Testing static quark-antiquark potentials with bottomonium

We investigate the question of whether experimental data on the energy levels of bottomonium can discriminate between quark-antiquark potentials which are motivated by what we know about QCD and potentials which are purely phenomenological. We restrict ourselves to bottomonium because, of all the quarkonia observed thus far, bottomonium is the least relativistic and therefore the best testing ground for the static quarkonium potential. We consider two potentials whose functional form is motivated from perturbative QCD at short quark-antiquark separations and from nonperturbative lattice QCD at large separations. We also consider three strictly phenomenological potentials. We find that the best of the three phenomenological potentials, which has never been previously used, fits the spin-averaged data at least as well as the best of the QCD-motivated potentials. We propose further measurements on bottomonium energy levels to provide additional tests.     

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 interaction. The retardation effects are consistently taken into account. Received: 22 April 1998 / Revised version: 9 September 1998 / Published online: 22 October 1998     

A short-distance quark-antiquark potential

Leading terms of the static quark-antiquark potential in background perturbation theory are reviewed, including perturbative, nonperturbative, and interference ones. The potential is shown to describe lattice data at short quark-antiquark separations with a good accuracy.     

The potential of quark-antiquark interaction

A phenomenological potential of quark-antiquark interaction (1) is considered within the quasiclassical framework. It is shown that the Van Royen-Weisskopf relation has a different origin for pseudoscalar and vector mesons. For pseudoscalar mesons, it follows from the SU(4) symmetry of strong interactions, while for vector mesons, the Van Royen-Weisskopf relation is a consequence of a certain dynamical mechanism of quark-antiquark interaction. On the basis of a nonrelativistic quark model it is shown that the parameter takes the same value =0.21 (GeV)² for different quark-antiquark systems. Taking this value of , the energy spectra of quark-antiquark (c¯c)-, (b¯b)-, and (t¯t)-systems are constructed, and the partial widths of the decays V⁰e⁺e^– of these levels, are determined. A condition for the occurrence of the first negative-energy level of a quark-antiquark (q₁¯q₂)-system is found. A comparison with the experiment is made.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 104–108, April, 1984.In conclusion, I want to thank Yu. P. Nikitin and I. L. Rozental' for useful discussions and critical comments.     

QCD box graphs and the quark-antiquark potential

The $t\bar t$ system allows a truly perturbative treatment of the potential. Completing previous computations, we calculate the contributions of QCD box graph corrections, which make the “relativistic”O(α ⁴) corrections in the non-Abelian case differ from the well known corrections of the same order in QED.     

On the quark-antiquark potential at short distances

We investigate the static quark-antiquark potential up to distances of 8 lattice units for pure SU(2) gauge theory on lattices with anisotropic couplings. The action is the Wilson action with a coupling for time-like plaquettes which differs from those for space-like ones. Numerical simulations are performed in a large range of β The potential is obtained by fitting “cooled” Wilson loops with up to four exponential terms. An interpolation of the potentials by a sum of a perturbative term, a linear term and by lattice artifacts shows poor scaling in comparison with he isotropic case. If the coupling in the time-like region is reduced, the linear term is much smaller than in the isotropic case, and vice versa. Consequences for the bag picture for hadrons are discussed.     

Relationship between quark-antiquark potential and quark-antiquark free energy in hadronic matter

In high-temperature quark-gluon plasma and its subsequent hadronic matter created in a high-energy nucleus-nucleus collision, the quark-antiquark potential depends on the temperature. The temperature-dependent potential is expected to be derived from the free energy obtained in lattice gauge theory calculations. This requires one to study the relationship between the quark-antiquark potential and the quark-antiquark free energy. When the system's temperature is above the critical temperature, the potential of a heavy quark and a heavy antiquark almost equals the free energy, but the potential of a light quark and a light antiquark, of a heavy quark and a light antiquark and of a light quark and a heavy antiquark is substantially larger than the free energy. When the system's temperature is below the critical temperature, the quark-antiquark free energy can be taken as the quark-antiquark potential. This allows one to apply the quark-antiquark free energy to study hadron properties and hadron-hadron reactions in hadronic matter.     

On a systematic derivation of the quark-antiquark potential

A systematic method of deriving the quark-antiquark potential is developed. The whole procedure is organized as a 1/c expansion. Up to order 1/c², the Eichten-Feinberg spin-dependent potential is recovered and new velocity-dependent terms are obtained. As essential step of the derivation is the identification of a Pauli-type two-particle propagator, which satisfies a suitable Schrödinger equation. The short- and large-distance behaviour of the potentials is studied.     

Decay rates of charmonia within a quark-antiquark confining potential

In this work, we investigate the spectroscopy and decay rates of charmonia within the framework of the non-relativistic Schro¨dinger equation by employing an approximate inter quark-antiquark potential. The spin hyperfine, spin-orbit and tensor components of the one gluon exchange interaction are employed to compute the spectroscopy of the excited S states and a few low-lying P and D waves. The resultant wave functions at zero interquark separation as well as some finite separations are employed to predict the di-gamma, di-leptonic and di-gluon decay rates of charmonia states using the conventional Van Royen-Weisskopf formula. The di-gamma and di-leptonic decay widths are also computed by incorporating the relativistic corrections of order v4 within the NRQCD formalism.We have observed that the NRQCD predictions with their matrix elements computed at finite radial separation yield results which are found to be in better agreement with experimental values for both di-gamma and di-leptonic decays.The same scenario is seen in the case when di-gamma and di-leptonic decay widths are computed with the Van RoyenWeisskopf formula. It is also observed that the di-gluon decay width with the inclusion of binding energy effects are in better agreement with the experimental data available for 1S-2S and 1P. The di-gluon decay width of 3S and 2P waves waves are also predicted. Thus, the present study of decay rates clearly indicates the importance of binding energy effects.     

A quark-antiquark potential from a superconducting model of confinement

The Landau-Ginzburg phenomenological theory of superconductivity is used as a model of flux confinement. A monopole pair of sources is included to simulate a quark-antiquark system. The interaction energy is found in the static approximation appropriate for heavy quark systems, and equated with the interquark potential. This potential is compared with other suggested phenomenological potentials and succeeds in reproducing heavy quark spectra.     

What does the data tell us about the quark-antiquark potential?

In view of the failure of the standard charmonium models to explain $\text{ψ?η}{}_{\mathrm{<mtext>c</mtext>}}\text{and}{}^3\text{P}\text{J}$ splittings, I consider various possible modifications to these models. In particular, I show that for power-law potentials the spin forces are most likely generated through the admixture of scalar-vector-Pauli moment exchanges and that this model can be tested by measuring the ¹p₁ mass. I also show that if instantons really generate a large spin-spin force, then the ¹p₁ mass must be as low as 3250–3270 MeV.     

Thermodynamic potential of a quark-antiquark plasma in a constant chromomagnetic field

Expressions are obtained for the thermodynamic potential of a quark-antiquark plasma in a non-Abelian gauge field of the magnetic type. Its behavior is studied in the case of high and low temperatures as a function of the strength of the external field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 33–38, January, 1985.     

Flavor dependence of spontaneous pair creation

In superstring models, contributions to the muon longitudinal polarizationP _L in the decay \(K_L \to \bar \mu \mu \) can arise from interactions involving the exoticD andD ^c superfields. It is shown that these interactions also contribute to the decay μ→eγ. After using the experimental limit to constrain this process, we find thatP _L arising from these new interactions is less than 10^?4.     

An exact argument against an effective vector exchange for the confining quark-antiquark potential

We derive an exact inequality involving the tensor and spin-spin potentials. It is in contradiction with an effective vector exchange for the confining potential while trivially fulfilled by a scalar.