Critical Behavior of Dynamical Chiral Symmetry Breaking with Gauge Boson Mass in QED3

Since the massless quantum electrodynamics in 2＋1 dimensions （QEDa） with nonzero gauge boson mass ζ can be used to explain some important traits of high-Tc superconductivity in planar cuprates, it is worthwhile to apply this model to analyze the nature of chiral phase transition at the critical value ζ. Based on the feature of chiral susceptibility, we show that the system at ζ exhibits a second-order phase transition which accords with the nature of appearance of the high-To superconductivity, and the estimated critical exponents around ζ are illustrated.

Observations on spontaneous chiral symmetry breaking and the mass gap of QCD in finite volume

We present a lattice quantum chromodynamics(QCD)simulation with 2+1+1 flavor full QCD ensembles using near-physical quark masses and different spatial sizes L,at a~0.055 fm.The results show that the scalar and pesudoscalar 2-point correlator with a valence pion mass of approximately 230 MeV become degenerated at L≤1.0 fm,and such an observation suggests that the spontaneous chiral symmetry breaking disappears effectively at this point.At the same time,the mass gap between the nucleon and pion masses remains larger thanΛQCDin the entire L∈[0.2,0.7]fm range.

Dynamical chiral symmetry breaking in NJL Model with a strong background magnetic field and Lorentz-violating extension of the Standard Model

The Eigenstate Method has been developed to deduce the fermion propagator with a constant external magnetic field. In general, we find its result is equivalent to other methods and this new method is more convenient,especially when one evaluates the contribution from the infinitesimal imaginary term of the fermion propagator. Using the Eigenstate Method we try to discuss whether the infinitesimal imaginary frequency of the fermion propagator in a strong magnetic field and Lorentz-violating extension of the minimal SU（3）×SU（2）×SU（1） Standard Model could have a significant influence on the dynamical mass. When the imaginary term of the fermion propagator in this model is not trivial（√（α-1）eB/3） 〈 σ 〈（√（α-1）2eB/3）, this model gives a correction to the dynamical mass.When one does not consider the influence from the imaginary term（σ 〉√（α-1）2eB/3）, there is another correction from the conventional term. Under both circumstances, chiral symmetry is broken.

Viscosities in chiral symmetry breaking phase

In the chiral symmetry breaking phase described by the NJL model at quark level,along with the chiral symmetry restoration the ratio of shear viscosity to entropy density η/s drops down monotonously and reaches the minimum at the critical point,while the ratio of bulk viscosity to entropy density ζ/s behaves oppositely.

Calculation of Quark Condensate in Nuclear Matter with the Chiral Symmetry Spontaneous Breaking Lagrangian

Using the chiral symmetry spontaneous breaking Lagrangian with mean-field approximation, we investigate the in-medium quark condensate . It is found that the condensate decreases as the nuclear matter density increases. Meanwhile, the desent deviates from the linear decrease and becomes remarkably slow as the density of the nuclear matter further increases. It shows that the chiral symmetry spontaneous breaking is only partially restored in densed nuclear matter.

Neutron Stars in the Model of Non—linear Realization of SU（2） Chiral Symmetry Spontaneous Breaking

The properties of neutron stars are studied in a relativistic mean-field model with SU(2) chiral symmetry spontaneous breaking being considered. The calculation results indicate that the effects of the chiral symmetry spontaneous breaking are not negligible.

Spontaneous Symmetry Breaking of Iridium and Ruthenium Metallophosphors for the Constructions of Chiral Light-Harvesting Systems

Symmetry breaking for chirality generation and lightharvesting for solar energy conversion are two momentous topics in natural systems.The construction of a chiral light-harvesting system completely based on symmetry breaking is a formidable challenge.Here,we report the spontaneous chiral symmetry breaking(CSB)of two iridium and ruthenium metallophosphors(IrD and RuA)with the assistance of achiral solvents.The subtle noncovalent intermolecular interactions between complexes and polar solvents play a vital role in the crystallization of homochiral molecules and the resulting CSB.Utilizing a molecular doping strategy,transferred,ampli-fied,and inverted circularly polarized luminescence(CPL)was achieved in the binary microcrystals(MCs)composed of chiral/achiral IrD and achiral/chiral RuA,with large dissymmetry factors(glum,up to 0.06)and enhanced emission quantum yields(over 35%).The use of only 0.05%of chiral RuA in the lattice of achiral IrD led to the chiral amplification with glum of 1×10−2 and morphology transition,while inverted and white CPL were obtained in MCs containing monodispersed chiral RuA in the lattice cavities of another polymorphic crystal of IrD.Diffuse reflection circular dichroism measurements gave information on the chirality transfer mechanisms behind these spin-related chiroptical properties.

Quark Loop Effects on Dressed Gluon Propagator in Framework of Global Color Symmetry Model

Based on the global color symmetry mode/ （GCM）, a method for obtaining the quark loop effects on the dressed gluon propagator in GCM is developed. In the chiral limit, it is found that the dressed gluon propagator containing the quark loop effects in the Nambu-Goldstone and Wigner phases are quite different. In solving the quark self-energy functions in the two different phases and subsequent study of bag constant one shouM use the above dressed gluon propagator as input. The above approach for obtaining the current quark mass effects on the dressed gluon propagator is quite general and can also be used to calculate the chemical potential dependence of the dressed gluon propagator.

A New Calculation of the In-Medium Quark Condensate at Finite Density and Temperature

The in-medium quark condensate is studied with an equivalent-mass approach in which one does not need to make assumptions on the derivatives of model parameters with respect to the quark current mass.It is shown that the condensate is generally a decreasing function of both the density and temperature with the decreasing speed depending on the confinement parameter.Specially,at given density,the condensate decreases on increasing temperature.The decreasing speed is comparatively small at lower temperature,and becomes very fast at higher temperature.

Interplay Between Quark-Antiquark and Diquark Condensates in Vacuum in a Two-Flavor Nambu-Jona-Lasinio Model

By means of a relativistic effective potential, we analytically research competition between the quark- antiquark condensates （qq） and the diquark condensates （qq） in vacuum in ground state of a two-flavor Nambu Jona Lasinio （NJL） model and obtain the Gs-Hs phase diagram, where Gs and Hs are the respective four-fermion coupling constants in scalar quark-antiquark channel and scalar color anti-triplet diquark channel. The results show that, in the chiral limit, there is only the pure （qq） phase when Gs/Hs 〉 2/3, and as Gs/Hs decreases to 2/3 〉 Gs/Hs ≥ 0 one will first have a coexistence phase of the condensates （qq） and （qq） and then a pure （qq） phase. In non-zero bare quark mass case, the critical value of Gs/Hs at which the pure （qq） phase will transfer to the coexistence phase of the condensates （qq） and （qq） will be less than 2/3. Our theoretical results, combined with present phenomenological fact that there is no diquark condensates in the vacuum of QCD, will also impose a real restriction to any given two-flavor NJL model which is intended to simulate QCD, i.e. in such model the resulting sma/lest ratio Gs/Hs after the Fierz transformations in the Hartree approximation must be larger than 2/3. A few phenomenological QCD-like NJL models are checked and analyzed.

Critical Mass of Gauge Boson in Rainbow QED3

In three-dimensional quantum electrodynamics (QED3) with a massive gauge boson, we investigate the coupled Dyson-Schwinger equations for the fermion and photon propagators in the rainbow approximation, and obtain the critical gauge boson mass for various numbers of the fermion flavors. A comparision with the previous results is presented.

Chiral symmetry restoration and deconfinement in the contact interaction model of quarks with parallel electric and magnetic fields

We study the impact of steady,homogeneous,and external parallel electric and magnetic field strengths(eE||eB)on the chiral symmetry breaking-restoration and confinement-deconfinement phase transition.We also sketch the phase diagram of quantum chromodynamics(QCD)at a finite temperature T and in the presence of background fields.The unified formalism for this study is based on the Schwinger-Dyson equations,symmetry preserving vector-vector contact interaction model of quarks,and an optimal time regularization scheme.At T=0,in the purely magnetic case(i.e.,eE→0),we observe the well-known magnetic catalysis effect.However,in a pure electric field background(eB→0),the electric field tends to restore the chiral symmetry and deconfinement above the pseudo-critical electric field eE^(x,C)_(c).In the presence of both eE and eB,we determine the magnetic catalysis effect in the particular region where eB dominates over eE,whereas we observe the chiral inhibition(or electric chiral rotation)effect when eE overshadows eB.At finite T,in the pure electric field case,the phenomenon of inverse electric catalysis appears to exist in the proposed model.Conversely,for a pure magnetic field background,we observe the magnetic catalysis effect in the mean-field approximation and inverse magnetic catalysis with eB-dependent coupling.The combined effects of eE and eB on the pseudo-critical T^(x,C)_(c)yields an inverse electromagnetic catalysis,with and without an eB-dependent effective coupling of the model.The findings of this study agree well with the already predicted results obtained via lattice simulations and other reliable effective models of QCD.

Nonperturbative Aspects of Axial Vector Vertex

It is shown how the axial vector current of current quarks is related to that of constituent quarks within the framework of the global color symmetry model.Gluon dressing of the axial vector vertex and the quark self-energy functions are described by the inhomogeneous Bethe-Salpeter equation in the ladder approximation and the Schwinger Dyson equation in the rainbow approximation,respectively.

Small Current Quark Mass Effects on Dressed-Quark Propagator in an Effective Quark-Quark Interaction Model

A method for obtaining the small current quark mass dependence of the dressed quark propagator from an effective quark-quark interaction model is developed. Within this approach the small current quark mass effects on dressed-quark propagator have been studied. A comparison with previous results is given.

Scalar Susceptibility of QCD from Dyson-Schwinger Approach

In quantum chromodynamics （QCD）, the scalar susceptibility represents the modification of the quark condensate, to a small perturbation of the parameter responsible for the explicit breaking of the symmetry, i.e., the current quark mass. By studying the linear response of the dressed quark propagator to the presence of a nonzero quark mass, we derive a model-independent formula for the scalar susceptibility, which contains the dressed quark propagator G（p） and the dressed scalar vertex F（p, 0）. The numerical values of the scalar susceptibility Xs are calculated within the framework of the rainbow-ladder approximation of the Dyson-Schwinger approach by employing two typical forms of model gluon propagator.

Quark Condensate in the Strange Matter

In a nonlinear chiral SU(3) framework, we investigate the quark condensate in the strange matter including and Λ, making use of chiral symmetry spontaneous breaking Lagrangian and mean-field approximation. The results show that the chiral symmetry is restored partially when the strange matter density increases and that plays a very important role in the strange matter which may approach the constituents of the neutron stars. In addition, we can find that the strange matter density where the π-condensate emerges leads to the ratio of the nucleon number to baryon number.

Collective Perspective on Advances in Dyson–Schwinger Equation QCD

We survey contemporary studies of hadrons and strongly interacting quarks using QCD's Dyson-Schwinger equations, addressing the following aspects: confinement and dynamical chiral symmetry breaking; the hadron spectrum; hadron elastic and transition form factors, from small-to large-Q2; parton distribution functions; the physics of hadrons containing one or more heavy quarks; and properties of the quark gluon plasma.

Exploring the light-quark interaction

Two basic motivations for an upgraded JLab facility are the needs： to determine the essential nature of light-quark confinement and dynamical chiral symmetry breaking （DCSB）; and to understand nucleon structure and spectroscopy in terms of QCD＇s elementary degrees of freedom. During the next ten years a programme of experiment and theory will be conducted that can address these questions. We present a Dyson- Schwinger equation perspective on this effort with numerous illustrations, amongst them： an interpretation of string^breaking; a symmetry-preserving truncation for mesons; the nucleon＇s strangeness σ-term; and the neutron＇s charge distribution.

Color-flavor dependence of the Nambu-Jona-Lasinio model and QCD phase diagram

We study the dynamical chiral symmetry breaking/restoration for various numbers of light quarks flavors N_(f) and colors N_(c) using the Nambu-Jona-Lasinio(NJL) model of quarks in the Schwinger-Dyson equation framework,dressed with a color-flavor dependence of effective coupling.For fixed N_(f)=2 and varying N_(c),we observe that the dynamical chiral symmetry is broken when N_(c) exceeds its critical value N_(c)^(c)≈2.2.For a fixed N_(c)=3 and varying N_(f),we observe that the dynamical chiral symmetry is restored when Nf reaches its critical value N_r^(c)≈8.Strong interplay is observed between N_(c) and N_(f),i.e.,larger values of N_(c) tend to strengthen the dynamical generated quark mass and quark-antiquark condensate,while higher values of N_(f) suppress both parameters.We further sketch the quantum chromodynamics(QCD) phase diagram at a finite temperature T and quark chemical potential μ for various N_(c) and N_(f).At finite T and μ,we observe that the critical number of colors N_(c)^(c) is enhanced,whereas the critical number of flavors N_(f)^(c) is suppressed as T and μ increase.Consequently,the critical temperature T_(c),μ_(c),and co-ordinates of the critical endpoint(T_(c)^(E),μ_(c)^(E)) in the QCD phase diagram are enhanced as N_(c) increases and suppressed when N_(f) increases.Our findings agree with the lattice QCD and Schwinger-Dyson equations predictions.

Temperature dependence of quarks and gluon vacuum condensate in the Dyson-Schwinger Equations at finite temperature

Based on the Dyson-Schwinger Equations （DSEs）, the two-quark vacuum condensate, the four-quark vacuum condensate, and the quark gluon mixed vacuum condensate in the non-perturbative QCD vacuum state are investigated by solving the DSEs with rainbow truncation at zero- and finite- temperature, respectively. These condensates are important input parameters in QCD sum rule with zero and finite temperature, and in studying hadron physics, as well as predicting the quark mean squared momentum rn02- also called quark virtuality in the QCD vacuum state. The present calculated results show that these physical quantities are almost independent of the temperature below the critical point temperature Tc=131 MeV, and above Tc the chiral symmetry is restored. For comparison we calculate the temperature dependence of the ＂in-hadron condensate＂ for pion. At the same time, we also calculate the ratio of the quark gluon mixed vacuum condensate to the two-quark vacuum condensate by using these condensates, and the unknown quark mean squared momentum in the QCD vacuum state has been obtained. The results show that the ratio m2/0（T） is almost fiat in the temperature region from 0 to To, although there are drastic changes of the quark vacuum condensate and the quark gluon mixed vacuum condensate at the region. Our predicted ratio comes out to be m2/0（T）=2.41 GeV2 at the Chiral limit, which is consistent with other theory model predictions, and strongly indicates the significance that the quark gluon mixed vacuum condensate has played in the virtuality calculations.