Long and short distance behavior of the imaginary part of the heavy-quark potential

The imaginary part of the effective heavy-quark potential can be related to the total in-medium decay width of of heavy quark-antiquark bound states. We extract the static limit of this quantity using classical-statistical simulations of the real-time Yang-Mills dynamics by measuring the temporal decay of Wilson loops. By performing the simulations on finer and larger lattices we are able to show that the nonperturbative results follow the same form as the perturbative ones. For large quark-antiquark separations, we quantify the magnitude of the non-perturbative long-range corrections to the imaginary part of the heavy-quark potential. We present our results for a wide range of temperatures, lattice spacings, and lattice volumes. We also extract approximations for the short-distance behavior of the classical potential.

The imaginary part of the heavy-quark potential from real-time Yang-Mills dynamics

We extract the imaginary part of the heavy-quark potential using classical-statistical simulations of real-time Yang-Mills dynamics in classical thermal equilibrium. The r-dependence of the imaginary part of the potential is extracted by measuring the temporal decay of Wilson loops of spatial length r. We compare our results to continuum expressions obtained using hard thermal loop theory and to semi-analytic lattice perturbation theory calculations using the hard classical loop formalism. We find that, when plotted as a function of mDr, where mD is the hard classical loop Debye mass, the imaginary part of the heavy-quark potential shows little sensitivity to the lattice spacing at small mDr ≲ 1 and agrees well with the semi-analytic hard classical loop result. For large quark-antiquark separations, we quantify the magnitude of the non-perturbative long-range corrections to the imaginary part of the heavy-quark potential. We present our results for a wide range of temperatures, lattice spacings, and lattice volumes. This work sets the stage for extracting the imaginary part of the heavy-quark potential in an expanding non-equilibrium Yang Mills plasma.

Holographic QCD and magnetic fields

We review the holographic approach to electromagnetic phenomena in large N QCD. After a brief discussion of earlier holographic models, we concentrate on the improved holographic QCD model extended to involve magnetically induced phenomena. We explore the influence of magnetic fields on the QCD ground state, focusing on (inverse) magnetic catalysis of chiral condensate, investigate the phase diagram of the theory as a function of magnetic field, temperature and quark chemical potential, and, finally discuss effects of magnetic fields on the quark–anti-quark potential, shear viscosity, speed of sound and magnetization.

Some properties of the QQq-quark potential in string models

We propose a string theory construction which allows us to study properties of the potential of two heavy quarks coupled to a light quark. In such a case, the potential is a function of separation between the heavy quarks. The results show the universality of the string tension and factorization at small separations expected from heavy quark-diquark symmetry. In addition, we make an estimate of the string breaking distance. With the parameter values we use, this distance is found to be almost the same as that for the heavy quark-antiquark potential. We also discuss the heavy quark-quark potential and its relation to Lipkin rule.

Effect of temperature gradient on heavy quark anti-quark potential using gravity dual model

Thermal systems have traditionally been modeled via Euclideanized space by analytical continuation of time to an imaginary time. We extend the concept to static thermal gradients by recasting the temperature variation as a variation in the Euclidean metric. We apply this prescription to determine the Quark anti-Quark potential in a system with thermal gradient. A naturally occurring QCD medium with thermal gradients is a Quark Gluon Plasma (QGP). However, the QGP evolves in time. Hence, we use a quasi-stationary approximation, which is applicable only if the rate of time evolution is slow. Hence the application of our proposal to a Quark anti-Quark potential in QGP can be seen as a step towards a more exact theory which would incorporate time varying thermal gradients. The effect of a static temperature gradient on the Quark anti-Quark potential is analyzed using a gravity dual model. A non-uniform black string metric is developed, by perturbing the Schwarzchild metric, which allows to incorporate the temperature gradient in the dual AdS space. Finally, an expression for the Quark anti-Quark potential, in the presence of a static temperature gradient, is derived.

Building bulk from Wilson loops

We provide formulas for holographically building a bulk metric from given expectation values of rectangular Wilson loops. As a corollary, we prove that any confining quark potential necessarily leads to the existence of a bulk IR bottom.

Relativistic Friedrichs–Lee model and quark-pair creation model

In this paper, we present how the Friedrichs–Lee model could be extended to the relativistic scenario and be combined with the relativistic quark pair creation model in a consistent way. This scheme could be applied to study the “unquenched” effect of the meson spectra. As an example, if the lowest $$J^{PC}=0^{++}$$ J PC = 0 + + $$(u\bar{u}+d\bar{d})/\sqrt{2}$$ ( u u ¯ + d d ¯ ) / 2 bound state in the potential model is coupled to the $$\pi \pi $$ π π continuum, two resonance poles could be found from the scattering amplitude for the continuum states. One of them could correspond to the $$f_0(500)/\sigma $$ f 0 ( 500 ) / σ and the other probably $$f_0(1370)$$ f 0 ( 1370 ) . This scheme might shed more light on why extra states could appear in the hadron spectrum other than the prediction of the quark potential model.

Are the XYZ states unconventional states or conventional states with unconventional properties?

We discuss three possible scenarios for the interpretation of mesons containing a heavy quark and its antiquark near and above the first threshold for a decay into a pair of heavy mesons in a relative [Formula: see text]-wave. View I assumes that these thresholds force the quark potential to flatten which implies that while in these energy ranges molecular states may be formed, there should not be any quark–antiquark states above these thresholds. View II assumes that the main part of the interaction between two mesons is due to the poles which originate from the [Formula: see text] interaction. The properties of the [Formula: see text] mesons are strongly influenced by opening thresholds but the number of states is given by the quark model. In View III, both types of mesons are admitted also near and above the open flavor thresholds: [Formula: see text] mesons and dynamically generated mesons. Experimental consequences of these different views are discussed.