H. L. L. Roberts, L. Chang, I. C. Cloet, C. D. Roberts
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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
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.
Quenched lattice-QCD data on the dressed-quark Schwinger function can be correlated with dressed-gluon data via a rainbow gap equation so long as that equation's kernel possesses enhancement at infrared momenta above that exhibited by the gluon alone. The required enhancement can be ascribed to a dressing of the quark-gluon vertex. The solutions of the rainbow gap equation exhibit dynamical chiral symmetry breaking and are consistent with confinement. The gap equation and related, symmetry-preserving ladder Bethe-Salpeter equation yield estimates for chiral and physical pion observables that s…
The structure of hadrons is described well by the Nambu--Jona-Lasinio (NJL) model, which is a chiral effective quark theory of QCD. In this work we explore the electromagnetic structure of the pion and kaon using the three-flavor NJL model, including effects of confinement and a pion cloud at the quark level. In the calculation there is only one free parameter, which we take as the dressed light quark ($u$ and $d$) mass. In the regime where the dressed light quark mass is approximately $0.25\,$GeV, we find that the calculated values of the kaon decay constant, current quark masses, and quark c…
Perturbation theory predicts that a massless fermion cannot possess a measurable magnetic moment. We explain, however, that the nonperturbative phenomenon of dynamical chiral symmetry breaking generates a momentum-dependent anomalous chromomagnetic moment for dressed light-quarks, which is large at infrared momenta; and demonstrate that consequently these same quarks also possess an anomalous electromagnetic moment with similar magnitude and opposite sign.
A Dyson-Schwinger equation calculation of the light hadron spectrum, which correlates the masses of meson and baryon ground- and excited-states within a single framework, produces a description of the Roper resonance that corresponds closely with conclusions drawn recently by EBAC. Namely, the Roper is a particular type of radial excitation of the nucleon's dressed-quark core augmented by a material meson cloud component. There are, in addition, some surprises.
The proton is arguably the most fundamental of Nature's readily detectable building blocks. It is at the heart of every nucleus and has never been observed to decay. It is nevertheless a composite object, defined by its valence-quark content: u+u+d -- i.e., two up (u) quarks and one down (d) quark; and the manner by which they influence, inter alia, the distribution of charge and magnetisation within this bound-state. Much of novelty has recently been learnt about these distributions; and it now appears possible that the proton's momentum-space charge distribution possesses a zero. Experiments…
The nucleon's axial charge, g_A, expresses features that are both fundamental to the strong interaction and crucial to its connection with weak interaction physics. We show that dynamical chiral symmetry breaking (DCSB) suppresses the axial-charge of a dressed-quark, g_A^q, at infrared momenta. Since this effect disappears as chiral symmetry is restored, one may argue that g_A vanishes with the restoration of chiral symmetry because no nucleon bound-state survives the associated transition. The suppression of g_A^q is shown to be part of an explanation for a 25% reduction of g_A from its nonre…
We present preliminary results on the longitudinal $and$ transverse form factors of the quark-gluon vertex as functions of the incoming and outgoing quark momenta and an angle $θ=2π/3$ between them. The expressions for these form factors were previously derived from Slavnov-Taylor identities, gauge covariance and multiplicative renormalizability that firmly constrain the fermion-boson vertex.
We construct the quark-antiquark scattering kernels of Bethe-Salpeter equation from the quark self-energy directly under two specific forms of quark-gluon vertices. The quark dressed tensor vertex is then calculated within this consistent framework and rainbow-ladder(RL) approximation. After employing a simplified nucleon model, the nucleon tensor charge can be defined with the tensor vertex. We then compute the tensor charge with the bare tensor vertex and the dressed vertices obtained in this framework and in RL approximation. The obtained results are consistent with the lattice QCD calculat…
We elucidate constraints imposed by confinement and dynamical chiral symmetry breaking on the infrared behaviour of the dressed-quark and -gluon propagators, and dressed-quark-gluon vertex. In covariant gauges the dressing of the gluon propagator is completely specified by P(k^2):= 1/[1+Pi(k^2)], where Pi(k^2) is the vacuum polarisation. In the absence of particle-like singularities in the dressed-quark-gluon vertex, extant proposals for the dressed-gluon propagator that manifest P(k^2=0)=0 and Max[P(k^2)]~10 neither confine quarks nor break chiral symmetry dynamically. This class includes all…
Features of the dressed-quark-gluon vertex and their role in the gap and Bethe-Salpeter equations are explored. It is argued that quenched lattice data indicate the existence of net attraction in the colour-octet projection of the quark-antiquark scattering kernel. This attraction affects the uniformity with which solutions of truncated equations converge pointwise to solutions of the complete gap and vertex equations. For current-quark masses less than the scale set by dynamical chiral symmetry breaking, the dependence of the dressed-quark-gluon vertex on the current-quark mass is weak. The s…
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, $H_π^{\rm v}(x,ξ,t)$. Our analysis focuses primarily on $ξ=0$, although we also capitalise on the symmetry-preserving nature of the RL truncation by connecting $H_π^{\rm v}(x,ξ=\pm 1,…
A Ward-Takahashi identity preserving Bethe-Salpeter kernel can always be calculated explicitly from a dressed-quark-gluon vertex whose diagrammatic content is enumerable. We illustrate that fact using a vertex obtained via the complete resummation of dressed-gluon ladders. While this vertex is planar, the vertex-consistent kernel is nonplanar and that is true for any dressed vertex. In an exemplifying model the rainbow-ladder truncation of the gap and Bethe-Salpeter equations yields many results; e.g., pi- and rho-meson masses, that are changed little by including higher-order corrections. Rep…
We construct a quark target model (QTM) to incorporate intrinsic glue into effective low-energy models of QCD, which often contain only quark degrees of freedom. This method guarantees the gauge invariance of observables order-by-order in the strong coupling. The quark and gluon PDFs for the dressed quarks are obtained in the QTM at leading order. We demonstrate gauge invariance of the results by comparing both covariant and light cone gauges, with the former including an explicit Wilson line contribution. A key finding is that in covariant gauges the Wilson line can carry a significant amount…
The radiative capture process $n p \to d γ$ is considered within the framework of a recently developed six-quark dressed-bag model for the nucleon-nucleon interaction. The calculations presented here include both the nucleon current and the meson-exchange current contributions. The latter uses short-range hadronic form factors for the pion exchange currents consistent with the soft cut-off parameter $Λ_{πNN}$ from the $NN$-potential. Contributions of the pion exchange current and $Δ$-isobar current to the total cross section still cannot explain the discrepancy between the theoretical and expe…
Recent progress in modeling QCD for hadron physics through truncated Dyson-Schwinger equations is reviewed. Special emphasis is put upon comparison of dressed quark propagators and the dressed quark-gluon vertex with lattice-QCD results.
We determine the quark condensate and the dressed Polyakov loop from the finite temperature Landau gauge quark propagator evaluated with U(1)-valued boundary conditions in an approximation to quenched QCD. These gauge invariant quantities allow for an investigation of the chiral and deconfinement transition. We compare results from Dyson-Schwinger equations on a lattice with infinite volume continuum results and study the temperature and quark mass dependence of both quantities. In particular we investigate the chiral condensate and the dressed Polyakov loop in the chiral limit. We also consid…
We describe expressions for pion and kaon dressed-quark distribution functions that incorporate contributions from gluons which bind quarks into these mesons and hence overcome a flaw of the commonly used handbag approximation. The distributions therewith obtained are purely valence in character, ensuring that dressed-quarks carry all a meson's momentum at a characteristic hadronic scale and vanishing as $(1-x)^2$ when Bjorken-$x\to 1$. Comparing such distributions within the pion and kaon, it is apparent that the size of SU(3)-flavour symmetry breaking in meson parton distribution functions i…
A detailed study of nucleon parton distribution functions is performed within a radiative Next-to-Next-to Leading Order (NNLO) parton model whose low-scale input is rigidly described by wave functions which include quarks and dressing meson-cloud. The light-front Hamiltonian dynamics fixes the three-quark wave functions and the meson cloud is introduced by means of high-order Fock component in time-ordered perturbation theory in the infinite momentum frame. Non-strange as well as strange mesons-baryon fluctuations are considered ($π$, $ρ$, $ω$, $K$ and $K^*$, together with $N$, $Δ$, $Λ$ and $Σ…
An exact form is presented for the axial-vector Bethe-Salpeter equation, which is valid when the quark-gluon vertex is fully dressed. A Ward-Takahashi identity for the Bethe-Salpeter kernel is derived therefrom and solved for a class of dressed quark-gluon vertex models. The solution provides a symmetry-preserving closed system of gap and vertex equations. The analysis can be extended to the vector equation. This enables a comparison between the responses of pseudoscalar- and scalar meson masses to nonperturbatively dressing the quark-gluon vertex. The result indicates that dynamical chiral sy…
In principle, the strong-interaction sector of the Standard Model is characterised by a unique renormalisation-group-invariant (RGI) running interaction and a unique form for the dressed--gluon-quark vertex, $Γ_μ$; but, whilst much has been learnt about the former, the latter is still obscure. In order to improve this situation, we use a RGI running-interaction that reconciles both top-down and bottom-up analyses of the gauge sector in quantum chromodynamics (QCD) to compute dressed-quark gap equation solutions with 1,660,000 distinct Ansaetze for $Γ_μ$. Each one of the solutions is then teste…
We construct the gauge invariant three-photon decay amplitude of particle-antiparticle bound states modeled by the Dyson-Schwinger and Bethe-Salpeter equations. Application to the quark-antiquark ($q\bar{q}$) bound states is emphasized. An essential aspect of our formulation is that it applies to any underlying quantum field theoretic model of the $q\bar{q}$ system, and not just to models, like exact QCD, where the quark self-energy $Σ$ couples to the electromagnetic field solely via dressed quark propagators. In this way, applications to effective field theories and other QCD motivated models…
The fundamental theory of the strong interaction -- quantum chromodynamics (QCD) -- provides the foundational framework with which to describe and understand the key properties of atomic nuclei. A deep understanding of the explicit role of quarks and gluons in nuclei remains elusive however, as these effects have thus far been well-disguised by confinement effects in QCD which are encapsulated by a successful description in terms of effective hadronic degrees of freedom. The observation of the EMC effect has provided an enduring indication for explicit QCD effects in nuclei, and points to the …
Recent lattice-QCD results for the dressed-gluon propagator are used within the quark Dyson-Schwinger equation to determine the gluon-quark vertex dressing necessary to reproduce the lattice-QCD results for the dressed-quark propagator. Both quenched and full QCD lattice simulations, for a range of low quark current masses, are analyzed. The chiral extrapolation is made through this continuum DSE form. Resulting chiral and physical pion observables are investigated.
A dressed-quark core contribution to nucleon electromagnetic form factors is calculated. It is defined by the solution of a Poincare' covariant Faddeev equation in which dressed-quarks provide the elementary degree of freedom and correlations between them are expressed via diquarks. The nucleon-photon vertex involves a single parameter; i.e., a diquark charge radius. It is argued to be commensurate with the pion's charge radius. A comprehensive analysis and explanation of the form factors is built upon this foundation. A particular feature of the study is a separation of form factor contributi…
A confining, symmetry-preserving, Dyson-Schwinger equation treatment of a vector-vector contact interaction is used to formulate Faddeev equations for the nucleon and Delta-baryon in which the kernel involves dynamical dressed-quark exchange and whose solutions therefore provide momentum-dependent Faddeev amplitudes. These solutions are compared with those obtained in the static approximation and with a QCD-kindred formulation of the Faddeev kernel. They are also used to compute a range of nucleon properties, amongst them: the proton's sigma-term; the large Bjorken-x values of separate ratios …
Aspects of the dressed-quark-gluon vertex and their role in the gap and Bethe-Salpeter equations are briefly surveyed using an intuitive model. The model allows one to elucidate why a linear extrapolation to the chiral limit of extant lattice data on the dressed-quark mass-function overestimates this function and hence the value of the vacuum quark condensate. The diagrammatic content of the vertex described is explicitly enumerable. This property is essential to the symmetry preserving study of bound state properties. It facilitates a realistic analysis of vector and pseudoscalar meson masses…
A symmetry-preserving Dyson-Schwinger equation treatment of a vector-vector contact interaction is used to compute dressed-quark-core contributions to the nucleon $σ$-term and tensor charges. The latter enable one to directly determine the effect of dressed-quark electric dipole moments (EDMs) on neutron and proton EDMs. The presence of strong scalar and axial-vector diquark correlations within ground-state baryons is a prediction of this approach. These correlations are active participants in all scattering events and thereby modify the contribution of the singly-represented valence-quark rel…
Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等技术学院）；Thomas Jefferson National Accelerator Facility (JLab)（托马斯·杰斐逊国家加速器设施（杰弗逊实验室））；College of William and Mary（威廉玛丽学院）；Universidade de Évora（埃武拉大学）
Charge symmetry breaking (CSB) effects associated with the $u$ and $d$ quark mass difference are investigated in the quark distribution functions and spacelike electromagnetic form factors of the pion and kaon. We use a confining version of the Nambu--Jona-Lasinio model, where CSB effects at the infrared scale associated with the model are driven by the dressed $u$ and $d$ quark mass ratio, which because of dynamical chiral symmetry breaking is much closer to unity than the associated current quark mass ratio. The pion and kaon are given as bound states of a dressed quark and a dressed antiqua…
We describe a symmetry-preserving calculation of the meson spectrum, which combines a description of pion properties with reasonable estimates of the masses of heavier light-quark mesons, including axial-vector states. The kernels used in formulating the problem are essentially nonperturbative. They incorporate effects of dynamical chiral symmetry breaking (DCSB) that were not previously possible to express. Our analysis clarifies a causal connection between DCSB and the splitting between vector and axial-vector mesons, and exposes a key role played by the anomalous chromomagnetic moment of dr…
A multi-component formalism is developed to describe three-body systems with nonstatic pairwise interactions and non-nucleonic degrees of freedom. The dressed-bag model for $NN$ interaction based on the formation of an intermediate six-quark bag dressed by a $σ$-field is applied to the $3N$ system, where it results in a new three-body force between the six-quark bag and a third nucleon. Concise variational calculations of $3N$ bound states are carried out in the dressed-bag model including the new three-body force. It is shown that this three-body force gives at least half the $3N$ total bindi…
We present a study of the dressed quark mass function and the pion structure in Minkowski space using the Covariant Spectator Theory. The quark propagators are dressed with the same kernel that describes the interaction between different quarks. We use an interaction kernel in momentum space that is a relativistic generalization of the linear confining q-qbar potential and a constant potential shift that defines the energy scale. The confining interaction has a Lorentz scalar part that is not chirally invariant by itself but decouples from the equations in the chiral limit and therefore allows…
The quark-meson coupling model for a nucleon is considered. The model describes a nucleon as an MIT bag, in which quarks are coupled to scalar and vector mesons. A set of coupled equations for the quark and the meson fields are obtained and are solved in a self-consistent way. It is shown that the mass of a nucleon as a dressed MIT bag interacting with sigma- and omega-meson fields significantly differs from the mass of a free MIT bag. A few sets of model parameters are obtained so that the mass of a dressed MIT bag becomes the nucleon mass. The results of our calculations imply that the self-…
A strongly momentum-dependent dressed-quark mass function is basic to QCD. It is central to the appearance of a constituent-quark mass-scale and an existential prerequisite for Goldstone modes. Dyson-Schwinger equation (DSE) studies have long emphasised these facts and are a natural way to exploit them.
We present a model for the quark-antiquark interaction formulated in Minkowski space using the Covariant Spectator Theory. The quark propagators are dressed with the same kernel that describes the interaction between different quarks. By applying the axial-vector Ward-Takahashi identity we show that our model satisfies the Adler-zero constraint imposed by chiral symmetry. For this model, our Minkowski-space results of the dressed quark mass function are compared to lattice QCD data obtained in Euclidean space. The mass function is then used in the calculation of the electromagnetic pion form f…
The maximum entropy method is used to compute the dressed-quark spectral density from the self-consistent numerical solution of a rainbow truncation of QCD's gap equation at temperatures above that for which chiral symmetry is restored. In addition to the normal and plasmino modes, the spectral function also exhibits an essentially nonperturbative zero mode for temperatures extending to 1.4-1.8-times the critical temperature, T_c. In the neighbourhood of T_c, this long-wavelength mode contains the bulk of the spectral strength and so long as this mode persists, the system may fairly be describ…
The pion electromagnetic form factor at spacelike momentum transfer is calculated in relativistic impulse approximation using the Covariant Spectator Theory. The same dressed quark mass function and the equation for the pion bound-state vertex function as discussed in the companion paper are used for the calculation, together with a dressed quark current that satisfies the Ward-Takahashi identity. The results obtained for the pion form factor are in agreement with experimental data, they exhibit the typical monopole behavior at high-momentum transfer, and they satisfy some remarkable scaling r…
The Covariant Spectator Theory is applied to the description of quarks and the pion. The dressed quark mass function is calculated dynamically in Minkowski space and used in the calculation of the pion electromagnetic form factor. The effects of the mass function on the pion form factor and the different quark-pole contributions to the triangle diagram are analyzed.
A method for obtaining the small current quark mass effect on the dressed quark propagator from an effective quark-quark interaction model is developed. Within this approach both explicit and dynamical chiral symmetry breaking has been analyzed. a comparision with previous results is given.
Dynamical chiral symmetry breaking (DCSB) is one of the keystones of low-energy hadronic phenomena. Dyson-Schwinger equations provide a model-independent quark-level understanding and correlate that with the behaviour of the pion's Bethe-Salpeter amplitude. This amplitude is a core element in the calculation of pion observables and combined with the dressed-quark Schwinger function required by DCSB it yields a valence-quark distribution function for the pion that behaves as (1-x)^2 for x~1, in accordance with perturbative analyses. This behaviour can be verified at contemporary experimental fa…
We compute the electromagnetic form factors of the nucleon in the Poincare-covariant Faddeev framework based on the Dyson-Schwinger equations of QCD. The general expression for a baryon's electromagnetic current in terms of three interacting dressed quarks is derived. Upon employing a rainbow-ladder gluon-exchange kernel for the quark-quark interaction, the nucleon's Faddeev amplitude and electromagnetic form factors are computed without any further truncations or model assumptions. The form factor results show clear evidence of missing pion-cloud effects below a photon momentum transfer of ~2…
We calculate the leading-twist, helicity-independent generalized parton distributions (GPDs) of the proton, at finite skewness, in the Nambu--Jona-Lasinio (NJL) model of quantum chomodynamics (QCD). The NJL model reproduces low-energy characteristics of QCD, including dynamical chiral symmetry breaking (DCSB). The proton bound-state amplitude is solved for using the Faddeev equation in a quark-diquark approximation, including both dynamical scalar and axial vector diquarks. GPDs are calculated using a dressed non-local correlator, consistent with DCSB, which is obtained by solving a Bethe-Salp…
We briefly report on a recent computation, with the help of a fruitful algebraic model, sketching the pion valence dressed-quark generalized parton distribution. Then, preliminary, we introduce on a sensible procedure to get reliable results in both Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) and Efremov-Radyushkin-Brodsky-Lepage (ERBL) kinematical regions, grounded on the GPD overlap representation and its parametrization of a Radon transform of the so-called double distribution (DD).
In this conference summary talk at Hadron03, questions and challenges for Hadron physics of light flavours are outlined. Precision data and recent discoveries are at last exposing the limitations of the naive constituent quark model and also giving hints as to its extension into a more mature description of hadrons. These notes also pay special attention to the positive strangeness baryon $Θ^+(1540)$ and include a pedagogic discussion of wavefunctions in the pentaquark picture, their relation with the Skyrme model and related issues of phenomenology.
A model for the dressed quark-gluon vertex, at zero gluon momentum, is formed from a nonperturbative extension of the two Feynman diagrams that contribute at 1-loop in perturbation theory. The required input is an existing ladder-rainbow model Bethe-Salpeter kernel from an approach based on the Dyson-Schwinger equations; no new parameters are introduced. The model includes an Ansatz for the triple-gluon vertex. Two of the three vertex amplitudes from the model provide a point-wise description of the recent quenched lattice-QCD data. An estimate of the effects of quenching is made.
Electromagnetic form factors of the baryon octet are studied using a Nambu--Jona-Lasinio model which utilizes the proper-time regularization scheme to simulate aspects of colour confinement. In addition, the model also incorporates corrections to the dressed quarks from vector meson correlations in the t-channel and the pion cloud. Comparison with recent chiral extrapolations of lattice QCD results shows a remarkable level of consistency. For the charge radii we find the surprising result $r_{E}^p < r_{E}^{Σ^+}$ and $|r_{E}^n| < |r_{E}^{Ξ^0}|$, whereas the magnetic radii have a pattern largely…
The form factor for gamma pi^+ -> pi^+ pi^0 was calculated in a simple-minded constituent model with a constant quark mass parameter, as well as in the Schwinger-Dyson approach. The comparative discussion of these and various other theoretical results on this anomalous process, as well as the scarce already available data (hopefully to be supplemented by more accurate CEBAF data soon), seem to favor Schwinger-Dyson modeling which would yield relatively small low-momentum values of the constituent (dynamically dressed) quark mass function.
We address the propagation and hadronization of a struck quark by studying the gauge invariance of the color-averaged cut quark propagator, and by relating this to the single inclusive quark fragmentation correlator by means of new sum rules. Using suitable Wilson lines, we provide a gauge-invariant definition for the mass of the color-averaged dressed quark and decompose this into the sum of a current and an interaction-dependent component. The latter, which we argue is an order parameter for dynamical chiral symmetry breaking, also appears in the sum rule for the twist-3 $\tilde{E}$ fragment…
We obtain the energy-momentum tensor (EMT) in the 't Hooft model of two-dimensional quantum chromodynamics. The EMT is decomposed into contributions from quark and gluon fields, with all of the (plus component of) the light front momentum being carried by the quark field. The energy is split between quark and gluon fields, with the gluon field carrying the self-energy of the dressed quarks. We consider the pion in the limit of small but non-zero quark masses -- which has previously withstood numerical treatment -- as as a concrete example. We solve for the pion wave function using a variationa…
A method for obtaining the low chemical potential dependence of the dressed quark propagator from an effective quark-quark interaction model is developed. From this the chemical potential dependence of the chiral quark condensate and bag constant are evaluated. It is found that the chiral order parameter decreases with the increasing chemical potential $μ$, which is qualitatively different from the results given by some authors in the literature. The reason for this discrepancy is discussed.
A Pomeron-exchange model of exclusive electroproduction of $ρ$-mesons is examined using a dressed-quark propagator. It is shown that by representing the photon-$ρ$-meson-Pomeron coupling by a nonperturbative, confined-quark loop, one obtains predictions for $ρ$-meson electroproduction that are in good agreement with experiment.
In treating the relativistic three-quark problem, a dressed-quark propagator parameterization is used which is compatible with recent lattice data and pion observables. Furthermore two-quark correlations are modeled as a series of quark loops in the scalar and axialvector channel. The resulting reduced Faddeev equations are solved for nucleon and delta. Nucleon electromagnetic form factors are calculated in a fully covariant and gauge--invariant scheme. Whereas the proton electric form factor $G_E$ and the nucleon magnetic moments are described correctly, the neutron electric form factor and t…
We considered the quark-meson coupling model for a nucleon. The model describes a nucleon as an MIT bag, in which quarks are coupled to the scalar and the vector mesons. A set of coupled equations for the quark and the meson fields are obtained and are solved in a self-consistent manner. We show that the mass of a dressed MIT bag interacting with $σ$- and $ω$-meson fields differs considerably from the mass of the free MIT bag. The effects of the density-dependent bag constant are investigated. The results of our calculations imply that the self-energy of the bag in the quark-meson coupling mod…
Using a ladder-rainbow kernel previously established for light quark hadron physics, we explore the extension to masses and electroweak decay constants of ground state pseudoscalar and vector quarkonia and heavy-light mesons in the c- and b-quark regions. We make a systematic study of the effectiveness of a constituent mass concept as a replacement for a heavy quark dressed propagator for such states. The difference between vector and axial vector current correlators is explored within the same model to provide an estimate of the four quark chiral condensate and the leading distance scale for …
We summarize recent progress in soft QCD modeling based on the set of Dyson--Schwinger equations truncated to ladder-rainbow level. We pay particular attention to electromagnetic elastic and transition form factors of the pion. This covariant approach accommodates quark confinement and implements the QCD one-loop renormalization group behavior. The dressed quark propagators are compared to the most recent lattice-QCD data.
