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Quantum field theory predicts a nonlinear response of the vacuum to strong electromagnetic fields of macroscopic extent. This fundamental tenet has remained experimentally challenging and is yet to be tested in the laboratory. A particularly distinct signature of the resulting optical activity of the quantum vacuum is vacuum birefringence. This offers an excellent opportunity for a precision test of nonlinear quantum electrodynamics in an uncharted parameter regime. Recently, the operation of the high-intensity laser ReLaX provided by the Helmholtz International Beamline for Extreme Fields (HIBEF) has been inaugurated at the High Energy Density (HED) scientific instrument of the European XFEL. We make the case that this worldwide unique combination of an x-ray free-electron laser and an ultra-intense near-infrared laser together with recent advances in high-precision x-ray polarimetry, refinements of prospective discovery scenarios, and progress in their accurate theoretical modelling have set the stage for performing an actual discovery experiment of quantum vacuum nonlinearity., Comment: 34 pages, 21 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

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

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

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

Solutions of a kinetic equation are investigated which describe, on a nonperturbative basis, the vacuum creation of quasiparticle electron-positron pairs due to a strong laser field. The dependence of the quasiparticle electron (positron) distribution function and the particle number density is explored in a wide range of the laser radiation parameters, i.e., the wavelength \lambda and amplitude of electric field strength E_0. Three domains are found: the domain of vacuum polarization effects where the density of the e-e+ pairs is small (the "calm valley"), and two accumulation domains in which the production rate of the e-e+ pairs is strongly increased and the e-e+ pair density can reach a significant value (the short wave length domain and the strong field one). In particular, the obtained results point to a complicated short-distance electromagnetic structure of the physical vacuum in the domain of short wavelengths \lambda \lessim \lambda_{acc} = \pi/m. For moderately strong fields E_0 \lesssim E_c=m^2/e, the accumulation regime can be realized where a plasma with a high density of e-e+ quasiparticles can be achieved. In this domain of the field strengths and in the whole investigated range of wavelengths, an observation of the dynamical Schwinger effect can be facilitated., Comment: 13 pages, 17 figures, references added, version accepted for publication 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

We consider the one-photon annihilation mechanism in a electron - positron quasiparticle plasma (EPP) created from the vacuum in a strong subcritical laser field due to the dynamical Schwinger mechanism. On the basis of a kinetic theory approach we show that the secondary photons have a radiation spectrum proportional to 1/k (flicker noise). This effect is very small for EPP excitations in the optical spectrum but can reach quite observable values in the gamma - ray region., Comment: 6 pages

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 the present work a closed system of kinetic equations is obtained for the description of the vacuum creation of an electron - positron plasma and secondary photons due to a strong laser field. An estimate for the photon energy distribution is obtained. In the Markovian approximation the photon distribution has a 1/k spectrum (flicker noise)., Comment: 6 pages, contribution to Proceedings of the International Bogolyubov Conference, Dubna (Russia), August 21-27, 2009

We consider the possibility of experimental verification of vacuum e^+e^- pair creation at the focus of two counter-propagating optical laser beams with intensities 10^{20}-10^{22} W/cm^2, achievable with present-day petawatt lasers, and approaching the Schwinger limit: 10^{29} W/cm^2 to be reached at ELI. Our approach is based on the collisionless kinetic equation for the evolution of the e^+ and e^- distribution functions governed by a non-Markovian source term for pair production. As possible experimental signals of vacuum pair production we consider e^+e^- annihilation into gamma-pairs and the refraction of a high-frequency probe laser beam by the produced e^+e^- plasma. We discuss the dependence of the dynamical pair production process on laser wavelength, with special emphasis on applications in the X-ray domain (X-FEL), as well as the prospects for \mu^+\mu^- and \pi^+\pi^- pair creation at high-intensity lasers. We investigate perspectives for using high-intensity lasers as ``boosters'' of ion beams in the few-GeV per nucleon range, which is relevant, e.g., to the exploration of the QCD phase transition in laboratory experiments., Comment: 18 pages, 23 figues, 2 tables, contribution to the topical issue of The European Physical Journal D on "Fundamental physics and unltra-high laser fields"

Electron-positron pair creation in a standing wave is explored using a parameter-free quantum kinetic equation. Field strengths and frequencies corresponding to modern optical lasers induce a material polarisation of the QED vacuum, which may be characterised as a plasma of e^+ e^- quasiparticle pairs with a density of ~10^{20}cm^{-3}. The plasma vanishes almost completely when the laser field is zero, leaving a very small residual pair density, n_r, which is the true manifestation of vacuum decay. The average pair density per period is proportional to the laser intensity but independent of the frequency, \nu. The density of residual pairs also grows with laser intensity but n_r \propto \nu^2. With optical lasers at the forefront of the current generation, these dynamical QED vacuum effects may generate 5-10 observable two-photon annihilation events per laser pulse., Comment: 4 pages, 3 figures

A continuum expression for the trace of the massive dressed-quark propagator is used to explicate a connection between the infrared limit of the QCD Dirac operator's spectrum and the quark condensate appearing in the operator product expansion, and the connection is verified via comparison with a lattice-QCD simulation. The pseudoscalar vacuum polarisation provides a good approximation to the condensate over a larger range of current-quark masses., Comment: 7 pages, LaTeX2e, revtex4

We study particle - antiparticle pair production under action of a strong time dependent space homogeneous electric field at the presence of a collinear constant magnetic field. We derive the kinetic equation for a such field configuration for fermions and bosons in the framework of the Schwinger mechanism of vacuum tunneling. We show the enhancement of pair production for fermions with the increasing of the magnetic field as in the case of the constant electromagnetic field. We have constructed closed set of equations, which can be applied to some actual problems with manifestation of strong electromagnetic fields, e.g., it is essential in the framework of the Flux Tube Model of Quark - Gluon Plasma generation; for describing some cosmological objects and especially because of the planned experiments on creation of subcritical fields in the X-Free Electron Laser pulses., Comment: 8 pages, 2 figures

The gap equation is a cornerstone in understanding dynamical chiral symmetry breaking and may also provide clues to confinement. A symmetry-preserving truncation of its kernel enables proofs of important results and the development of an efficacious phenomenology. We describe a model of the kernel that yields: a momentum-dependent dressed-quark propagator in fair agreement with quenched lattice-QCD results; and chiral limit values: f_pi= 68 MeV and = -(190 MeV)^3. It is compared with models inferred from studies of the gauge sector., Comment: 5 pages, 3 figures; contribution to the proceedings of Quark Nuclear Physics (QNP 2002), Juelich, Germany, 9-14 Jun 2002

A quantum kinetic equation coupled with Maxwell's equation is used to estimate the laser power required at an XFEL facility to expose intrinsically quantum effects in the process of QED vacuum decay via spontaneous pair production. A 9 TW-peak XFEL laser with photon energy 8.3 keV could be sufficient to initiate particle accumulation and the consequent formation of a plasma of spontaneously produced pairs. The evolution of the particle number in the plasma will exhibit non-Markovian aspects of the strong-field pair production process and the plasma's internal currents will generate an electric field whose interference with that of the laser leads to plasma oscillations., Comment: 4 pages, LaTeX2e

We derive quantum kinetic equations for fermion and boson production starting from a phi^4 Lagrangian with minimal coupling to fermions. Decomposing the scalar field into a mean-field part and fluctuations we obtain spontaneous pair creation driven by a self-interacting strong background field. The produced fermion and boson pairs are self-consistently coupled. Consequently back reactions arise from fermion and boson currents determining the time dependent self-interacting background mean-field. We explore the numerical solution in flux tube geometry for the time evolution of the mean-field as well as for the number- and energy densities for fermions and bosons. We find that after a characteristic time all energy is converted from the background mean-field to particle creation. Applying this general approach to the production of ``quarks'' and ``gluons'' a typical time scale for the collapse of the flux tube is 1.5 fm/c., Comment: 9 pages, latex, epsfig, 7 figures

Poincare' covariant Faddeev equations for the nucleon and Delta are solved to illustrate that an internally consistent description in terms of confined-quark and nonpointlike confined-diquark-correlations can be obtained. pi N-loop induced self-energy corrections to the nucleon's mass are analysed and shown to be independent of whether a pseudoscalar or pseudovector coupling is used. Phenomenological constraints suggest that this self-energy correction reduces the nucleon's mass by up to several hundred MeV. That effect does not qualitatively alter the picture, suggested by the Faddeev equation, that baryons are quark-diquark composites. However, neglecting the pi-loops leads to a quantitative overestimate of the nucleon's axial-vector diquark component., Comment: 17 pages, 6 figures, REVTEX4

These proceedings contain research results presented during the Workshops "Quark Matter in Astro- and Particle Physics" held at the University of Rostock, November 27-29, 2000 and "Dynamical Aspects of the QCD Phase Transition" held at the ECT* in Trento, March 12-15, 2001., Comment: 206 pages, Proceedings of the Workshops on "Quark Matter in Astro- and Particle Physics", Rostock, November 2000, and "Dynamical Aspects of the QCD Phase Transition", Trento, March 2001. Listed authors are the editors

The production of (eta,eta')- mesons during the decay of a CP-odd phase is studied within an evolution operator approach. We derive a quantum kinetic equation starting from the Witten-DiVecchia-Veneziano Lagrangian for pseudoscalar mesons containing a U_A(1) symmetry breaking term. The non-linear vacuum mean field for the flavour singlet pseudoscalar meson is treated as a classical, self-interacting background field with fluctuations assumed to be small. The numerical solution provides the time evolution of momentum distribution function of produced eta'- mesons after a quench at the deconfinement phase transition. We show that the time evolution of the momentum distribution of the produced mesons depend strongly on the shape of the effective potential at the end of the quench, exhibiting either parametric or tachyonic resonances. Quantum statistical effects are essential and lead to a pronounced Bose enhancement of the low momentum states., Comment: 10 pages, latex, epsfig, 6 figures

Using a quantum kinetic equation coupled to Maxwell's equation we study the possibility that focused beams at proposed X-ray free electron laser facilities can generate electric field strengths large enough to cause spontaneous electron-positron pair production from the QED vacuum. Our approach yields the time and momentum dependence of the single particle distribution function. Under conditions reckoned achievable at planned facilities, repeated cycles of particle creation and annihilation take place in tune with the laser frequency. However, the peak particle number density is insensitive to this frequency and one can anticipate the production of a few hundred particle pairs per laser period. Field-current feedback and quantum statistical effects are small and can be neglected in this application of non-equilibrium quantum mean field theory., Comment: 4 pages, LaTeX2e

A succinct review of the QCD gap equation and dynamical chiral symmetry breaking; their connection with Bethe-Salpeter equations and resolving the dichotomous nature of the pion; the calculation of the pion's valence-quark distribution; and first results for the pi-exchange contribution to the gamma N -> omega N cross-section, which is important in the search for missing nucleon resonances., Comment: 9 pages, LaTeX2e, ws-p8-50x6-00.cls, Contribution to the Proceedings of the "Workshop on Lepton-Scattering, Hadrons and QCD," Adelaide, 26 March-6 April, 2001

Aspects of the formation and equilibration of a quark-gluon plasma are explored using a quantum kinetic equation, which involves a non-Markovian, Abelian source term for quark and antiquark production and, for the collision term, a relaxation time approximation that defines a time-dependent quasi-equilibrium temperature and collective velocity. The strong Abelian field is determined via the simultaneous solution of Maxwell's equation. A particular feature of this approach is the appearance of plasma oscillations in all thermodynamic observables. Their presence can lead to a sharp increase in the time-integrated dilepton yield., Comment: 9 pages, latex, epsfig, 14 figures

Contributions to the neutron's EDM, are calculated using a well-constrained Ansatz for the nucleon's Poincare' covariant Fadde'ev amplitude. The momentum-dependent quark dressing amplifies the contribution from the current-quarks' EDMs; and dressed-quark confinement and binding make distinguishable the effect of the two CP and T violating interactions: i gamma_5 sigma_{mu nu} (p_1-p_2)_nu and gamma_5 (p_1+p_2)_mu, where p_{1,2} are the current-quarks' momenta. The value of |d_n| obtained using the current-quark EDMs generated by a minimal three Higgs doublet model of spontaneous CP violation is close to the current experimental upper bound., Comment: 9 pages, LaTeX2e. Errors in Table 1 corrected; five references added. To appear in Phys. Rev. C

We describe aspects of particle creation in strong fields using a quantum kinetic equation with a relaxation-time approximation to the collision term. The strong electric background field is determined by solving Maxwell's equation in tandem with the Vlasov equation. Plasma oscillations appear as a result of feedback between the background field and the field generated by the particles produced. The plasma frequency depends on the strength of the initial background field and the collision frequency, and is sensitive to the necessary momentum-dependence of dressed-parton masses., Comment: 11 pages, revteX, epsfig.sty, 5 figures; Proceedings of 'Quark Matter in Astro- and Particlephysics', a workshop at the University of Rostock, Germany, November 27 - 29, 2000. Eds. D. Blaschke, G. Burau, S.M. Schmidt

We describe aspects of the role that diquark correlations play in understanding baryon structure and interactions. The significance of diquarks in that application motivates a study of the possibility that dense hadronic matter may exhibit diquark condensation; i.e., quark-quark pairing promoted by a quark chemical potential. A Gorkov-Nambu-like gap equation is introduced for QCD and analysed for 2-colour QCD (QC2D) and, in two qualitatively different truncations, for QCD itself. Among other interesting features, we illustrate that QC2D with massive fermions undergoes a second-order transition to a superfluid phase when the chemical potential exceeds 0.5 m.pi. In the QCD application we illustrate that the sigma= .neq. 0 phase, which determines the properties of the mass spectrum at zero temperature and chemical potential, is unstable with respect to the superfluid phase when the chemical potential exceeds approx. 2 sigma, and that at this point the diquark gap is large, approx. 0.5 sigma. The superfluid phase survives to temperatures greater than that expected in the core of compact stars., Comment: 16 pages, LaTeX2e, Contribution to the Proceedings of "Physics of Neutron Star Interiors," a workshop at ECT$\ast$, Trento, Italy, June-July/2000, Eds. D. Blaschke, N.K. Glendenning and A. Sedrakian. No changes

The contemporary use of Dyson-Schwinger equations in hadronic physics is exemplified via applications to the calculation of pseudoscalar meson masses, and inclusive deep inelastic scattering with a determination of the pion's valence-quark distribution function., Comment: 4 pages. Contribution to the Proceedings of ``DPF 2000,'' the Meeting of the Division of Particles and Fields of the American Physical Society, August 9-12, 2000, Department of Physics, the Ohio State University, Columbus, Ohio

We illustrate the contemporary application of Dyson-Schwinger equations using two examples: the calculation of pseudoscalar meson masses, an associated model-independent mass formula and the approach to the heavy-quark limit; and the study of nucleon observables, including a calculation of its mass, $M$, via a covariant Fadde'ev equation and an estimate of pion-loop contributions to $M$., Comment: 13 pages, 1 figure. Contribution to the Proceedings of ``Confinement IV: The 4th International Conference on Quark Confinement and the Hadron Spectrum,'' 3-8/Jul./2000, Vienna, Austria

We calculate the pion's valence-quark momentum-fraction probability distribution using a Dyson-Schwinger equation model. Valence-quarks with an active mass of 0.30 GeV carry 71% of the pion's momentum at a resolving scale q_0=0.54 GeV = 1/(0.37 fm). The shape of the calculated distribution is characteristic of a strongly bound system and, evolved from q_0 to q=2 GeV, it yields first, second and third moments in agreement with lattice and phenomenological estimates, and valence-quarks carrying 49% of the pion's momentum. However, pointwise there is a discrepancy between our calculated distribution and that hitherto inferred from parametrisations of extant pion-nucleon Drell-Yan data., Comment: 8 pages, 3 figures, REVTEX, aps.sty, epsfig.sty, minor corrections, version to appear in PRC

A perspective on the contemporary use of Dyson-Schwinger equations, focusing on some recent phenomenological applications: a description and unification of light-meson observables using a one-parameter model of the effective quark-quark interaction, and studies of leptonic and nonleptonic nucleon form factors., Comment: 7 pages, sprocl.sty, epsfig.sty. Contribution to the Proceedings of the Workshop on Light-Cone QCD and Nonperturbative Hadron Physics, Adelaide, Australia, 13-22 Dec 1999

Continuum strong QCD is the application of models and continuum quantum field theory to the study of phenomena in hadronic physics, which includes; e.g., the spectrum of QCD bound states and their interactions; and the transition to, and properties of, a quark gluon plasma. We provide a contemporary perspective, couched primarily in terms of the Dyson-Schwinger equations but also making comparisons with other approaches and models. Our discourse provides a practitioners' guide to features of the Dyson-Schwinger equations [such as confinement and dynamical chiral symmetry breaking] and canvasses phenomenological applications to light meson and baryon properties in cold, sparse QCD. These provide the foundation for an extension to hot, dense QCD, which is probed via the introduction of the intensive thermodynamic variables: chemical potential and temperature. We describe order parameters whose evolution signals deconfinement and chiral symmetry restoration, and chronicle their use in demarcating the quark gluon plasma phase boundary and characterising the plasma's properties. Hadron traits change in an equilibrated plasma. We exemplify this and discuss putative signals of the effects. Finally, since plasma formation is not an equilibrium process, we discuss recent developments in kinetic theory and its application to describing the evolution from a relativistic heavy ion collision to an equilibrated quark gluon plasma., Comment: 103 Pages, LaTeX, epsfig. To appear in Progress in Particle and Nuclear Physics, Vol. 45

We describe some applications of the Dyson-Schwinger equations at nonzero-(T,mu). Employing a simple model dressed-gluon propagator we determine the boundary of the deconfinement phase transition and the medium dependence of rho-meson properties. We introduce an extension to describe the time-evolution of scalar and vector self energies., Comment: 6 pages, LaTeX with 3 EPS figures; Contribution to the 'International Workshop XXVIII on Gross Properties of Nuclei and Nuclear Excitations', Hirschegg, Austria, 16-22.01.2000

Inhomogeneous pseudoscalar and scalar Bethe-Salpeter equations solved using a renormalisation-group-improved rainbow-ladder truncation exhibit bound state poles below and above T_c, the critical temperature for chiral symmetry restoration. Above T_c the bound state amplitudes are identical, as are the positions and residues of the pseudoscalar and scalar poles in the vertices. In the chiral limit the pi^0 -> gamma gamma coupling vanishes at T_c, as do f_pi, m_sigma, g_{sigma pi pi}. For light current-quark masses the 2-pi decay channel of the isoscalar-scalar meson remains open until very near T_c, and the widths of the dominant pion decay modes remain significant in the vicinity of the crossover., Comment: 11 pages, REVTEX, 10 figures, epsfig

A covariant, composite scalar diquark, Fadde'ev amplitude model for the nucleon is used to calculate pseudoscalar, isoscalar- and isovector-vector, axial-vector and scalar nucleon form factors. The last yields the nucleon sigma-term and on-shell sigma-nucleon coupling. The calculated form factors are soft, and the couplings are generally in good agreement with experiment and other determinations. Elements in the dressed-quark-axial-vector vertex that are not constrained by the Ward-Takahashi identity contribute ~20% to the magnitude of g_A. The calculation of the nucleon sigma-term elucidates the only unambiguous means of extrapolating meson-nucleon couplings off the meson mass-shell., Comment: 12 pages, REVTEX, 5 figures, epsfig

We study the evolution of a strong field plasma using a quantum Vlasov equation with a non-Markovian source term and a simple collision term, and calculate the time dependence of the energy- and number-density, and the temperature. The evolution of a plasma produced with RHIC-like initial conditions is well described by a low density approximation to the source term. However, non-Markovian aspects should be retained to obtain an accurate description of the early stages of an LHC-like plasma., Comment: 4 pages, REVTEX, 3 figures, epsfig.sty

We explore the Delta-I= 1/2 rule and epsilon'/epsilon in K -> pi pi transitions using a Dyson-Schwinger equation model. Exploiting the feature that QCD penguin operators direct K^0_S transitions through 0^{++} intermediate states, we find an explanation of the enhancement of I=0 K -> pi pi transitions in the contribution of a light sigma-meson. This mechanism also affects epsilon'/epsilon., Comment: 7 pages, REVTEX

Nucleon form factors are calculated on q^2 in [0,3] GeV^2 using an Ansatz for the nucleon's Fadde'ev amplitude motivated by quark-diquark solutions of the relativistic Fadde'ev equation. Only the scalar diquark is retained, and it and the quark are confined. A good description of the data requires a nonpointlike diquark correlation with an electromagnetic radius of 0.8 r_pi. The composite, nonpointlike nature of the diquark is crucial. It provides for diquark-breakup terms that are of greater importance than the diquark photon absorption contribution., Comment: 5 pages, REVTEX, epsfig, 3 figures

We employ a bispinor gap equation to study superfluidity at nonzero chemical potential: mu .neq. 0, in two- and three-colour QCD. The two-colour theory, QC2D, is an excellent exemplar: the order of truncation of the quark-quark scattering kernel: K, has no qualitative impact, which allows a straightforward elucidation of the effects of mu when the coupling is strong. In rainbow-ladder truncation, diquark bound states appear in the spectrum of the three-colour theory, a defect that is eliminated by an improvement of K. The corrected gap equation describes a superfluid phase that is semi-quantitatively similar to that obtained using the rainbow truncation. A model study suggests that the width of the superfluid gap and the transition point in QC2D provide reliable quantitative estimates of those quantities in QCD., Comment: 7 pages, 3 figures, REVTEX, epsfig

We solve the quantum Vlasov equation for fermions and bosons, incorporating spontaneous pair creation in the presence of back-reactions and collisions. Pair creation is initiated by an external impulse field and the source term is non-Markovian. A simultaneous solution of Maxwell's equation in the presence of feedback yields an internal current and electric field that exhibit plasma oscillations with a period tau_pl. Allowing for collisions, these oscillations are damped on a time-scale, tau_r, determined by the collision frequency. Plasma oscillations cannot affect the early stages of the formation of a quark-gluon plasma unless tau_r >> tau_pl and tau_pl approx. 1/Lambda_QCD approx 1 fm/c., Comment: 16 pages, 6 figure, REVTEX, epsfig.sty