Heavy quarkonia: Models and theory

Theoretical approaches in heavy quarkonia physics are reviewed. Anomalies in spectra and decays of recently discovered charmonium and bottomoniumstates are highlighted, and exotic interpretations for these states are discussed.     

Heavy quark potential and quarkonia dissociation rates

Quenched lattice data for the interaction (in terms of heavy quark free energies) in the color-singlet channel at finite temperatures are fitted and used within the non-relativistic Schrödinger equation formalism to obtain binding energies and scattering phase shifts for the lowest eigenstates in the charmonium and bottomonium systems in a hot gluon plasma. The partial dissociation rate due to the Bhanot-Peskin process is calculated using different assumptions for the gluon distribution function, including free massless gluons, massive gluons, and massive damped gluons. It is demonstrated that a temperature dependent gluon mass has an essential influence on the heavy quarkonia dissociation, but that this process alone is insufficient to describe the heavy quarkonia dissociation rates.Arrival of the final proofs: 8 July 2005PACS: 12.38.Gc, 12.38.Mh, 14.40.GxD. Blaschke: Present address: GSI mbH, 64291 Darmstadt, Germany     

Heavy quarkonia survival in potential model

We investigate the quarkonia correlators in QCD with no light quarks within a potential model with different screened potentials. Our results for the temperature dependence of the charmonium and bottomonium correlators are qualitatively consistent with existing and preliminary lattice results. We identify however, a much richer structure in the correlators than the one seen on the lattice.Arrival of the final proofs: 3 March 2005PACS: 11.15.Ha, 11.10.Wx, 12.38.Mh, 25.75.Nq     

Heavy quarkonia properties at high temperatures

The spectra and e ⁺ e ⁻ decay widths of the heavy quarkonia as a function of the temperature of medium generated in the ultrarelativistic heavy-ion collisions are discussed. The fluctuations of the vacuum gluon fields are estimated within the instanton liquid model approach. It is noticed that the parameters that are considered can be used to indicate the gluon warming.     

Heavy quarkonia in a stochastic vacuum

We investigate Green functions for heavy quarkonia in a stochastic vacuum. We derive rigorous results for an Abelian model and expressions for the non-Abelian case which are suited for phenomenological analysis.     

Meson hyperfine splittings and asymptotic freedom

Meson hyperfine splittings give empirical evidence that the short-ranged part of the potential binding quarks has the behavior expected of single color gluon exchange in an asymptotically free theory. Since the interaction of light confined quarks depends on only one length scale, while that of heavy confined quarks depends on two length scales, it is argued that the spin-dependent interactions are qualitatively different in the cases. Phenomenological evidence suggests that the spin-dependent interactions of light quarks are short-ranged only, while that of heavy quarks are predominantly long-ranged. It is proposed that a measurement of the F¹-F mass-difference will help clarify the nature of a possible long-ranged spin-spin interaction of strange quarks.     

Regge behavior under asymptotic freedom

By a new method, we show that the asymptotically free ø₆³ field theory has a point of accumulation of Regge poles but no fixed cut. It is plausible that nonabelian gauge theories have an analogous singularity at j = 1.     

Is asymptotic freedom enough?

Quantum field theories with strong interactions are usually required to be not only renormalizable but also asymptotically free, in order to avoid diseases such as the Landau ghost. In this paper we suggest an even more restrictive requirement: “asymptotic convergence”, which means that at high energies it must be possible to formulate a convergent resummation procedure for the perturbation expansion. Such a convergent resummation technique exists in QCD in the infinite color limit (N → ∞). We give an outline of a proof of this statement, and a brief account of possible consequences of our asymptotic convergence condition on model building.     

More comments on asymptotic freedom

The effective Coulomb interaction between sources with SU(2) color charge is reinvestigated at the one-loop order of perturbation theory. This quantity is shown to be formally identical with the effective Coulomb interaction between electric charges in the QED of massless, charged, vector fields with anomalous magnetic moments. This correspondence allows the one-loop Yang-Mills charge renormalization factor to be deduced from a knowledge of the size and origins of this quantity in massless scalar and spinor QED. Careful consideration of the analogy with QED suggests a mechanism for asymptotic freedom in the Feynman gauge.     

Renormalizability and asymptotic freedom in quantum gravity

We discuss a previously proposed renormalizable theory of gravity involving R²_μν, and N massless fermion (vector boson) fields in which the unitarity problem is resolved within a $\text{1}\text{N}$ expansion. The infrared limit is precisely Einstein's theory, but the high-energy behavior is determined by the dimensionless, asymptotically free coupling of the R²_μν. Various attractive possible consequences of the theory are pointed out.     

Dual Feynman rules—Topological asymptotic freedom

Feynman-graph rules are formulated for the strong—interaction components of the topological expansion—defined as those graphs all of whose vertices are zero—entropy connected parts. These rules imply a “topological asymptotic freedom” and admit a corresponding perturbative evaluation where the zeroth order exhibits topological supersymmetry.     

Heavy quarkonia from classical SU(3) Yang-Mills configurations

A generalized Cho-Faddeev-Niemi ansatz for SU(3) Yang-Mills is investigated. The corresponding classical field equations are solved for its simplest parametrization. From these solutions it is possible to define a confining non-relativistic central potential used to study heavy quarkonia. The associated spectra reproduces the experimental spectra with an error of less than 3% for charmonium and 1% for bottomonium. Moreover, the recently discovered new charmonium states can be accomodate in the spectra, keeping the same level of precision. The leptonic widths show good agreement with the recent measurements. The charmonium and bottomonium E1 electromagnetic transitions widths are computed and compared with the experimental values.     

Has asymptotic freedom something to do with charmonium

We analyse the effects of logarithmic corrections due to asymptotic freedom in the potential describing short-range forces in charmonium. This allows us to show that due to the size of the effective quark-gluon coupling ($\text{α}{}_{\mathrm{<mtext>s</mtext>}}\text{(M}{}_{\mathrm{J/\Psi }}{}^2\text{) ? 0.4}$), the wave function extensions are much larger than the region of space where asymptotic freedom really has predictive power. The resulting ambiguities in the spin-dependent medium-range forces are explored. Also, such a value of α_s makes perturbative calculations of widths unreliable. We point out that the situation is not significantly improved for quark masses of 5 GeV. Indeed, below 20 GeV, short-range forces play a marginal role as compared to confinement forces.     

A possibility of asymptotic freedom without non-Abelian gauge theories

We discuss solutions of the renormalization group equations for a Yukawa field theory. For an increasing effective boson mass we find that the leading terms in the vertex functions in the high-energy region are given by diagrams which contain no internal boson lines. In e⁺e^? annihilation into hadrons we get the parton model formula R(s) = Σ_iQ_i², whereas in the deep inelastic e^?p scattering the simple parton model behaviour is modified by the (in general) non-canonical dimension of the quark field.     

Running flavor number and asymptotic freedom in the normal phase of QED

In the normal phase (where no dynamical fermion mass generation occurs) of the D-dimensional quantum electrodynamics with N_f flavors of fermions, we derive an integral equation which should be satisfied by (the inverse of) the wave function renormalization of the fermion in the Landau gauge. For this we use the inverse Landau-Khalatnikov transformation connecting the nonlocal gauge with the Landau gauge. This leads to a similar equation for the running flavor number in the framework of the 1/N_f resumed Schwinger-Dyson equation. Solving the equation analytically and numerically, we study the infrared behavior and the critical exponent of the 3-dimensional QED (QED₃). This confirms that the flavor number in QED₃ runs according to the β function which is consistent with the asymptotic freedom as that in 4-dimensional QCD.     

Infrared instability of the vacuum state of gauge theories and asymptotic freedom

The radiative corrections to the Yang-Mills massless theory are found to lead to an instability of the vacuum state. This fact is in full compliance with the asymptotic freedom of gauge theories and is due to infrared singularities.