Interquark Potential Research Articles

Weak decays of pseudoscalar mesons with the formation of leptons in the final state

Leptonic and semileptonic decays of pseudoscalar mesons are considered. The functional dependence of the weak form factors on the wave functions of the (q1¯q2) system is found. Numerical values of the coefficients α and β (for π, K, D, and F mesons) determining the interquark potential are obtained. Within the framework of the Coulomb and oscillator models, the probability of semileptonic decays of D and F mesons is found. For D mesons, comparison with experiment is undertaken. Agreement with experiment is observed.

On the Martin potential

The interquark potential V( r) = A + Br α accounts for all spin-averaged levels and ratios of leptonic widths within each heavy-quark spectroscopy. We find, however, that ratios of leptonic widths between different spectroscopies are inconsistent with flavor-independence. Modification of the Martin potential by a Coulomb short-range part restores complete flavor-independence.

Lattice predictions for low-Q2phenomenology

Recent results of Monte Carlo simulations for SU(3) lattice gauge theories are used to make quantitative predictions which can be compared with QCD phenomenology. In particular, lattice results are used to predict the onset of nonperturbative effects and to determine the interquark potential. The relationship between ${\ensuremath{\Lambda}}_{0}$ and the short-distance scale of the $q\overline{q}$ potential is also calculated. The predictions are in agreement with theoretical expectations, but indicate that fermions must be incorporated into the lattice calculations before any realistic results relevant to QCD can be derived.

An elementary derivation of Wilson's and Polyakov's confinement tests from the Hamiltonian formulation

Starting from the Hamiltonian approach to lattice gauge theory, we show how the correlation functions introduced by Wilson and Polyakov in the Lagrangian approach are related to the evolution operator projected in the sector of the Hilbert space corresponding to external quark-antiquark charges (meson sector), thus asymptotically related to the meson interquark potential. We generalize this to introduce correlation functions both in the Wilson and the Polyakov scheme which are related to the interquark potential for three external quarks (baryon potential).

Why the Σ and Ξ hyperfine splittings are different

The Σ and Ξ splittings, predicted to be equal in the SU(6) quark model, are shown to differ because the smaller size of the Ξ wave function enhances the short-range hyperfine interaction. The change in the relative motion of a u-s pair in the hyperon produced by a change in the mass of the third quark is not a simple scale change and is sensitive to details of the interquark potential. This effect is absent in the harmonic oscillator model, where the third quark is completely decoupled from the relative motion within the other pair, but is appreciable and has the right order of magnitude in the logarithmic potential model.

Beyondϒ: Heavier quarkonia and the interquark force

A quarkonium potential constructed by inverse-scattering methods from the masses and leptonic decay widths of the $\ensuremath{\Upsilon}$ vector mesons provides a basis for extrapolation to heavier quark-antiquark bound states. Level spacings and leptonic widths are predicted for systems with ground-state masses up to 60 ${\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c}}^{2}$. It is found that present uncertainties in the potential at short distances would be most conclusively resolved by measurement of the $1^{3}S_{1}$ leptonic decay rate. Less definitive but still of value would be determinations of the $2S\ensuremath{-}1S$ or $2S\ensuremath{-}2P$ level spacings, and measurement of the ratio of $2S$ and $1S$ leptonic widths. Other properties of the next quarkonium family are less sensitive indicators of short-range behavior, and can be anticipated with some confidence from experimental results already in hand. These serve to test further the flavor independence of the interquark potential.

The interquark potential of lattice QCD

Abstract The static interquark potential, the restoration of rotational symmetry and roughening phenomena in lattice gauge theory are studied using Hamiltonian methods. One finds power law corrections to linear confinement and unbounded transverse fluctuations of off-axis electric flux tubes. The on-axis flux tube acquires these properties for g smaller than a critical value gR.

Further evidence for flavor independence of the quark-antiquark potential

An inverse-scattering algorithm is used to construct the interquark potential from the masses and leptonic widths of vector mesons. There is substantial agreement between potentials constructed from the $1S$ and $2S$ levels of the $\ensuremath{\psi}$ family, and those based upon the $1S\ensuremath{-}4S$ levels of the $\ensuremath{\Upsilon}$ family. This agreement provides evidence that the quark-antiquark interaction is independent of heavy-quark flavor for interquark separations between about 0.1 and 1 fm. Self-consistency of the various determinations is explored at some length, and the uncertainties inherent in the method are investigated in detail. Predictions are made for electric-dipole transition rates in the $\ensuremath{\Upsilon}$ family, and the significance of future measurements for refining and extending present knowledge of the potential is discussed.

The two confining phases of lattice gauge theories

I suggest that the roughening transition of lattice gauge theories is the boundary between two different confining phases: In the hot phase the short-distance interquark potential is exponentially decreasing, while in the cool confining phase it is proportional to 1 R , independently of space dimensionality d. As d increases, the cool confining phase shrinks to zero and the system undergoes a first-order deconfining transition.

Elementary derivation of the universal attractive coulomb term in the interquark potential

We provide a simple derivation of the universal 1 R term in the interquark potential at large distances. We discuss a physical analogy which makes the existence of such a universal term easier to understand. We go on to briefly treat the behavior of the Wilson loop in other regimes, to further illustrate this analogy.

Information on the QCD phase transition and the vacuum permeability from the interquark potential

A method for the calculation of the interquark potential resulting from the instanton induced phase transition in the QCD vacuum is described and it is shown that good agreement is obtained with successful phenomenological potentials for parameter values close to those expected from naive instanton calculations.

Study of a model Lagrangian in QCD for soft bag

The effective Lagrangian of Kogut-Susskind and 't Hooft is examined in connection with interpretation of the additional scalar field as a gluon-pairing field. The pairing effect on the short distance potential is found to be small. A bag limit of the Lagrangian is investigated. Integral representations for interquark potential and nontrivial bag shape are given for heavy quark-antiquark bag states.

Instantons and the interquark potential

It is argued that the contributions to the interquark potential from instantons of all scale sizes may be calculated in a consistent, cut-off-independent manner using the dilute-gas approximation; and that an interquark potential dominated at intermediate distances by these contributions is similar to already successful phenomenological potentials.

Strong decays ofΨ(4.03) andΨ(4.16) as radial excitations of charmonium

Considering the signals detected at 4.03 and 4.16 GeV as radial excitations of charmonium, we study their relative decay rates intoD\(\bar D\),D\(\bar D^* \),D*\(\bar D\),D*\(\bar D^* \). We point out that one can understand these two peaks as ac\(\bar c\)3S−2D wave state system with a large mixing angle in a Coulomb+linear interquark potential. We also examine the possibility that these two signals are respectively 3S and 4S wave excitations by studying a logarithmic charmonium potential model. We show that both these interpretations lead to drastically different predictions for the Ψ (4.16) decay rates (eitherD\(\bar D^* \)+D*\(\bar D\) orD\(\bar D\) mode is strongly suppressed) which would be very instructive to test experimentally.

Exact selection rules for “chromo-harmonic” diquonium decay into mesons

Using a “chromo-harmonic” interquark potential we study the stability of “diquoniums” against the decay into mesons. We find an exact selection rule which implies that “true-diquoniums” are uncoupled from open meson channels for orbital excitation greater than 1. “Mock-diquoniums” only appear for an orbital excitation greater than 8 and are coupled to mesons and to pairs of orbitally excited baryons.

Inverse scattering problem for quarkonium systems. II. Applications toψandϒfamilies

The inverse scattering formalism for reflectionless potentials is extended to the reconstruction of central potentials in three space dimensions. An approximate interquark potential is derived from the psi (3.095) and psi' (3.684) levels and leptonic decay widths. Remaining ambiguities are discussed in detail. Consequences for the UPSILON family and prospects for refining the interquark potential are explored.