Radial excitations of the quark-antiquark string sweeping the Wilson-loop area are considered in the framework of the effective-action formalism. Identifying these excitations with the daughter Regge trajectories, we find corrections which they produ
ce to the constituent quark mass. The energy of the quark-antiquark pair turns out to be mostly saturated by the constituent quark masses, rather than by the elongation of the quark-antiquark string. Specifically, while the constituent quark mass turns out to increase as the square root of the radial-excitation quantum number, the energy of the string increases only as the fourth root of that number.
We suggest the possibility of creation in the early Universe of stable domains of radius a few kilometers wide, formed by coherently excited states of $pi$-mesons. Such domains appear dark to an external observer, since the decay rate of the said coh
erent pionic states into photons is vanishingly small. The related thermal insulation of the domains from the outer world could have allowed them to survive till present days. The estimated maximum radius and the period of rotation of such objects turn out to be compatible with those of certain pulsars.
The quark condensate is calculated in terms of the effective string tension and the constituent quark mass. For 3 colors and 2 light flavors, the constituent mass is bounded from below by the value of 460 MeV. This value is only accessible when the s
tring tension decreases linearly with the Schwinger proper time. For this reason, the Hausdorff dimension of a light-quark trajectory is equal to 4, indicating that these trajectories are similar to branched polymers, which can describe a weak first-order deconfinement phase transition in SU(3) Yang-Mills theory. Using this indication, we develop a gluon-chain model based on such trajectories.
We explore the thermodynamics of the gluon plasma in SU(3) Yang-Mills theory emerging from the non-trivial spatial dynamics of valence gluons. The lattice data suggest that these gluons interact with each other linearly at large spatial separations.
At high temperatures, valence gluons should reproduce the pressure of the non-interacting Stefan-Boltzmann plasma along with the leading perturbative correction. These properties of valence gluons can be modeled in terms of the integral over their trajectories. We calculate such a world-line integral analytically and obtain the pressure and the interaction measure $(varepsilon-3p)/T^4$ of the gluon plasma. Additionally, we account for the contributions of stochastic background fields to these thermodynamic quantities. The results turn out to be in a good agreement with the corresponding lattice data. In particular, the lattice-simulated peak of the interaction measure near the deconfinement critical temperature is reproduced.
We argue that the radiative energy loss of a parton traversing the quark-gluon plasma is determined by Landau damping of soft modes in the plasma. Using this idea, we calculate the jet quenching parameter of a gluon. The calculation is done in SU(3)
quenched QCD within the stochastic vacuum model. At the LHC-relevant temperatures, the result depends on the gluon condensate, the vacuum correlation length, and the gluon Debye mass. Numerically, when the temperature varies from T=T_c to T=900 MeV, the jet quenching parameter rises from hat q=0 to approximately 1.8 GeV^2/fm. We compare our results with the predictions of perturbative QCD and other calculations.
