Wolfgang Lucha

Bound states of quarks

Abstract This review consists of two parts, the phenomenology of non-relativistic potential models and the theoretical understanding of the forces between quarks. The first part reports on the description of hadrons as bound states of quarks by non-relativistic potential models. It starts with a brief sketch of the way in which information on the interquark potential may be gained from quantum chromodynamics. Some general theorems related to the potential-model approach are proven. The significance of the treatment of relativistically moving constituents by an effective non-relativistic Schrodinger equation is discussed. A brief survey of the motivations for various proposed potential models is given. Finally, the application of the developed theoretical framework is illustrated by a few selected examples. The second part starts with a review of the approach via the Bethe-Salpeter equation. Although this has not led to a breakthrough in our understanding, it has played an important role in the past and is still indispensable for several questions. The next topic is the Wilson loop approach, together with its extensions for the inclusion of spin-dependent corrections. Here great progress has been made in the last few years. Connections with perturbation theory, lattice gauge theory, and the non-trivial QCD vacuum are exploited at the end.

SEMIRELATIVISTIC TREATMENT OF BOUND STATES

This review discusses several aspects of the semirelativistic description of bound states by the spinless Salpeter equation (which represents the simplest equation of motion incorporating relativistic effects) and, in particular, presents or recalls some very simple and elementary methods which allow us to derive rigorous statements on the corresponding solutions, that is, on energy levels as well as wave functions.

Decay constants of heavy pseudoscalar mesons from QCD sum rules

We revisit the sum-rule extraction of the decay constants of the D, Ds, B and Bs mesons from the two-point correlator of heavy?light pseudoscalar currents. We use the operator product expansion of this correlator expressed in terms of the heavy-quark mass for which the perturbative expansion exhibits a reasonable convergence. Our main emphasis is laid on the control over the uncertainties in the decay constants, related both to the input quantum chromodynamics (QCD) parameters and to the limited intrinsic accuracy of the method of QCD sum rules. This becomes possible due to the application of our procedure of extracting hadron observables that involves as novel feature dual thresholds depending on the Borel parameter. For charmed mesons, we find the decay constants and . For beauty mesons, the decay constants turn out to be extremely sensitive to the precise value of . By requiring our sum-rule estimate to match the average of the lattice results for fB, a very accurate value is extracted, leading to fB = (193.4 ? 12.3(OPE) ? 4.3(syst))?MeV and .

Systematic uncertainties of hadron parameters obtained with QCD sum rules

We study the uncertainties of the determination of the ground-state parameters from Shifman-Vainshtein-Zakharov (SVZ) sum rules, making use of the harmonic-oscillator potential model as an example. In this case, one knows the exact solution for the polarization operator

Decay constants of the charmed vector mesons D⁎ and Ds⁎ from QCD sum rules

\ensuremath{\Pi}(\ensuremath{\mu})

OPE, charm-quark mass, and decay constants of D and Ds mesons from QCD sum rules.

, which allows one to obtain both the operator product expansion (OPE) to any order and the spectrum of states. We start with the OPE for

DISCRETE SPECTRA OF SEMIRELATIVISTIC HAMILTONIANS

\ensuremath{\Pi}(\ensuremath{\mu})

Energy bounds for the spinless Salpeter equation: harmonic oscillator

and analyze the extraction of the square of the ground-state wave function,

Accuracy of bound-state form-factors extracted from dispersive sum rules

R\ensuremath{\propto}|{\ensuremath{\Psi}}_{0}(\stackrel{\ensuremath{\rightarrow}}{r}=0){|}^{2}

Extraction of ground-state decay constant from dispersive sum rules: QCD vs potential models

, from an SVZ sum rule, setting the mass of the ground state