Dyson-Schwinger Equation Approach Research Articles

Nucleon Resonance Structure from Exclusive Meson Electroproduction with CLAS

Studies of the nucleon resonance electroexcitation amplitudes in a wide range of photon virtualities offer unique information on many facets of strong QCD behind the generation of all prominent excited nucleon states. Advances in the evaluation of resonance electroexcitation amplitudes from the data measured with the CLAS detector and the future extension of these studies with the CLAS12 detector at Jefferson Lab are presented. For the first time, analyses of $\pi^0p$, $\pi^+n$, $\eta p$, and $\pi^+\pi^-p$ electroproduction off proton channels have provided electroexcitation amplitudes of most resonances in the mass range up to 1.8 GeV and at photon virtualities $Q^2 < 5$~GeV$^2$.Studies of the resonance electroexcitation amplitudes revealed the $N^*$ structure as a complex interplay between the inner core of three dressed quarks and the external meson-baryon cloud. The successful description of the $\Delta(1232)3/2^+$ and $N(1440)1/2^+$ electrocouplings achieved within the Dyson-Schwinger Equation approach under a traceable connection to the QCD Lagrangian and supported by the novel light front quark model demonstrated the relevance of dressed quarks with dynamically generated masses as an active structural component in baryons. Future experiments with the CLAS12 detector will offer insight into the structure of all prominent resonances at the highest photon virtualities, $Q^2 < 12$~GeV$^2$, ever achieved in exclusive reactions, thus addressing the most challenging problems of the Standard Model on the nature of hadron mass, quark-gluon confinement, and the emergence of nucleon resonance structures from QCD. A search for new states of hadronic matter, the so-called hybrid-baryons with glue as a structural component, will complete the long term efforts on the resonance spectrum exploration.

Revisiting the equation of state of hybrid stars in the Dyson-Schwinger equation approach to QCD

We investigate the equation of state(EoS) and the effect of the hadron-quark phase transition of strong interaction matter in compact stars. The hadron matter is described with the relativistic mean field theory,and the quark matter is described with the Dyson-Schwinger equation approach of QCD. The complete EoS of the hybrid star matter is constructed with not only the Gibbs construction but also the 3-window interpolation. The mass-radius relation of hybrid stars is also investigated. We find that, although the EoSs of both the hadron matter with hyperon and $\Delta$-baryon and the quark matter are generally softer than that of the nucleon matter, the 3-window interpolation construction may provide an EoS stiff enough for a hybrid star with mass exceeding 2$M_{\odot}^{}$ and, in turn, solve the so called "hyperon puzzle".

Interface effect in QCD phase transitions via Dyson-Schwinger equation approach

With the chiral susceptibility criterion we obtain the phase diagram of strong-interaction matter in terms of temperature and chemical potential in the framework of Dyson-Schwinger equations (DSEs) of QCD.After calculating the pressure and some other thermodynamic properties of the matter in the DSE method, we get the phase diagram in terms of temperature and baryon number density. We also obtain the interface tension and the interface entropy density to describe the inhomogeneity of the two phases in the coexistence region of the first order phase transition. After including the interface effect, we find that the total entropy density of the system increases in both the deconfinement (dynamical chiral symmetry restoration) and the hadronization (dynamical chiral symmetry breaking) processes of the first order phase transitions and thus solve the entropy puzzle in the hadronization process.

Nucleon Resonance Physics

Recent results of meson photo-production at the existing electron machines with polarized real photon beams and the measurement of polarization observables of the final state baryons have provided high precision data that led to the discovery of new excited nucleon and $\Delta$ states using multi-channel partial wave analyses procedures. The internal structure of several prominent excited states has been revealed employing meson electroproduction processes. On the theoretical front, lattice QCD is now predicting the baryon spectrum with very similar characteristics as the constituent quark model, and continuum QCD, such as is represented in the Dyson-Schwinger Equations approach and in light front relativistic quark models, describes the non-perturbative behavior of resonance excitations at photon virtuality of $Q^2 > 1.5GeV^2$. In this talk I discuss the need to continue a vigorous program of nucleon spectroscopy and the study of the internal structure of excited states as a way to reveal the effective degrees of freedom underlying the excited states and their dependence on the distance scale probed.

Ward identities, B → V transition form factors and applications

Long distance effects are studied in the rare exclusive semileptonic B(d,s) → Vℓ+ℓ− decays, where V denotes a K* or ϕ meson. The form factors, which describe the meson transition amplitudes in the effective Hamiltonian approach, are calculated by means of Ward identities, experimental constraints and extrapolated within a general vector meson dominance framework. These form factors are then compared to the ones obtained in Lattice QCD simulations, with Light Cone Sum Rules and a Dyson-Schwinger equation approach. Additionally, the Bd → K*ℓ+ℓ− and Bs → ϕℓ+ℓ− branching ratios are computed and the differential branching fractions are given as a function of the squared-momentum transfer.

Infrared behavior of dynamical fermion mass generation inQED3

Extensive investigations show that QED$_{3}$ exhibits dynamical fermion mass generation at zero temperature when the fermion flavor $N$ is sufficiently small. However, it seems difficult to extend the theoretical analysis to finite temperature. We study this problem by means of Dyson-Schwinger equation approach after considering the effect of finite temperature or disorder-induced fermion damping. Under the widely used instantaneous approximation, the dynamical mass displays an infrared divergence in both cases. We then adopt a new approximation that includes an energy-dependent gauge boson propagator and obtain results for dynamical fermion mass that do not contain infrared divergence. The validity of the new approximation is examined by comparing to the well-established results obtained at zero temperature.

Nonlinear susceptibilities under the framework of Dyson-Schwinger equations

Since the baryon-number susceptibilities are correlated with the cumulant of baryon-number fluctuations in experiments, we do calculations of the susceptibilities and compare them with the experimental fluctuation data under the framework of the Dyson-Schwinger equations (DSEs) approach. We compare our results with lattice QCD and experimental data at RHIC. The fitness of the results indicates that under the framework of DSEs, we can deal with the problems of heavy ion collisions properly.

Quark number fluctuations at finite temperature and finite chemical potential via the Dyson-Schwinger equation approach

We investigate the quark number fluctuations up to the fourth order in the matter composed of two light flavor quarks with isospin symmetry and at finite temperature and finite chemical potential using the Dyson-Schwinger equation approach of QCD. In order to solve the quark gap equation, we approximate the dressed quark-gluon vertex with the bare one and adopt both the Marris-Tandy (MT) model and the infrared constant (Qin-Chang) model for the dressed gluon propagator. Our results indicate that the second, third, and forth order fluctuations of net quark number all diverge at the critical end point (CEP). Around the CEP, the second order fluctuation possesses obvious pump while the third and fourth order ones exhibit distinct wiggles between positive and negative. For the MT model and the Qin-Chang model, we give the pseudo-critical temperature at zero quark chemical potential as $T_{c}=146$ MeV and $150$ MeV, and locate the CEP at $({\mu_{E}^{q}}, {T_{E}^{}}) = (120, 124)$ MeV and $(124,129)$ MeV, respectively. In addition, our results manifest that the fluctuations are insensitive to the details of the model, but the location of the CEP shifts to low chemical potential and high temperature as the confinement length scale increases.

Chiral phase transition of QCD at finite chemical potential

In the framework of Dyson-Schwinger equation (DSE) approach, we propose a chemical potential dependent effective gluon propagator and the quark gap equation is solved with such a gluon propagator. It is found for the first time in DSE approach that with light current quark mass m not equal 0, the Wigner solution will appear at some chemical potential mu(W). Based on this, the chiral phase transition at finite chemical potential is studied and the result shows that it is a first-order phase transition. The results are compared with the known results in the literature.

Chiral phase diagram inQED3

We study the dynamical chiral symmetry breaking of three-dimensional quantum electrodynamics (${\mathrm{QED}}_{3}$) at finite temperature and chemical potential in the leading order of Dyson-Schwinger equation approach. After considering the chemical potential dependence of the boson propagator, we derive the expression for the boson polarization and then obtain the corresponding chiral phase diagram in the ($T\mathrm{\text{\ensuremath{-}}}\ensuremath{\mu}$) plane. A comparison between the phase diagram obtained above and the one obtained without considering the chemical potential dependence of the boson propagator is made. It is found that in a self-consistent study of the chiral phase diagram of ${\mathrm{QED}}_{3}$, the chemical potential dependence of the boson propagator cannot be neglected.

Hadronic contribution to the muon [formula omitted]: A Dyson–Schwinger perspective

We summarize our results for hadronic contributions to the anomalous magnetic moment of the muon (aμ), the one from hadronic vacuum-polarization (HVP) and the light-by-light scattering contribution (LBL), obtained from the Dyson–Schwinger equations (DSEs) of QCD. In the case of HVP we find good agreement with model independent determinations from dispersion relations for aμHV P as well as for the Adler function with deviations well below the ten percent level. From this we conclude that the DSE approach should be capable of describing aμLBL with similar accuracy. We also present results for LBL using a resonance expansion of the quark–anti-quark T-matrix. Our preliminary value is aμLBL=(217±91)×10−11.

Width of the QCD transition in a Polyakov-loop Dyson-Schwinger equation model

We consider the pseudocritical temperatures for the chiral and deconfinement transitions within a Polyakov-loop Dyson-Schwinger equation approach which employs a nonlocal rank-2 separable model for the effective gluon propagator. These pseudocritical temperatures differ by a factor of 2 when the quark and gluon sectors are considered separately, but get synchronized and become coincident when their coupling is switched on. The coupling of the Polyakov loop to the chiral quark dynamics narrows the temperature region of the QCD transition in which chiral symmetry and deconfinement is established. We investigate the effect of rescaling the parameter ${T}_{0}$ in the Polyakov-loop potential on the QCD transition for both the logarithmic and polynomial forms of the potential. While the critical temperatures vary in a similar way, the width of the transition is more strongly affected for the logarithmic potential. For this potential, the character of the transition changes from crossover to a first-order one when ${T}_{0}&lt;210\text{ }\text{ }\mathrm{MeV}$, but it remains crossover in the whole range of relevant ${T}_{0}$ values for the polynomial form.

Temperature dependence of the effective bag constant and the radius of a nucleon in the global color symmetry model of QCD

We study the temperature dependence of the effective bag constant, the mass, and the radius of a nucleon in the formalism of the simple global color symmetry model in the Dyson-Schwinger equation approach of QCD with a Gaussian-type effective gluon propagator. We obtain that, as the temperature is lower than a critical value, the effective bag constant and the mass decrease and the radius increases with the temperature increasing. As the critical temperature is reached, the effective bag constant and the mass vanish and the radius tends to infinity. At the same time, the chiral quark condensate disappears. These phenomena indicate that the deconfinement and the chiral symmetry restoration phase transitions can take place at high temperature. The dependence of the critical temperature on the interaction strength parameter in the effective gluon propagator of the approach is given.

Recent Progress on the Study of Dyson-Schwinger Equations Approach Description of Phase Transitions of Strong Interaction System

We review concisely the recent progress on the study of the QCD phase structure and its transition in vacuum and in medium in the the framework of Dyson-Schwinger equations approach of QCD.

STABILITY OF VACUUM AND QCD PHASE TRANSITION IN DYSON-SCHWINGER EQUATION APPROACH OF QCD

We describe briefly the effects of the running coupling strength, the current quark mass, the temperature and density on the QCD phase structure and its transition in the framework of Dyson-Schwinger equation approach of QCD. With a simple model, we show that the chiral susceptibility can identify the stability of the vacuum and plays an important role in describing the QCD Phase transition.

QCD PHASE TRANSITION IN DYSON–SCHWINGER EQUATION APPROACH OF QCD

We review briefly the effects of the running coupling strength, the current quark mass, the density and the finite size of the matter on the QCD phase structure and its transition in the framework of Dyson–Schwinger equation approach of QCD. It provides a visual view to understanding the QCD phase transition with respect to the medium effects and the intrinsic characteristics.

Chemical potential dependence of chiral quark condensate in Dyson–Schwinger equation approach of QCD

Abstract We propose a chemical potential-dependent effective gluon propagator and study the chiral quark condensate in strongly interacting matter in the framework of Dyson–Schwinger equation approach. The obtained results manifest that, as the effect of the chemical potential on the effective gluon propagator is taken into account, the chiral quark condensate decreases gradually with the increasing of the chemical potential if it is less than the critical value, and the condensate vanishes suddenly at the critical chemical potential. The inclusion of the chemical potential in the effective gluon propagator enhances the decreasing rate and decreases the critical chemical potential. It indicates that the chiral symmetry can be restored completely at a critical chemical potential and restored partially as the chemical potential is less than the critical value. If the effective gluon propagator is independent of the chemical potential, the chiral symmetry can only be restored suddenly but no gradual restoration.

THE SOLUTIONS OF THE DYSON–SCHWINGER EQUATION FOR QUARK PROPAGATOR IN THE CASE OF NONZERO CURRENT QUARK MASS

In the framework of rainbow approximation of the Dyson–Schwinger equation approach, it is shown that there exist two qualitatively distinct solutions of the Dyson–Schwinger equation for the quark propagator in the case of nonzero current quark mass. One solution corresponds to the "Nambu–Goldstone" phase and the other one corresponds to the "Wigner" phase in the chiral limit.

On the Chiral Quark Condensate at Finite Chemical Potential

We analyze the variation behavior of chiral quark condensates in vacuum and in strong interacting matter against the parameters in the effective gluon propagators in Dyson-Schwinger equation approach. The obtained results indicate that the quark confinement enhances the quark condensate, and the screening of the confinement suppresses the response of the condensate to the chemical potential.

Some Aspects of QCD Phase Transitions in Dense Strong Interaction Matter in Dyson-Schwinger Equation Approach(Hadrons at finite density)

Some Aspects of QCD Phase Transitions in Dense Strong Interaction Matter in Dyson-Schwinger Equation Approach(Hadrons at finite density)