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We study the leading-twist unpolarized generalized parton distributions (GPDs) of light and heavy vector mesons, i.e., the $\rho$, $J/\psi$ and $\Upsilon$, at zero skewness. An ansatz incorporating the zero mode contribution is introduced to modify the light front overlap representation of GPDs. The leading Fock-state light front wave functions (LF-LFWFs) of vector mesons from DS-BSEs approach are then employed to study the meson GPDs. The light front spatial distribution of valence quarks within vector mesons is then studied with the impact parameter dependent GPD (IPD GPD). We also investigate the electromagnetic and gravitational form factors, which are the first and second Mellin moments of the GPDs. The light-cone mass radius of $\rho$ is determined to be 0.30 fm, close to a recent NJL model prediction 0.32fm. For $J/\psi$ and $\Upsilon$, they are predicted to be 0.151fm and 0.089 fm respectively., Comment: 9 pages, 9 figures

Lepton scattering is an established ideal tool for studying inner structure of small particles such as nucleons as well as nuclei. As a future high energy nuclear physics project, an Electron-ion collider in China (EicC) has been proposed. It will be constructed based on an upgraded heavy-ion accelerator, High Intensity heavy-ion Accelerator Facility (HIAF) which is currently under construction, together with a new electron ring. The proposed collider will provide highly polarized electrons (with a polarization of $\sim$80%) and protons (with a polarization of $\sim$70%) with variable center of mass energies from 15 to 20 GeV and the luminosity of (2-3) $\times$ 10$^{33}$ cm$^{-2}$ s$^{-1}$. Polarized deuterons and Helium-3, as well as unpolarized ion beams from Carbon to Uranium, will be also available at the EicC. The main foci of the EicC will be precision measurements of the structure of the nucleon in the sea quark region, including 3D tomography of nucleon; the partonic structure of nuclei and the parton interaction with the nuclear environment; the exotic states, especially those with heavy flavor quark contents. In addition, issues fundamental to understanding the origin of mass could be addressed by measurements of heavy quarkonia near-threshold production at the EicC. In order to achieve the above-mentioned physics goals, a hermetical detector system will be constructed with cutting-edge technologies. This document is the result of collective contributions and valuable inputs from experts across the globe. The EicC physics program complements the ongoing scientific programs at the Jefferson Laboratory and the future EIC project in the United States. The success of this project will also advance both nuclear and particle physics as well as accelerator and detector technology in China., EicC white paper, written by the whole EicC working group

A symmetry-preserving treatment of a vector$\times$vector contact interaction is used to compute spectra of ground-state $J^P = 0^\pm, 1^\pm$ $(f\bar g)$ mesons, their partner diquark correlations, and $J^P=1/2^\pm, 3/2^\pm$ $(fgh)$ baryons, where $f,g,h \in \{u,d,s,c,b\}$. Results for the leptonic decay constants of all mesons are also obtained, including scalar and pseudovector states involving heavy quarks. The spectrum of baryons produced by this chiefly algebraic approach reproduces the 64 masses known empirically or computed using lattice-regularised quantum chromodynamics with an accuracy of 1.4(1.2)%. It also has the richness of states typical of constituent-quark models and predicts many baryon states that have not yet been observed. The study indicates that dynamical, nonpointlike diquark correlations play an important role in all baryons; and, typically, the lightest allowed diquark is the most important component of a baryon's Faddeev amplitude., Comment: 21 pages, 7 tables, 5 figures. arXiv admin note: text overlap with arXiv:1903.00160

Within the framework of Polyakov-Nambu-Jona-Lasinio model and by means of Multiple Reflection Expansion, we study the finite volume effects on chiral phase transition, especially its influence on the location of the possible critical end point (CEP) and masses of mesons. Our result shows that as the radius of spherical volume decreases, the location of CEP shifts toward smaller temperature while changes little in chemical potential. As for the finite volume effects on the masses of mesons, the masses of $\pi$ and $K$ increase with decreasing volume, while for $\sigma$, $\eta$ and $\eta '$ the situation is the opposite. Especially, the masses of chiral parters $\pi$ and $\sigma$ get closer as the volume decreases, indicating that the dynamical chiral symmetry breaking effect reduces with decreasing volume., Comment: 8 pages, 11 figures

Based on the experimental observation that there is a coexisting region between the antiferromagnetic (AF) and d-wave superconducting (dSC) phases, the influences of gauge boson mass m a on chiral symmetry restoration and deconfinement phase transitions in QED3 are investigated simultaneously within a unified framework, i.e., Dyson–Schwinger equations. The results show that the chiral symmetry restoration phase transition in the presence of the gauge boson mass m a is a typical second-order phase transition; the chiral symmetry restoration and deconfinement phase transitions are coincident; the critical number of fermion flavors N c f decreases as the gauge boson mass m a increases, which implies that there exists a boundary that separates the N c f –m a plane into chiral symmetry breaking/confinement region for (N c f , m a ) below the boundary and chiral symmetry restoration/deconfinement region for (N c f , m a ) above it.

The quark condensate and quark number density are commonly used to determine the QCD phase transition. However, the usually defined quark condensate is divergent in the case of non-chiral limit, and the quark number density suffers from the superficial divergence in numerical calculation. In order to address these issues, we redefine the quark condensate at finite temperature and density and propose a technique to deal with the divergence of the quark condensate and the superficial divergence of the quark number density in numerical calculations. Based on these improvements, we further discuss various susceptibilities as criteria to determine the critical points in the phase transition. It is found that different susceptibilities give different locations of the critical points in the crossover region, which suggests us to define a critical band, instead of some exclusive line in the phase diagram.

In this paper, we study the pseudo-Wigner solution of the quark gap equation with a recently proposed algorithm in the framework of the ($2+1$)-flavor Nambu-Jona-Lasinio (NJL) model. We find that for the current quark mass ${m}_{u,d}=5.5\text{ }\text{ }\mathrm{MeV}$ and chemical potential $\ensuremath{\mu}l{\ensuremath{\mu}}_{\mathrm{TCP}}=272.5\text{ }\text{ }\mathrm{MeV}$, the Nambu solution and the positive pseudo-Wigner solution obtained via this algorithm is consistent with the physical solution obtained with the iterative method. Furthermore, the algorithm we used can help to illustrate the evolution of the solutions of the gap equation from the chiral limit to nonchiral limit and gives a prediction where the crossover line is located in the phase diagram for $\ensuremath{\mu}l272.5\text{ }\text{ }\mathrm{MeV}$. In addition, we also study the chiral susceptibilities as well as the loss of solutions for different chemical potentials.

Using a confining, symmetry-preserving regularisation of a vector$\times$vector contact interaction, we compute the spectra of ground-state pseudoscalar and vector $(f\bar g)$ mesons, scalar and axial-vector $(fg)$ diquarks, and $J^P=1/2^+, 3/2^+$ $(fgh)$ baryons, where $f,g,h \in \{u,d,s,c,b\}$. The diquark correlations are essentially dynamical and play a key role in formulating and solving the three-valence-quark baryon problems. The baryon spectrum obtained from this largely-algebraic approach reproduces the 22 known experimental masses with an accuracy of $2.9(2.4)$%. It also possesses the richness of states typical of constituent-quark models, predicting many heavy-quark baryons not yet observed. This study indicates that diquark correlations are an important component of all baryons; and owing to the dynamical character of the diquarks, it is typically the lightest allowed diquark correlation which defines the most important component of a baryon's Faddeev amplitude., Comment: 18 pages, 5 figures, 5 tables

According to the extensive theoretical and experimental investigations, it is widely accepted that the long-range Coulomb interaction is too weak to generate a dynamical excitonic gap in graphene with a perfect Dirac cone. We study the impact of the deformation of a Dirac cone on dynamical gap generation. When a uniaxial strain is applied to graphene, the Dirac cone is made elliptical on the equal-energy plane, and the fermion velocity becomes anisotropic. The applied uniaxial strain has two effects: It decreases the mean value of fermion velocity; it increases the velocity anisotropy. After solving the Dyson-Schwinger gap equation, we show that dynamical gap generation is promoted by the former effect but suppressed by the latter. For suspended graphene, we find that the system undergoes an excitonic insulating transition when the strain is roughly 7.34%. We also solve the gap equation in case the Dirac cone is tilted, which might be realized in the organic material $\ensuremath{\alpha}\ensuremath{-}{(\mathrm{BEDT}\ensuremath{-}\mathrm{TTF})}_{2}{\mathrm{I}}_{3}$ and find that the tilt of the Dirac cone can suppress dynamical gap generation. It turns out that the geometry of the Dirac cone plays an important role in the formation of excitonic pairing.

In this paper, we investigate the behaviors of dual fermion condensate in QED3 under variation of temperature. By means of Dyson-Schwinger equation for the fermion propagator, we extract the dual fermion condensate and compare its behavior with the ordinary chiral fermion condensate and the chiral susceptibility. It is found that the dual fermion condensate cannot be regarded as the order parameter for the confinement-deconfinement phase transition in QED3. Furthermore, the change of the dual fermion condensate around the chiral phase transition point observed in the present work must therefore be interpreted as solely induced by the chiral transition.

In a realistic interacting system described by ($2+1$)-dimensional quantum electrodynamics (${\mathrm{QED}}_{3}$), there is always a certain number of impurities by which fermions are scattered. In general, impurity scattering can generate a finite density of states at the Fermi level, which screens the temporal component of the gauge field. This effect is expected to weaken dynamical fermion mass generation. Within the Born approximation, by introducing a damping term in the energy component of the fermion propagator, the influences of finite temperature and impurity scattering on the chiral phase transition in ${\mathrm{QED}}_{3}$ are investigated. Pursuing this aim, we solve the Dyson-Schwinger equations for the fermion and boson propagators to the leading order in $1/{N}_{f}$ expansion at zero frequency and then calculate the chiral condensate, the chiral susceptibility, and the thermal susceptibility within a range of the impurity scattering rates $\mathrm{\ensuremath{\Gamma}}$ and the numbers of fermion flavors ${N}_{f}$. It is found that impurity scattering leads to an obvious suppression of the dynamical fermion mass generation and critical temperature ${T}_{c}$.

In this paper, we investigate dynamical mass generation in (2+1)-dimensional quantum electrodynamics at finite temperature. Many studies are carried out within the instantaneous-exchange approximation, which ignores all but the zero-frequency component of the boson propagator and fermion self-energy function. We extend these studies by taking the retardation effects into consideration. In this paper, we get the explicit frequency n and momentum p dependence of the fermion self-energy function and identify the critical temperature for different fermion flavors in the chiral limit. Also, the phase diagram for spontaneous symmetry breaking in the theory is presented in T c-N f space. The results show that the chiral condensate is just one-tenth of the scale of previous results, and the chiral symmetry is restored at a smaller critical temperature.

At zero temperature and density, the nature of the chiral phase transition in QED$_3$ with $\textit{N}_{f}$ massless fermion flavors is investigated. To this end, in Landau gauge, we numerically solve the coupled Dyson-Schwinger equations for the fermion and boson propagator within the bare and simplified Ball-Chiu vertices separately. It is found that, in the bare vertex approximation, the system undergoes a high-order continuous phase transition from the Nambu-Goldstone phase into the Wigner phase when the number of fermion flavors $\textit{N}_{f}$ reaches the critical number $\textit{N}_{f,c}$, while the system exhibits a typical characteristic of second-order phase transition for the simplified Ball-Chiu vertex., 9 pages, 9 figures

In this paper, the relations of four different susceptibilities (i.e., the chiral susceptibility, the fermion number susceptibility, the thermal susceptibility, and the staggered spin susceptibility) are investigated both in and beyond the chiral limit. To this end, we numerically solve the finite-temperature version of the truncated Dyson-Schwinger equations for the fermion and boson propagator. It is found that, in the chiral limit, the four susceptibilities give the same critical temperature and signal a typical second order phase transition. But the situation changes beyond the chiral limit: the critical temperatures from the chiral and the thermal susceptibilities are different, which shows that to define a critical region instead of an exclusive point for crossover might be a more suitable choice. Meanwhile, both the fermion number and the staggered spin susceptibilities have no singular behaviors any more; this may mean that they are no longer available to describe the crossover properties of the system.

In the framework of Dyson–Schwinger equations, we employ two kinds of criteria (one kind is the chiral condensate, the other kind is thermodynamic quantities, such as the pressure, the entropy, and the specific heat) to investigate the nature of chiral phase transitions in QED3 for different fermion flavors. It is found that the chiral phase transitions in QED3 for different fermion flavors are all typical second-order phase transitions; the critical temperature and order of the chiral phase transition obtained from the chiral condensate and susceptibility are the same with that obtained by the thermodynamic quantities, which means that they are equivalent in describing the chiral phase transition; the critical temperature decreases as the number of fermion flavors increases and there is a boundary that separates the [Formula: see text] plane into chiral symmetry breaking and restoration regions.

Based on the truncated Dyson-Schwinger equation, we first study the influence of the vertex correction on the staggered spin susceptibility chi(s). The numerical results show that the vertex correction plays an important role in the study of the staggered spin susceptibility. We then generalize the above work to the case of finite temperature. It is found for the first time that, as the temperature increases, the chiral condensate vanishes at the phase transition point where chi(s) reveals an obvious skip, and therefore as a physical observable, the staggered spin susceptibility could be regarded as the order parameter of chiral phase transition in QED(3).