Interquark Potential Research Articles

Effects of nonperturbatively improved dynamical fermions in QCD at fixed lattice spacing

We present results for the static interquark potential, lightest glueballs, light hadron spectrum, and topological susceptibility using a nonperturbatively improved action on a ${16}^{3}\ifmmode\times\else\texttimes\fi{}32$ lattice at a set of values of the bare gauge coupling and bare dynamical quark mass chosen to keep the lattice size fixed in physical units (\ensuremath{\sim}1.7 fm). By comparing these measurements with a matched quenched ensemble, we study the effects due to two degenerate flavors of dynamical quarks. With the greater control over residual lattice spacing effects which these methods afford, we find some evidence of charge screening and some minor effects on the light hadron spectrum over the range of quark masses studied ${(M}_{\mathrm{PS}}{/M}_{V}>~0.58,$ where PS denotes pseudoscalar and $V$ denotes vector). More substantial differences between quenched and unquenched simulations are observed in measurements of topological quantities.

On the dilaton and axion potentials

We extend the Vecchia–Veneziano–Witten model of quantum chromodynamics in the chiral limit and for large colour number Nc, by introducing an effective dilaton–gluon coupling from which we derive both the axion and dilaton potentials. Furthermore, using a string-inspired model, we determine a new interquark potential as a perturbative series in terms of the interquark distance r. Our potential goes beyond Dick's potential (Dick R 1999 Eur. Phys. J. C 6 701) and shares the same features as those of the Bian–Huang–Shen potential (VBHS) which depends only on odd powers of r (Bian J G, Huang T and Shen Q X 1994 Commun. Theor. Phys. 21 333).

S, P, D, F, G-waves KN phase shifts in a constituent quark model with a spin–orbit interaction

The I=1 and I=0 kaon–nucleon s, p, d, f, g-waves phase shifts have been calculated in a nonrelativistic quark potential model using the resonating group method (RGM). The interquark potential includes gluon exchanges with a spin–orbit interaction. This force has been determined to reproduce as well as possible the meson and baryon spectra. The same force is employed for the cluster and intercluster dynamics and the relative KN wave-function is calculated without any approximation. While some channels are correctly described, the theory is still unable to explain others.

On some positivity properties of the interquark potential in QCD.

We argue that the Fourier transform of the exponential e(-betaV(R)) of the static interquark potential in QCD is positive. It has been shown by Lieb some time ago that this property allows in the same limit of static, spin independent potential, to prove a certain mass relation between baryons with different quark flavors.

Functional relation of interquark potential with interquark distance

The functional relation between interquark potential and interquark distance is explicitly derived by considering the Nambu–Goto action in the AdS 5× S 5 background. It is also shown that a similar relation holds in a general background. The implications of this relation for confinement are briefly discussed.

D0-branes as light-front confined quarks

We argue that different aspects of Light-Front QCD at confined phase can be recovered by the Matrix Quantum Mechanics of D0-branes. The concerning Matrix Quantum Mechanics is obtained from dimensional reduction of pure Yang-Mills theory to 0+1 dimension. The aspects of QCD dynamics which are studied in correspondence with D0-branes are: 1) phenomenological inter-quark potentials, 2) whiteness of hadrons and 3) scattering amplitudes. In addition, some other issues such as the large-N behavior, the gravity--gauge theory relation and also a possible justification for involving ``non-commutative coordinates'' in a study of QCD bound-states are discussed.

Color dynamics in phase space: The Balescu–Lenard–Vlasov approach

We propose to use the Balescu-Lenard-Vlasov (BLV) equation to describe relativistic heavy ion collisions. We use an inter-quark Richardson's potential consistent with the indications of Lattice QCD calculations. The color degrees of freedom are explicitly taken into account. We explicitly demonstrate that the Vlasov approach alone is insufficient in the hadronization region. In order to overcome this problem we prepare the initial condition for many events using molecular dynamics with frictional cooling and a Thomas-Fermi approximation to the Fermi motion. These events are averaged and propagated in time using the Vlasov approach. The fluctuations are used to evaluate the collision term and in turn the number of q-$\bar q$ created.

Color dynamics in phase space

We describe the properties of quark matter at zero temperature and finite baryon densities within microscopic Vlasov/molecular dynamics approaches. We use an inter-quark Richardson's potential consistent with the indications of Lattice QCD calculations. The color degrees of freedom are explicitly taken into account. We explicitly demonstrate that the Vlasov approach alone is insufficient in the hadronization region. In order to overcome this problem we prepare the initial condition for many events using molecular dynamics with frictional cooling and a Thomas-Fermi approximation to the Fermi motion. These events are averaged and propagated in time using the Vlasov approach. We find some evidence for a second order phase transition from nuclear to quark matter at high baryon densities. An order parameter suitable to describe the phase transition is discussed. At low densities the quark condensate into approximately color white clusters (nucleon).

Remark on the computation of mode sums

The computation of mode sums of the types encountered in basic quantum field theoretic applications is addressed with an emphasis on their expansions into functions of distance that can be interpreted as potentials. We show how to regularize and calculate the Casimir energy for the continuum Nambu-Goto string with massive ends as well as for the discrete Isgur-Paton non-relativistic string with massive ends. As an additional example, we examine the effect on the interquark potential of a constant Kalb-Ramond field strength interacting with a QCD string.

Can lattice data for two heavy-light mesons be understood in terms of simply two-quark potentials?

By comparing lattice data for the two heavy-light meson system ( Q 2−2 q) with a standard many-body approach employing only interquark potentials, it is shown that the use of unmodified two-quark potentials leads to a gross overestimate of the binding energy.

The glueball spectrum from novel improved actions

Results for the inter-quark potential and low-lying SU(3) glueball spectrum from simulations using a new improved action are presented. The action, suitable for highly anisotropic lattices, contains a two-plaquette term coupling with a negative coefficient as well as incorporating Symanzik improvement.

On the confining potential in 4D $SU(N_{\mathrm c})$ gauge theory with dilaton

Using the formal analogy between the Dick superstring inspired model and the problem of the building of an Eguchi–Hanson metric in 4D N = 2 harmonic superspace (HS), we derive a general formula for the quark–quark interaction potential V(r) including the Dick confining potential. The interquark potential V(r) depends on the dilaton–gluon coupling and may be related to the parameterization of confinement by the quark and gluon vacuum condensates. It is also shown how the axion field may be incorporated in agreement with 10D type IIB superstring requirements. Others features are also discussed.

The structure of the QCD potential in 2+1 dimensions

We calculate the screening and anti-screening contributions to the inter-quark potential in 2+1 dimensions, which is relevant to the high temperature limit of QCD. We demonstrate that the relative strength of screening to anti-screening agrees with the 3+1 dimensional theory to better than one percent accuracy.

On the confining potential in 4D

Using the formal analogy between the Dick superstring inspired model of ref.[6] and the problem of building of Eguchi Hanson metric in 4d N=2 harmonic superspace (hs), we derive a general formula for the quark-quark interaction potential V(r) including the Dick confining potential. The interquark potential V(r) depends on the dilaton-gluon coupling and may be related to the parameterization of confinement by the quark and gluon vacuum condensates. It is also shown how the axion field may be incorporated in agreement with 10d type IIB superstring requirements. Others features are also discussed.

Beyond the adiabatic approximation: The impact of thresholds on the hadronic spectrum

In the adiabatic approximation, most of the effects of quark-antiquark loops on spectroscopy can be absorbed into a static interquark potential. I develop a formalism which can be used to treat the residual nonadiabatic effects associated with the presence of nearby hadronic thresholds for heavy quarks. I then define a potential which includes additional high energy corrections to the adiabatic limit which would be present for finite quark masses. This "improved" potential allows a systematic low energy expansion of the impact of thresholds on hadronic spectra.

Quark Contribution to the Nucleon Polarizabilities and Three-Body Forces

We study the response of the nucleon, as a system of three bound (constituent) non relativistic quarks, to external (quasi static) electric and magnetic fields. The approach, based on a sum rule technique, is applied to a large class of two and three-body interquark potentials. Lower and upper bounds to the electric polarizability and para-magnetic susceptibility are explicitly calculated within a large variety of constituent models and their values related to the features of the interquark interaction picture. The r\^ole of three-body forces is investigated in details as well as the effects of SU(6) breaking terms in the potential model. Our results can be used to extract the mesonic contributions to the static polarizabilty and susceptibility. The quark degrees of freedom give a quite sizeable contributions to both and the meson cloud accounts roughly for 30% and 60% of the electric proton and neutron polarizability respectively. The quark contribution to the paramagnetic susceptibility is even higher and the mesonic effects are rather uncertain.

A remark on the glueball-gluon coupling

The QCD trace anomaly motivates the consideration of a low energy glueball-gluon coupling $\phi G_{\mu\nu}{}^a G^{\mu\nu}{}_a$ . We point out that this should constitute the leading kinetic term for the gluons at low energies. Anti-screening of the gluons by the glueball then induces a classical Coulomb potential of color charges which increases at large distances $\sim r^{1/3}$ and motivates the inclusion of a corresponding term in the inter-quark potential.

The quark mass correction to the string potential

Following recent work by Lambiase and Nesterenko we study in detail the interquark potential for a Nambu–Goto string with point masses attached to its ends. We obtain accurate solutions to the gap equations for the Lagrange multipliers and metric components and determine the potential without simplifying assumptions. We also discuss the Lüscher term and argue that it remains universal.

The glue around quarks and the interquark potential

The quarks of quark models cannot be identified with the quarks of the QCD Lagrangian. We review the restrictions that gauge field theories place on any description of physical (colour) charges. A method to construct charged particles is presented. The solutions are applied to a variety of applications. Their Green's functions are shown to be free of infra-red divergences to all orders in perturbation theory. The interquark potential is analysed and it is shown that the interaction responsible for anti-screening results from the force between two separately gauge invariant constituent quarks. A fundamental limit on the applicability of quark models is identified.

OPEN RIGID STRING WITH GAUSS–BONNET TERM IN THE ACTION

The effect of the Gaussian curvature in the rigid string action on the interquark potential is investigated. The linearized equations of motion and boundary conditions, following from the modified string action, are obtained. The equation which defines the eigen-frequency spectrum of the string oscillations is derived. On this basis the interquark potential generated by the string is calculated in one-loop approximation. A substantial influence of the topological term in the string action on the interquark potential at the distances of order of hadronic size or less is revealed.