1440) form factors. Notably, our quark core contribution to F_2*(Q^2) exhibits a zero at Q^2~0.5mN^2. Faddeev equation treatments of a hadron's quark core usually underestimate its magnetic properties, hence we consider the effect produced by a dressed-quark anomalous e.m. moment. Its inclusion much improves agreement with experiment. On the domain 0

We provide an inkling of recent progress in hadron physics made using QCD's Dyson-Schwinger equations, reviewing: the notion of in-hadron condensates and a putative solution of a gross problem with the cosmological constant; a symmetry-preserving computation that simultaneously correlates the masses of meson and baryon ground- and excited-states, and contributes to a resolution of the conundrum of the Roper resonance; and a prediction for the Q^2-dependence of u- and d-quark Dirac and Pauli form factors in the proton, which exposes the critical role played by diquark correlations within the nucleon., Comment: 7 pages, 2 figures. Plenary-based contribution to the Proceedings of the International Conference on the Structure of Baryons - Baryons 2010, Suita Campus, Osaka University, Japan 7-11 December 2010

We present a unified Dyson-Schwinger equation treatment of static and electromagnetic properties of pseudoscalar and vector mesons, and scalar and axial-vector diquark correlations, based upon a vector-vector contact-interaction. A basic motivation for this study is the need to document a comparison between the electromagnetic form factors of mesons and those diquarks which play a material role in nucleon structure. This is an important step toward a unified description of meson and baryon form factors based on a single interaction. A notable result, therefore, is the large degree of similarity between related meson and diquark form factors. The simplicity of the interaction enables computation of the form factors at arbitrarily-large spacelike-Q^2, which enables us to expose a zero in the rho-meson electric form factor at z_Q^\rho ~ Sqrt[6] m_\rho. Notably, r_\rho*z_Q^\rho ~ r_D*z_Q^D, where r_\rho, r_D are, respectively, the electric radii of the rho-meson and deuteron., Comment: 12 pages, 7 figures, 2 tables

We present the first Dyson-Schwinger equation calculation of the light hadron spectrum that simultaneously correlates the masses of meson and baryon ground- and excited-states within a single framework. At the core of our analysis is a symmetry-preserving treatment of a vector-vector contact interaction. In comparison with relevant quantities the root-mean-square-relative-error/degree-of freedom is 13%. Notable amongst our results is agreement between the computed baryon masses and the bare masses employed in modern dynamical coupled-channels models of pion-nucleon reactions. Our analysis provides insight into numerous aspects of baryon structure; e.g., relationships between the nucleon and Delta masses and those of the dressed-quark and diquark correlations they contain., Comment: 25 pages, 7 figures, 4 tables

We provide a glimpse of recent progress in hadron physics made using QCD's Dyson-Schwinger equations, reviewing: the notion of in-hadron condensates and a putative solution of a gross problem with the cosmological constant; the dynamical generation of quark anomalous chromo- and electro-magnetic moments, and their material impact upon the proton's electric/magnetic form factor ratio; a computation that simultaneously correlates the masses of meson and baryon ground- and excited-states; and a prediction for the x->1 value of the ratio of neutron/proton distribution functions., Comment: 7 pages, 3 figures. Contribution to the proceedings of "T(r)opical QCD 2010: Cairns CSSM 2010 Workshop," Cairns Colonial Club, Cairns, Australia, 26 September - 1 October

We show that in fully-self-consistent treatments of the pion; namely, its static properties and elastic and transition form factors, the asymptotic limit of the product Q^2 G_{\gamma * \gamma \pi ^0}(Q^2), determined a priori by the interaction employed, is not exceeded at any finite value of spacelike momentum transfer. Furthermore, in such a treatment of a vector-vector contact-interaction one obtains a \gamma * \gamma -> \pi ^0 transition form factor that disagrees markedly with all available data. We explain that the contact interaction produces a pion distribution amplitude which is flat and nonvanishing at the endpoints. This amplitude characterises a pointlike pion bound-state. Such a state has the hardest possible form factors; i.e., form factors which become constant at large momentum transfers and hence are in striking disagreement with completed experiments. On the other hand, interactions with QCD-like behaviour produce soft pions, a valence-quark distribution amplitude that vanishes as ~(1-x)^2 for x~1, and results that agree with the bulk of existing data. Our analysis supports a view that the large-Q^2 data obtained by the BaBar Collaboration is not an accurate measure of the \gamma * \gamma -> \pi ^0 form factor., Comment: 11 pages, 6 figures

We provide a glimpse of recent progress in meson physics made via QCD's Dyson-Schwinger equations with: a perspective on confinement and dynamical chiral symmetry breaking (DCSB); a pre'cis on the physics of in-hadron condensates; results for the masses of the \pi, \sigma, \rho, a_1 mesons and their first-radial excitations; and an illustration of the impact of DCSB on the pion form factor., Comment: 6 pages, 3 figures, 1 table. Contribution to Proceedings of the 11th International Workshop on Meson Production, Properties and Interaction, Uniwersytet Jagiellonski, Instytut Fizyki, Krakow, Poland, 10-15 June 2010

This snapshot of recent progress in hadron physics made in connection with QCD's Dyson-Schwinger equations includes: a perspective on confinement and dynamical chiral symmetry breaking (DCSB); a pre'cis on the physics of in-hadron condensates; results on the hadron spectrum, including dressed-quark-core masses for the nucleon and Delta, their first radial excitations, and the parity-partners of these states; an illustration of the impact of DCSB on the electromagnetic pion form factor, thereby exemplifying how data can be used to chart the momentum-dependence of the dressed-quark mass function; and a prediction that F_1^{p,d}/F_1^{p,u} passes through zero at Q^2\approx 5m_N^2 owing to the presence of nonpointlike scalar and axial-vector diquark correlations in the nucleon., Comment: 10 pages, 4 figures, 2 tables. Contribution to the Proceedings of the 4th Workshop on Exclusive Reactions at High Momentum Transfer, Thomas Jefferson National Accelerator Facility Newport News, Virginia, 18-21 May 2010

We present a proposal for testing the prediction of non-equilibrium quantum field theory below the Schwinger limit. The proposed experiments should be able to detect a measurable number of gamma rays resulting from the annihilation of pairs in the focal spot of two opposing high intensity laser beams. We discuss the dependence of the expected number of gamma rays with the laser parameters and compare with the estimated background level of gamma hits for realistic laser conditions., Comment: 14 pages, 1 table

In a Poincare'-covariant vector-boson-exchange theory, the pion possesses components of pseudovector origin, which materially influence its observable properties. For a range of such quantities, we explore the consequences of a momentum-independent interaction, regularised in a symmetry-preserving manner. The contact interaction, whilst capable of describing pion static properties, produces a form factor whose: evolution for Q^2>0.17GeV^2 disagrees markedly with experiment; and asymptotic power-law behaviour conflicts strongly with perturbative-QCD., Comment: 5 pages

We review theoretical approaches to form factors that arise in heavy-meson decays and are hadronic expressions of non-perturbative QCD. After motivating their origin in QCD factorisation, we retrace their evolution from quark-model calculations to non-perturbative QCD techniques with an emphasis on formulations of truncated heavy-light amplitudes based upon Dyson-Schwinger equations. We compare model predictions exemplarily for the B\to\pi transition form factor and discuss new results for the g_{D*D\pi} coupling in the hadronic D* decay., Comment: Based on a talk given at Light Cone 2009: Relativistic Hadronic And Particle Physics, 8-13 July 2009, Sao Jose dos Campos, Sao Paulo, Brazil

This document outlines major directions in theoretical support for the measurement of nucleon resonance transition form factors at the JLab 12 GeV upgrade with the CLAS12 detector. Using single and double meson production, prominent resonances in the mass range up to 2 GeV will be studied in the range of photon virtuality $Q^2$ up to 12 GeV$^2$ where quark degrees of freedom are expected to dominate. High level theoretical analysis of these data will open up opportunities to understand how the interactions of dressed quarks create the ground and excited nucleon states and how these interactions emerge from QCD. The paper reviews the current status and the prospects of QCD based model approaches that relate phenomenological information on transition form factors to the non-perturbative strong interaction mechanisms, that are responsible for resonance formation., Comment: 52 pages, 19 figures, White Paper of the Electromagnetic N-N* Transition Form Factor Workshop at Jefferson Lab, October 13-15, 2008, Newport News, VA, USA