Order Parameter Of Chiral Symmetry Research Articles

Thermal properties of pi and rho meson

We computed the pole masses and decay constants of pi and rho meson at finite temperature in the framework of Dyson–Schwinger equations and Bethe–Salpeter equations approach. Below transition temperature, pion pole mass increases monotonously, while rho meson seems to be temperature independent. Above transition temperature, pion mass approaches the free field limit of screening mass sim 2pi T, whereas rho meson is about twice as large as that limit. Pion and the longitudinal projection of rho meson decay constants have similar behaviour as the order parameter of chiral symmetry, whereas the transverse projection of rho meson decay constant rises monotonously as temperature increases. The inflection point of decay constant and the chiral susceptibility get the same phase transition temperature. Though there is no access to the thermal width of mesons within this scheme, it is discussed by analyzing the Gell-Mann-Oakes-Renner (GMOR) relation in medium. These thermal properties of hadron observables will help us understand the QCD phases at finite temperature and can be employed to improve the experimental data analysis and heavy ion collision simulations.

Thermalization and dynamical spectral properties in the quark-meson model

We investigate the nonequilibrium evolution of the quark-meson model using two-particle irreducible effective action techniques. Our numerical simulations, which include the full dynamics of the order parameter of chiral symmetry, show how the model thermalizes into different regions of its phase diagram. In particular, by studying quark and meson spectral functions, we shed light on the real-time dynamics approaching the crossover transition, revealing e.g. the emergence of light effective fermionic degrees of freedom in the infrared. At late times in the evolution, the fluctuation-dissipation relation emerges naturally among both meson and quark degrees of freedom, confirming that the simulation successfully reaches thermal equilibrium.

Long-range Coulomb interaction effects on the topological phase transitions between semimetals and insulators

Topological states may be protected by a lattice symmetry in a class of topological semi-metals. In three spatial dimensions, the Berry flux around gapless excitations in momentum space defines a chirality concretely, so a protecting symmetry may be referred to as a chiral symmetry. Prime examples include Dirac semi-metal (DSM) in a distorted spinel, BiZnSiO$_4$, protected by a mirror symmetry and DSM in Na$_3$Bi, protected by a rotational symmetry. In these states, topology and a chiral symmetry are intrinsically tied. In this work, we investigate characteristics interplay between a chiral symmetry order parameter and instantaneous long-range Coulomb interaction with the standard renormalization group method. We show that a topological transition associated with a chiral symmetry is stable under the presence of the Coulomb interaction and the electron velocity always becomes faster than one of a chiral symmetry order parameter. Thus, the transition {\it must not} be relativistic, which implies a supersymmetry is intrinsically forbidden by the long-range Coulomb interaction. {Asymptotically exact} universal ratios of physical quantities such as energy gap ratio are obtained, and connections with experiments and recent theoretical proposals are also discussed.

A novel probe of chiral restoration in nuclear medium

We propose measuring the mass shift and width broadening of the f1(1285) meson together with those of the ω from a nuclear target as a means to experimentally probe the partial restoration of chiral symmetry inside the nuclear matter. The relation between the order parameter of chiral symmetry and the difference in the correlation functions of the f1(1285) current and the ω current is discussed in the limit where the disconnected diagrams are neglected. A QCD sum rule analysis of the f1(1285) meson mass leads to about 100 MeV attraction in nuclear matter, which can be probed in future experiments.

Fluctuation signals and the critical point

We explore the potential of fluctuation measurements to investigate the properties of hot and dense matter created in relativistic heavy-ion collisions to investigate signals expected from the critical point and the first-order phase transition. Contrary to calculations in a grand canonical ensemble we combine the dynamics of the systems with the nonequilibrium propagation of the order parameter of chiral symmetry. We find an enhancement of the fluctuations of the order parameter at the phase transition. Furthermore, we study the effect of exact baryon charge conservation on the net-baryon and the net-proton kurtosis for central (b ⩽ 2.75 fm) Pb+Pb/Au+Au collisions from Elab = 2A GeV to GeV from the UrQMD model. The results are compared to experimentally applied cuts and corrections.

Baryons in AdS/QCD

Abstract We construct a holographic model for baryons in the context of AdS/QCD and study the spin- 1 2 nucleon spectra and its couplings to mesons, taking full account of the effects from the chiral symmetry breaking. A pair of 5D spinors is introduced to represent both left and right chiralities. Our model contains two adjustable parameters, the infrared cutoff and the Yukawa coupling of bulk spinors to bulk scalars, corresponding to the order parameter of chiral symmetry. Taking the lowest-lying nucleon mass as an input, we calculate the mass spectrum of excited nucleons and the nucleon couplings to pions. The excited nucleons show a parity-doubling pattern with smaller pion–nucleon couplings.

Lattice QCD without tuning, mixing and current renormalization

The classically perfect action of QCD requires no tuning to get the pion massless in the broken phase: the critical bare mass m q c is zero. Neither the vector nor the flavour non-singlet axial vector currents need renormalization. Further, there is no mixing between 4-fermion operators in different chiral representations. The order parameter of chiral symmetry requires, however, a subtraction which is given here explicitly. These results are based on the fact that the fixed point action satisfies the Ginsparg-Wilson remnant chiral symmetry condition. On chiral symmetry related questions any other local solution of this condition will produce similar results.

Scaling of Chiral Order Parameter in Two-Flavor QCD

The finite temperature transition of QCD with two degenerate light quarks is studied on the lattice with a renormalization group improved gauge action and the Wilson quark action. We have made simulations on an $8^3\times 4$ lattice near the chiral transition point. It is shown that the chiral condensate which is the order parameter of chiral symmetry satisfies remarkably a scaling relation with the exponents of the three dimensional O(4) Heisenberg model. This indicates that the chiral transition in two-flavor QCD is of second order in the continuum limit.

Inhomogeneous chiral condensate in the Schwinger model at finite density.

The behavior of the chiral symmetry order parameter [l angle][bar [psi]][psi][r angle] in the (1+1)-dimensional Schwinger model at finite chemical potential is studied. We find an inhomogeneous chiral condensate.

Spontaneous symmetry breaking in QCD

We study dynamical chiral symmetry breaking in massless QCD by the use of the generalized Hartree-Fock method. As the order parameter of chiral symmetry we choose the dynamical quark mass in the zero momentum limit which we call low energy quark mass. We calculate the low energy mass to the second order of diagrammatic expansion around shifted perturbative vacuum. We then show that the mass is finite and renormalization group invariant. After the improvement of the result by the method of effective charges we estimate the mass in the true vacuum under the gap and stationarity conditions and demonstrate that both of them produce non-zero mass proportional to a conventional scale, which breaks down the chiral symmetry.

Parallel-transported multigrid and its application to the schwinger model

We present an efficient multigrid algorithm to invert the Dirac-Operator in simulations of lattice gauge theories. The coarse-level gauge and “fermionic” fields are derived from the fine-level fields using the appropriate gauge fields as parallel transporters; for this reason the method is called Parallel-Transported Multigrid (PTMG). We demonstrate the algorithm by computing the chiral symmetry order parameter and the pseudoscalar meson mass in the quenched Schwinger Model. In a considerable part of the physically relevant parameter space the method is superior over the one-level relaxation algorithms by several orders of magnitude. The method can be generalized in a straightforward way to SU(3) lattice gauge theory in 4 dimensions.

Fermion simulations using parallel transported multigrid

Using a parallel transported multigrid (PTMG) technique, we compute the chiral symmetry order parameter and the pseudo-scalar meson mass in the quenched Schwinger model. In our PTMG method, the coarse level gauge and “fermionic” fields are derived from the fine level fields using the appropriate gauge fields as parallel transporters. For small quark masses and moderate correlation lengths we obtain a very rapid convergence (about one order of magnitude per cycle). In the same range of parameters, the one-level relaxation algorithms are slower by many orders of magnitude. We then show how to use this solver for dynamical fermions.

Monopoles and chiral-symmetry breaking in three-dimensional lattice QED.

The chiral-symmetry order parameter $〈\overline{\ensuremath{\chi}}\ensuremath{\chi}〉$ and the monopole density ${\ensuremath{\rho}}_{m}$ are calculated for lattice QED in 2+1 dimensions for zero and two fermion flavors. A comparison of the results for the compact and the noncompact lattice action yields a strong correlation between $〈\overline{\ensuremath{\chi}}\ensuremath{\chi}〉$ and ${\ensuremath{\rho}}_{m}$ being essentially independent of the type of lattice action. This is interpreted as evidence that monopole condensation drives chiral-symmetry breaking in three-dimensional lattice QED.

A Langevin simulation off the Gross-Neveu spectrum

We study the order parameter of chiral symmetry, and fermion and boson masses in the Gross-Neveu model as a function of the flavour number N and of the Langevin time step ε, in the scaling region. The 1/N dependence of the ϵ=0 value of the order parameter is in excellent agreement with an analytical calculation up to second order. Care is taken of the important two fermion contribution in the bosonic correlation functions. Mass ratios are found to be ϵ dependent, but their ϵ=0 extrapolation is compatible with the analytic expectation.

Chiral-symmetry order parameter, the lattice, and nucleosynthesis.

I discuss an order parameter for the chiral-symmetry restoration phase transition which may be useful in computations of big-bang nucleosynthesis, a phenomenon which requires a finite baryon-number density. This parameter is strictly speaking an order parameter in the large-N limit, and distinguishes between a parity-doubled and a massless-fermion realization of chiral-symmetry restoration. This order parameter may be evaluated at a zero net baryon-number density at finite temperature, and is useful as long as the baryon chemical potential ..mu.. is much less than the temperature T.

Chiral symmetry on the lattice with Wilson fermions

Abstract The chiral properties of the continuum limit of lattice QCD with Wilson fermions are studied. We show that a partially conserved axial current can be defined, satisfying the usual current algebra requirements. A proper definition of the chiral symmetry order parameter, 〈0| ψ ψ|0〉 , is given, and the chiral properties of composite operators are investigated. The implications of our analysis to the lattice determination of non-leptonic weak amplitudes are also discussed.