Chiral and deconfinement phase transitions in QED<Subscript>3</Subscript> with finite gauge boson mass

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.     

Dimuon production in ultrarelativistic nuclear collisions and QCD phase transitions

Dilepton production rates in nuclear collisions are calculated in order to study their sensitivity to the quark-gluon plasma and to the hadronic phases. This treatment differs from previous work on the subject in two respects: The width of the rho-meson, being exchanged in annihilation, is made temperature dependent, thus taking into account resonance melting as the critical deconfinement temperatureT _d is approached. Secondly, we study in addition to the standard scenario where chiral symmetry restoration and deconfinement occur at the same temperature (T _c =T _d ), an alternative possibility where deconfinement preceeds chiral symmetry restoration (T _d T _c ). Results differ substantially from those obtained assuming a temperature independent rho-meson width, andT _c =T _d .     

Confront holographic QCD with Regge trajectories of vectors and axial-vectors

By matching the predictions of the Dp–Dq soft-wall model in type II superstring theory with the spectra of vector and axial-vector mesons, we show the dependence of the Regge trajectories parameters on the metric parameters of the model. From the experimental results of Regge parameters for vector mesons, it is found that the D3 background brane with both q=5 and q=7 probe brane and D4 background brane with q=4 probe brane are close to the realistic holographic QCD. We also discuss how to realize chiral symmetry breaking in the vacuum and asymptotic chiral symmetry restoration in high excitation states. We find that the constant component of the 5-dimension mass square of axial-vector mesons plays an efficient role to realize the chiral symmetry breaking, and a small negative z ⁴ correction in the 5-dimension mass square is helpful to realize the chiral symmetry restoration in high excitation states.     

Axial-vector mesons and the problem of π<Emphasis Type="Italic">a</Emphasis><Subscript>1</Subscript> mixing

In the framework of the Nambu–Jona-Lasinio (NJL) model, a mechanism for eliminating the off-diagonal πa ₁ transitions from the effective meson Lagrangian is investigated. The problem is considered in the oneloop approximation for the quark loops. We employ the minimal superposition linear in the fields, a _μ ^' = a _μ ? c?_μπ, and show that the covariant transformation properties of both the axial-vector and vector physical fields are affected by this substitution. Contrary to some claims found in the literature, we demonstrate that the discussed change in covariant transformation properties of these fields does not result in various violations of chiral symmetry, but rather reduces to a redefinition of the S-matrix elements beyond the mass shell. At the same time, the covariant and noncovariant approaches yield identical on-shell results.     

Dissolving of mesons and soliton baryons in 2-dimensional gauge theories

We analyse two-dimensional fermionic models with a nonabelian gauge and chiral symmetry in the largeN limit. We show that there is a transition temperature at which the chiral symmetry is restored. At this transition temperature the meson bound states and the chiral solitons, the baryons of the model, dissolve. We interpret this as a simultaneous chiral symmetry restoration and deconfinement transition.     

Chiral and deconfinement phase transitions of two-flavour QCD at finite temperature and chemical potential

We present results for the chiral and deconfinement transition of two flavor QCD at finite temperature and chemical potential. To this end we study the quark condensate and its dual, the dressed Polyakov loop, with functional methods using a set of Dyson-Schwinger equations. The quark propagator is determined self-consistently within a truncation scheme including temperature and in-medium effects of the gluon propagator. For the chiral transition we find a crossover turning into a first order transition at a critical endpoint at large quark chemical potential, μEP/TEP≈3. For the deconfinement transition we find a pseudo-critical temperature above the chiral transition in the crossover region but coinciding transition temperatures close to the critical endpoint.     

PARISI-SOURLAS CONFINEMENT MECHANISM OF QUANTUM CHROMODYNAMICS

Using Parisi and Sourlas dimensional reduction, four-dimensional quantum chromodynamics is reduced to a two-dimensional principal chiral model by suitable superspace embedding. The frame T^a cannot be regarded as a fixed one and the frame connection field \varω_μ(x) becomes a dynamical gauge field in two dimensions, giving rise to a confining potential. As a result of the original SU(3) Yang-Mills field obtains another SU(3) local symmetry and turns into SU(3)×SU(3) local symmetry－one group element as exp (iδ\varphi^aT^a) with fixed frame T^a, the other gauging the frame T^a.     

The high-temperature behaviour of lattice QCD with fermions

By Monte Carlo simulation on the lattice, we calculate the high-temperature behaviour of the energy density ? in SU(2) and SU(3) QCD with Wilson fermions. From the leading term of the hopping parameter expansion, we find that ? converges very rapidly to the Stefan-Boltzmann limit of an asymptotically free quark-gluon gas. The behaviour in the non-asymptotic region indicates that chiral symmetry restoration occurs at a higher temperature (T_ch) than colour deconfinement (T_c), with $\text{T}{}_{\mathrm{<mtext>ch</mtext>}}\text{T}{}_{\mathrm{<mtext>c</mtext>}}\text{≈ 1.3}$.     

Effective lagrangian analysis of the chiral phase transition at finite density

Introducing a finite chemical potential μ for the quark number density ψ^°ψ, we study analytically the restoration of Π^° chiral symmetry as μ is varied. In the strong coupling limit, the effective lagrangian for SU(N) gauge theories coupled to fermion fields in d dimensions is derived for all N. In the case of SU(2) we predict a second order chiral symmetry restoration phase transition, whereas for all N?3 the transition is first order. Predictions are given for the critical values of the chemical potential μ.     

QED with vector and axial vector types of interaction and dynamical generation of particle masses

We consider a model of electrodynamics with two types of interaction, the vector \((e\bar \psi (\gamma ^\mu A_\mu )\psi )\) and axial vector \((e_A \bar \psi (\gamma ^\mu \gamma ^5 B_\mu )\psi )\) interactions, i.e., with two types of vector gauge fields, which corresponds to the local nature of the complete massless-fermion symmetry group U(1) ? U _A (1). We present a phenomenological model with spontaneous symmetry breaking through which the fermion and the axial vector field B_μ acquire masses. Based on an approximate solution of the Dyson equation for the fermion mass operator, we demonstrate the phenomenon of dynamical chiral symmetry breaking when the field B_μ has mass. We show the possibility of eliminating the axial anomalies in the model under consideration when introducing other types of fermions (quarks) within the standard-model fermion generations. We consider the polarization operator for the field B_μ and the procedure for removing divergences when calculating it. We demonstrate the emergence of a mass pole in the propagator of the particles that correspond to the field B_03BC when chiral symmetry is broken and consider the problems of regularizing closed fermion loops with axial vector vertices in connection with chiral symmetry breaking.     

q-deformed supersymmetric Newton oscillators

We propose that in QCD with dynamical quarks, colour deconfinement occurs when an external field induced by the chiral condensate strongly aligns the Polyakov loop. This effect sets in at the chiral symmetry restoration temperature and thus makes deconfinement and chiral symmetry restoration coincide. The predicted singular behaviour of Polyakov loop susceptibilities at is shown to be supported by finite temperature lattice calculations. Received: 27 September 2000 / Published online: 8 December 2000     

Effect of Wigner energy on the symmetry energy coefficient in nuclei

The nuclear symmetry energy coefficient(including the coefficient a_(sym)~((4)) of the I~4 term) of finite nuclei is extracted by using the differences of available experimental binding energies of isobaric nuclei.It is found that the extracted symmetry energy coefficient a_(sym)~*(A,I) decreases with increasing isospin asymmetry I,which is mainly caused by Wigner correction,since e_(sym)~* is the summation of the traditional symmetry energy e_(sym) and the Wigner energy ew.We obtain the optimal values J = 30.25±0.10 MeV,a_(ss)=56.18±1.25 MeV,a_(sym)~((4)) = 8.33±1.21 MeV and the Wigner parameter x= 2.38 ±0.12 through a polynomial fit to 2240 measured binding energies for nuclei with20 ≤ A ≤ 261 with an rms deviation of 23.42 keV.We also find that the volume symmetry coefficient J■ 30 MeV is insensitive to the value x,whereas the surface symmetry coefficient a_(ss) and the coefficient a_(sym)~((4)) are very sensitive to the value of x in the range 1≤x≤4.The contribution of the a_(sym)~((4)) term increases rapidly with increasing isospin asymmetry I.For very neutron-rich nuclei,the contribution of the a_(sym)~((4)) term will play an important role.     

The spectrum of hot hadronic matter and finite-temperature QCD sum rules

The sum rules method, which is widely used for the investigation of the resonance physics within the QCD framework, is generalized to the case of finite temperatures and densities. Conditions are formulated under which this method is quite efficient for the determination of the spectrum of hadronic matter at T ≠ 0. The finite-temperature QCD sum rules are analysed in the vector channel J^PC = 1⁻⁻. Sharp and qualitative changes in the spectrum are found in the temperature interval T = 130–150 MeV. It is naturally explained as a consequence of the disappearance of confinement at the temperature T_c = 140±10 MeV. The finite-temperature QCD sum rules also show that the restoration of chiral symmetry at some temperature T_F cannot precede deconfinement. In the case T_F⪢T_c the sum rules indicate that the intermediate phase at T_c<T<T_F is dominated by quasi-free quarks with nonzero dynamical mass m_q^T ≈ 300 MeV.     

Excited quark-quark interactions in a bag model

We calculate the colour magnetic and electric fields,B ^a andE ^a , in the static cavity approximation of the MIT bag model. This is done rigorously for all direct and exchange four-currents of quarks in theS _1/2,P _1/2 andP _3/2 bag states. We then find the quark-quark colour interaction for direct and exchange diagrams. The one-pion exchange diagrams due to chiral symmetry are also calculated.     

New spectral representation and evaluation of f π and the quark condensate \left\langle {\bar qq} \right\rangle in the terms of string tension

New spectral representations for f _π and chiral condensate are derived in QCD and used for calculations in the large-N _c limit. Both quantities are expressed in this limit through string tension σ and gluon correlation length T _g without fitting parameters. As a result, one obtains $\left\langle {\bar qq} \right\rangle = - N_c \sigma ^2 T_g a_1 $ , $f_\pi = \sqrt {N_c } \sigma T_g a_2 $ , with a ₁=0.0823, a ₂=0.30. Taking σ=0.18 GeV² and T _g=1 GeV^?1, as known from analytic and lattice calculations, this yields $\left\langle {\bar qq} \right\rangle $ (μ=2 GeV)=?(0.225 GeV)³, f _π=0.094 GeV, which is close to the standard values.     

Meson screening masses from lattice QCD with two light quarks and one strange quark

We present results for screening masses of mesons built from light and strange quarks in the temperature range of approximately between 140 MeV to 800 MeV. The lattice computations were performed with 2+1 dynamical light and strange flavors of improved (p4) staggered fermions along a line of constant physics defined by a pion mass of about 220 MeV and a kaon mass of 500 MeV. The lattices had temporal extents N _τ =4, 6 and 8 and aspect ratios of N _s /N _τ ≥4. At least up to a temperature of 140 MeV the pseudo-scalar screening mass remains almost equal to the corresponding zero temperature pseudo-scalar (pole) mass. At temperatures around 3T _c (T _c being the transition temperature) the continuum extrapolated pseudo-scalar screening mass approaches very close to the free continuum result of 2πT from below. On the other hand, at high temperatures the vector screening mass turns out to be larger than the free continuum value of 2πT. The pseudo-scalar and the vector screening masses do not become degenerate even for a temperature as high as 4T _c . Using these mesonic spatial correlation functions we have also investigated the restoration of chiral symmetry and the effective restoration of the axial symmetry. We have found that the vector and the axial-vector screening correlators become degenerate, indicating chiral symmetry restoration, at a temperature which is consistent with the QCD transition temperature obtained in previous studies. On the other hand, the pseudo-scalar and the scalar screening correlators become degenerate only at temperatures larger than 1.3T _c , indicating that the effective restoration of the axial symmetry takes place at a temperature larger than the QCD transition temperature.     

Charmed baryons in quantum chromodynamics

We consider a three-phase model of strongly interacting matter, treating each phase as an ideal gas modified by a simple phenomenological interaction feature. For nuclear matter, we take into account the baryonic repulsion; for the quark-gluon plasma, we include the bag pressure; the constituent quark phase has a non-zero effective quark mass as well as an independent bag pressure. By studying which phase dominates thermodynamically in what region of temperature and baryon number density, we obtain a phase diagram for strongly interacting matter and gain some insight on the relation between deconfinement and chiral symmetry restoration.     

Global SO(3) × SO(3) × U(1) symmetry of the Hubbard model on bipartite lattices

In this paper the global symmetry of the Hubbard model on a bipartite lattice is found to be larger than SO(4). The model is one of the most studied many-particle quantum problems, yet except in one dimension it has no exact solution, so that there remain many open questions about its properties. Symmetry plays an important role in physics and often can be used to extract useful information on unsolved non-perturbative quantum problems. Specifically, here it is found that for on-site interaction U ≠ 0 the local SU(2) × SU(2) × U(1) gauge symmetry of the Hubbard model on a bipartite lattice with N_a^D sites and vanishing transfer integral t = 0 can be lifted to a global [SU(2) × SU(2) × U(1)]/Z₂² = SO(3) × SO(3) × U(1) symmetry in the presence of the kinetic-energy hopping term of the Hamiltonian with t > 0. (Examples of a bipartite lattice are the D-dimensional cubic lattices of lattice constant a and edge length L = N_aa for which D = 1, 2, 3,... in the number N_a^D of sites.) The generator of the new found hidden independent charge global U(1) symmetry, which is not related to the ordinary U(1) gauge subgroup of electromagnetism, is one half the rotated-electron number of singly occupied sites operator. Although addition of chemical-potential and magnetic-field operator terms to the model Hamiltonian lowers its symmetry, such terms commute with it. Therefore, its 4^N_aD energy eigenstates refer to representations of the new found global [SU(2) × SU(2) × U(1)]/Z₂² = SO(3) × SO(3) × U(1) symmetry. Consistently, we find that for the Hubbard model on a bipartite lattice the number of independent representations of the group SO(3) × SO(3) × U(1) equals the Hilbert-space dimension 4^N_aD. It is confirmed elsewhere that the new found symmetry has important physical consequences.     

Light-Front Zero-Mode Issue for the Transition Form Factors Between Pseudoscalar and Vector Mesons

We study the light-front zero-mode contribution to the transition form factors (g, f, a _±, T _i ) (i = 1, 2, 3) for the exclusive semileptonic P → V ?ν _? and rare P → V ? ⁺?^? decays using a covariant fermion field theory model in (3+1) dimensions. While the zero-mode contribution in principle depends on the form of the vector meson vertex Γ ^μ  = γ ^μ ? (2k ? P _V ) ^μ /D, the six form factors (g, f, a ₊, T ₁, T ₂, T ₃) are found to be free from the zero mode if the denominator D contains the term proportional to the light-front longitudinal momentum fraction factor (1/x) ⁿ of the struck quark with the power n > 0. Although the form factor a _? is not free from the zero mode, the zero-mode contribution comes only either from the simple vertex Γ ^μ  = γ ^μ term or from the other term just with a constant D (i.e. n = 0). We identify the zero-mode operator that is convoluted with the initial- and final-state valence wave functions to generate the zero-mode contribution to a _?.     

A model for chiral symmetry breaking in QCD

A recently proposed model for dynamical breaking of chiral symmetry in QCD is extended and developed for the calculation of pion and chiral symmetry breaking parameters. The pion is explicitly realized as a massless Goldstone boson and as a bound state of the constituent quarks. We compute, in the limit of exact chiral symmetry, M_Q, the constituent quark mass $\text{?}{}_{\mathrm{\pi }}$ the pion decay coupling, $\text{〈}\text{u}\text{u〉}$, the constituent quark loop density, μ_π²/m_q, the ratio of the Goldstone boson mass squared to the bare quark mass, and 〈r²〉_π, the pion electromagnetic charge radius squared.