JASPER: a software for quantum chromodynamics Dyson-Schwinger equation numerical calculation

The JASPER program is the first part of the high-performance computing information system for estimate some elementary particle properties, developing at Petersburg Nuclear Physics Institute. The JASPER is an implementation of the Dyson-Schwinger equation numerical solution for simple dressed quark propagator calculation in rainbow approximation. The Dyson-Schwinger equation solution with the Marice-Tandy Ansatz is one of several phenomenological approaches to obtain quantitative results in quantum chromodynamics (QCD) within strong coupling regime. The JASPER program is programmed in the C++ language and uses the numerical algorithms from the GNU Scientific Library (GSL). The numerical results for dynamical quark mass in complex Euclidean space were obtained. This result will be employed to study the hadron spectrum with the Bethe-Salpeter equation approach.

Dynamical quark mass generation in QCD3 within the Hamiltonian approach in Coulomb gauge

We investigate the equal-time (static) quark propagator in Coulomb gauge within the Hamiltonian approach to QCD in d = 2 spatial dimensions. Although the underlying Clifford algebra is very different from its counterpart in d = 3, the gap equation for the dynamical mass function has the same form. The additional vector kernel which was introduced in d = 3 to cancel the linear divergence of the gap equation and to preserve multiplicative renormalizability of the quark propagator makes the gap equation free of divergences also in d = 2.

On the connection between quark propagation and hadronization

We investigate the properties and structure of the recently discussed “fully inclusive jet correlator”, namely, the gauge-invariant field correlator characterizing the final state hadrons produced by a free quark as this propagates in the vacuum. Working at the operator level, we connect this object to the single-hadron fragmentation correlator of a quark, and exploit a novel gauge invariant spectral decomposition technique to derive a complete set of momentum sum rules for quark fragmentation functions up to twist-3 level; known results are recovered, and new sum rules proposed. We then show how one can explicitly connect quark hadronization and dynamical quark mass generation by studying the inclusive jet’s gauge-invariant mass term. This mass is, on the one hand, theoretically related to the integrated chiral-odd spectral function of the quark, and, on the other hand, is experimentally accessible through the E and $${\widetilde{E}}$$ E ~ twist-3 fragmentation function sum rules. Thus, measurements of these fragmentation functions in deep inelastic processes provide one with an experimental gateway into the dynamical generation of mass in Quantum Chromodynamics.

Gluons, Heavy and Light Quarks in the QCD Vacuum

We are discussing the properties of the QCD vacuum which might be important especially for the understanding of hadrons with small quark core size ~ 0:3 fm: We assume that at these distances the QCD vacuum can be described by the Instanton Liquid Model (ILM). At larger distances, where confinement is important, ILM should be extended to Dyons Liquid Model (DLM). The ILM has only two free parameters, average instanton size ρ ≈ 0:3 fm and average inter-instanton distance R ≈ 1 fm, and can successfully describe the key features of light hadron physics. One of the important conceptual results was prediction of the momentum dependent dynamical quark mass M ~ (packing f raction)1/2 ρ-1 ≈ 360 MeV, later confirmed numerically by evaluations in the lattice. The estimates show that gluon-instanton interaction strength is also big and is controlled by the value of dynamical gluon mass Mg ≈ M. Heavy quarks interact with instantons much weaker. The heavy quark-instanton interaction strength is given by ΔmQ ~ packing fraction ρ-1 ≈ 70 MeV: Nevertheless, the direct instanton contribution to the colorless heavy-heavy quarks potential is sizable and must be taken into account. At small distances, where one-gluon exchange contribution to this potential is dominated, we have to take into account dynamical gluon mass Mg. Also, instantons are generating light-heavy quarks interactions and allow to describe the nonperturbative effects in heavy-light quarks systems.

Dilepton production in finite baryonic quark–gluon plasma

We study the evolution of hot plasma through a statistical model in the hadronic medium. Evolution of the plasma can be expressed by the free energy at finite temperature and quark chemical potential of the constituent particles in the system. In this study, the dynamical quark mass is dependent on momentum and temperature. The evolution is explained through thermodynamic variables like free energy and entropy curve. These variables show the behaviour of the system for the different chemical potentials, μ, at these transition temperatures T = 150–170 MeV. Moreover, the study of the dilepton production at these finite temperatures and quark chemical potentials from the fireball of quark–gluon plasma shows a specific structure of dilepton spectrum in the intermediate mass region of 1.0–4.0 GeV and its production rate is observed to be a strong increasing function of quark chemical potential for quark and antiquark annihilation. We further observe lepton spectra coming from the hadronic phase in the low mass M = 0–1.2 GeV region.