Heavy Quark-antiquark Potential Research Articles

Unscreened forces in the quark-gluon plasma?

We study the correlator of temporal Wilson lines at nonzero temperature in 2+1 flavor lattice QCD with the aim to define the heavy quark-antiquark potential at nonzero temperature. For temperatures 153 MeV≤T≤352 MeV the spectral representation of this correlator is consistent with a broadened peak in the spectral function, position, or width of which then defines the real or imaginary parts of the heavy quark-antiquark potential at nonzero temperature, respectively. We find that the potential’s real part is not screened contrary to the widely held expectations. We comment on how this fact may modify the picture of quarkonium melting in the quark-gluon plasma. Published by the American Physical Society 2024

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.

The effect of temperature gradient on the heavy quark–antiquark potential using a gravity dual model

Abstract 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–antiquark potential in a system with a 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. The application of our proposal to a quark–antiquark potential in QGP can be seen as a step towards a more exact theory that would incorporate time-varying thermal gradients. The effect of a static temperature gradient on the quark–antiquark potential is analyzed using a gravity dual model. A non-uniform black string metric is developed by perturbing the Schwarzschild metric, which allows us to incorporate the temperature gradient in the dual anti-de Sitter space. Finally, an expression for the quark–antiquark potential in the presence of a static temperature gradient is derived.

Strongly coupled N=4 supersymmetric Yang-Mills plasma on the Coulomb branch. I. Thermodynamics

We study $\mathcal{N} = 4$ super Yang-Mills theory on the Coulomb branch (cSYM) in the strong coupling limit by using the AdS/CFT correspondence. The dual geometry is the rotating black 3-brane Type IIB supergravity solution with a single non-zero rotation parameter $r_{0}$ which sets a fixed mass scale corresponding to the scalar condensate $<\mathcal{O}>\,\,\sim r_{0}^4$ in the Coulomb branch. We introduce a new ensemble where $T$ and $<\mathcal{O}>$ are held fixed, i.e., the free energy $F(T,<\mathcal{O}>)$ is a function of $T$ and $<\mathcal{O}>$. We compute the equation of state (EoS) of $\mathcal{N} = 4$ cSYM at finite $T$, as well as the heavy quark-antiquark potential and the quantized mass spectrums of the scalar and spin-2 glueballs at $T=0$. By computing the Wilson loop (minimal surface) at $T=0$, we determine the heavy quark-antiquark potential $V(L)$ to be the Cornell potential, which is confining for large separation $L$. At $T\neq 0$, we find two black hole branches: the large black hole and small black hole branches. For the large black hole branch, that has positive specific heat, we find qualitatively similar EoS to that of pure Yang-Mills theory on the lattice. For the small black hole branch, that has negative specific heat, we find an EoS where the entropy and energy densities decrease with $T$. We also find a second-order phase transition between the large and small black hole branches with critical temperature $T_c=T_{min}$.

Heavy quarkonium moving in hot and dense deconfined nuclear matter

We study the behavior of the complex potential between a heavy quark and its antiquark, which are in relative motion with respect to a hot and dense medium. The heavy quark-antiquark complex potential is obtained by correcting both the Coulombic and the linear terms in the Cornell potential through a dielectric function estimated within the real-time formalism using the hard thermal loop approximation. We show the variation of both the real and the imaginary parts of the potential for different values of velocities when the bound state ($ Q\bar{Q}$ pair) is aligned in the direction parallel as well as perpendicular to the relative velocity of the $ Q\bar{Q}$ pair with the thermal medium. With an increase of the relative velocity the screening of the real part of the potential becomes weaker at short distances and stronger at large distances for the parallel case. However, for the perpendicular case the potential decreases with an increase of the velocity at all distances which results in the larger screening of the potential. In addition, the inclusion of the string term makes the screening of the potential weaker as compared to the Coulombic term alone for both cases. Therefore, by combining all these effects we expect a stronger binding of a $ Q\bar{Q} $ pair in a moving medium in the presence of the string term as compared to the Coulombic term alone. The imaginary part decreases (in magnitude) with an increase of the relative velocity, leading to a decrease of the width of the quarkonium state at higher velocities. The inclusion of the string term increases the magnitude of the imaginary part, which results in an increase of the width of the quarkonium states. All of these effects lead to the modification in the dissolution of quarkonium states.

Towards next-to-leading order corrections to the heavy quark potential in the effective string theory

We present our calculation of the non-relativistic corrections to the heavy quark-antiquark potential up to leading and next-to-leading order (NLO) via the effective string theory (EST). Full systematics of effective field theory (EFT) are discussed in order for including the NLO contribution that arises in the EST. We also show how the number of dimensionful parameters arising from the EST are reduced by the constraints between the Wilson coeffcients from non-relativistic EFTs for QCD.

Effective string theory and the long-range relativistic corrections to the quark-antiquark potential

The complete expression of the heavy quark-antiquark potential up to order $1/m^2$ is known from QCD in terms of Wilson loop expectation values. We use that expression and a mapping, assumed to be valid at large distances, between Wilson loop expectation values and correlators evaluated in the effective string theory, to compute the potential. We obtain previously unknown results for the spin and momentum-independent parts of the potential. These are linearly rising with the distance and may be interpreted as relativistic corrections to the string tension. We confirm known results for the other parts of the potential. Finally, we compute the discrete spectrum of a heavy quark-antiquark pair whose interaction is just given by the obtained potential.

Holographic quark–antiquark potential in hot, anisotropic Yang–Mills plasma

Using the gauge/gravity duality we calculate the heavy quark–antiquark potential in a hot, anisotropic and strongly coupled Yang–Mills plasma in (3+1)-dimensions. As the anisotropic medium we take a deformed version of N=4 super Yang–Mills theory at finite temperature following a recent work where the dual type IIB supergravity solution is also proposed. We turn on a small value of the anisotropy parameter, for which the gravity dual is known analytically (perturbatively), and compute the velocity-dependent quark–antiquark interaction potential when the pair is moving through the plasma with a velocity v. By setting v=0 we recover the static quark–antiquark potential. We numerically study how the potential is modified in the presence of anisotropy. We further show numerically how the quark–antiquark separation (both in the static and the velocity-dependent case) and hence, the screening length gets modified by anisotropy. We discuss various cases depending upon the direction of the dipole and the direction of its propagation and make a comparative study of these cases. We are also able to obtain an analytical expression for the screening length of the dipole moving in a hot, anisotropic plasma in a special case.

Quark-antiquark potential to order1/mand heavy quark masses

An updated heavy quark-antiquark potential is constructed by matching the short-distance perturbative part to long-distance lattice QCD results at an intermediate r scale. The static potential and the order 1/m potential are both analyzed in this way. Effects if order 1/m in charmonium and bottomonium spectra are discussed in comparison. Charm and bottom quark masses are deduced from the spectra and related to the quark masses of other schemes.

Phenomenology of AdS/QCD and its gravity dual

We construct the dilaton potential in the gravity dual theory of AdS/QCD for the warp factor of Pirner and Galow [1] and Nian and Pirner [2]. Using this AdS 5 -metric with properties similar to QCD, we find that the gravity dual leads to a meaningful gauge coupling in the region between the charmonium and bottonium mass, but differs slightly from QCD in the extreme UV. When we fix the ultraviolet behavior in accord with the β-function, we can obtain good agreement with the overall heavy quark–antiquark potential. Although the leading order proportional to − α 4 / 3 r differs from perturbative QCD, the full potential agrees quite well with the short distance QCD potential in NNLO.

Bottomonium Spectrum with Screened Potential

As a sister work of [Phys. Rev. D 79 (2009) 094004], we incorporate the color-screening effect due to light quark pair creation into the heavy quark-antiquark potential, and investigate the effects of screened potential on the spectrum of bottomonium. We calculate the masses, electromagnetic decays, and E1 transitions of bottomonium states. We find that the fine splittings between χbJ (J = 0, 1, 2) states are in good agreement with experimental data, and the E1 transition rates of γ(2S) → γχbJ (1P) and γ(3S) → γχbJ (2P) (J = 0, 1, 2) all agree with data within experimental errors. In particular, the mass of γ(6S) is lowered down to match that of the γ(11020), which is smaller than the predictions of the linear potential models by more than 100 MeV. Comparison between charmonium and bottomonium in some related problems is also discussed.

Higher charmonia andX,Y,Zstates with screened potential

We incorporate the color-screening effect due to light quark pair creation into the heavy quark-antiquark potential, and investigate the effects of screened potential on the spectrum of higher charmonium. We calculate the masses, electromagnetic decays, and E1 transitions of charmonium states in the screened potential model, and propose possible assignments for the newly discovered charmonium or charmoniumlike ``$X$, $Y$, $Z$'' states. We find the masses of higher charmonia with screened potential are considerably lower than those with unscreened potential. The ${\ensuremath{\chi}}_{c2}(2P)$ mass agrees well with that of the $Z(3930)$, and the mass of $\ensuremath{\psi}(4415)$ is compatible with $\ensuremath{\psi}(5S)$ rather than $\ensuremath{\psi}(4S)$. In particular, the discovered four $Y$ states in the initial state radiation process, i.e., $Y(4008)$, $Y(4260)$, $Y(4320/4360)$, $Y(4660)$ may be assigned as the $\ensuremath{\psi}(3S)$, $\ensuremath{\psi}(4S)$, $\ensuremath{\psi}(3D)$, $\ensuremath{\psi}(6S)$ states, respectively. The $X(3940)$ and $X(4160)$ found in the double charmonium production in ${e}^{+}{e}^{\ensuremath{-}}$ annihilation may be assigned as the ${\ensuremath{\eta}}_{c}(3S)$ and ${\ensuremath{\chi}}_{c0}(3P)$ states. Based on the calculated E1 transition widths for ${\ensuremath{\chi}}_{c1}(2P)\ensuremath{\rightarrow}\ensuremath{\gamma}J/\ensuremath{\psi}$ and ${\ensuremath{\chi}}_{c1}(2P)\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\psi}(2S)$ and other results, we argue that the $X(3872)$ may be a ${\ensuremath{\chi}}_{c1}(2P)$ dominated charmonium state with some admixture of the ${D}^{0}{\overline{D}}^{*0}$ component. Possible problems encountered in these assignments and comparisons with other interpretations for these $X$, $Y$, $Z$ states are discussed in detail. We emphasize that more theoretical and experimental investigations are urgently needed to clarify these assignments and other interpretations.

The Cornell potential from general geometries in AdS/QCD

We consider the heavy quark–antiquark potential in the AdS/QCD correspondence, focusing in particular on a recently calculated AdS-like metric deformed by back-reaction effects. We find that tuning the long-distance behaviour of the potential leads to a discrepancy at small distances, and discuss how to better constrain AdS/QCD geometries. A systematic comparison of various geometries is presented, based on goodness of fit to lattice data in the quenched approximation. The back-reacted geometry is seen to be phenomenologically favoured over an alternative geometry with the same number of parameters, although it does not perform as well as some other geometries.

Gravity duals for the Coulomb branch of marginally deformed Script N = 4 Yang-Mills

Supergravity backgrounds dual to a class of exactly marginal deformations of N supersymmetric Yang-Mills can be constructed through an SL(2,R) sequence of T-dualities and coordinate shifts. We apply this transformation to multicenter solutions and derive supergravity backgrounds describing the Coulomb branch of N=1 theories at strong 't Hooft coupling as marginal deformations of N=4 Yang-Mills. For concreteness we concentrate to cases with an SO(4)xSO(2) symmetry preserved by continuous distributions of D3-branes on a disc and on a three-dimensional spherical shell. We compute the expectation value of the Wilson loop operator and confirm the Coulombic behaviour of the heavy quark-antiquark potential in the conformal case. When the vev is turned on we find situations where a complete screening of the potential arises, as well as a confining regime where a linear or a logarithmic potential prevails depending on the ratio of the quark-antiquark separation to the typical vev scale. The spectra of massless excitations on these backgrounds are analyzed by turning the associated differential equations into Schrodinger problems. We find explicit solutions taking into account the entire tower of states related to the reduction of type-IIB supergravity to five dimensions, and hence we go beyond the s-wave approximation that has been considered before for the undeformed case. Arbitrary values of the deformation parameter give rise to the Heun differential equation and the related Inozemtsev integrable system, via a non-standard trigonometric limit as we explicitly demonstrate.

Deconfinement and the Hagedorn transition in string theory.

We introduce a new definition of the thermal partition function in string theory. With this new definition, the thermal partition functions of all of the string theories obey thermal duality relations with self-dual Hagedorn temperature beta(2)(H) = 4pi(2)alpha('). A beta-->beta(2)(H)/beta transformation maps the type I theory into a new string theory (type I) with thermal D p-branes, spatial hypersurfaces supporting a p-dimensional finite temperature non-Abelian Higgs-gauge theory for p< or =9. We demonstrate a continuous phase transition in the behavior of the static heavy quark-antiquark potential for small separations r(2)(*)<<alpha(') transitioning through a precise inverse power law at a critical temperature T(D) = T(H)r(*)/(2alpha('))(1/2)pi.

Some aspects of the quark-antiquark Wilson loop formalism in the NRQCD framework

Starting from the NRQCD Lagrangian the heavy quark-antiquark potential is written in terms of field strength insertions on a static Wilson loop. The relevant matching coefficients are given at the present status of knowledge. The short-range, perturbatively dominated, behaviour of the spin-dependent terms is discussed.

Relativistic properties of the quark-antiquark potential

The relativistic transformation properties of the heavy quark-antiquark interaction potential are considered in the framework of the relativistic quark model. A special attention is paid to the long-range (confining) contribution to the spin-independent part of $q\bar q$ interaction. The retardation effects are consistently taken into account.

Relativistic properties of the quark-antiquark potential

The relativistic transformation properties of the heavy quark-antiquark interaction potential are considered in the framework of the relativistic quark model. A special attention is paid to the long-range (confining) contribution to the spin-independent part of qq bar interaction. The retardation effects are consistently taken into account.

Heavy quark-antiquark potential from lattice QCD with light dynamical fermions

The expected break-up of the string within the quark-antiquark potential is investigated in lattice QCD calculations with light dynamical fermions.

THE CALCULATION OF HEAVY QUARK FORCE AND POTENTIAL IN SU(2) LATTICE GAUGE THEORY

The heavy quark-antiquark force and potential are calculated by means of Monte Carlo method in 4 dimensional symmetry lattice gauge theory for a single plaquette EXP action which has a good scaling behaviour. The renormalization group treatment and the icosahedral subgroup approximation to SU(2) are used. The resultes agreet with Coulomb plus linear form obtained from phenomenological string theories.