Hans Gunter Dosch

Gluon condensate and effective linear potential

Abstract It is shown that a model in which the QCD vacuum is simulated by a stochastic background field leads to an asymptotically linear potential. If the fluctuations are assumed to be gaussian, a correlation length of 0.4 to 0.8 fm is obtained.

The Area Law of the Wilson Loop and Vacuum Field Correlators

The Wilson loop average in the background vacuum fields is expressed via the cumulant expansion in terms of irreducible correlators of the gluon field. Assuming a fast fall-off of the latter at large distance one obtains the area law for large contours.

Light-Front Holographic QCD and Emerging Confinement

Abstract In this report we explore the remarkable connections between light-front dynamics, its holographic mapping to gravity in a higher-dimensional anti-de Sitter (AdS) space, and conformal quantum mechanics. This approach provides new insights into the origin of a fundamental mass scale and the physics underlying confinement dynamics in QCD in the limit of massless quarks. The result is a relativistic light-front wave equation for arbitrary spin with an effective confinement potential derived from a conformal action and its embedding in AdS space. This equation allows for the computation of essential features of hadron spectra in terms of a single scale. The light-front holographic methods described here give a precise interpretation of holographic variables and quantities in AdS space in terms of light-front variables and quantum numbers. This leads to a relation between the AdS wave functions and the boost-invariant light-front wave functions describing the internal structure of hadronic bound-states in physical space–time. The pion is massless in the chiral limit and the excitation spectra of relativistic light-quark meson and baryon bound states lie on linear Regge trajectories with identical slopes in the radial and orbital quantum numbers. In the light-front holographic approach described here currents are expressed as an infinite sum of poles, and form factors as a product of poles. At large q 2 the form factor incorporates the correct power-law fall-off for hard scattering independent of the specific dynamics and is dictated by the twist. At low q 2 the form factor leads to vector dominance. The approach is also extended to include small quark masses. We briefly review in this report other holographic approaches to QCD, in particular top-down and bottom-up models based on chiral symmetry breaking. We also include a discussion of open problems and future applications.

Field correlators in QCD: Theory and applications

Abstract This review is aimed to demonstrate the basics and use of formalism of gauge-invariant nonlocal correlators in nonabelian gauge theories. Many phenomenologically interesting nonperturbative aspects of gluodynamics and QCD can be described in terms of correlators of the nonabelian field strength tensors. It is explained how the properties of correlator ensemble encode the structure of QCD vacuum and determine different nonperturbative observables. It is argued that in gluodynamics and QCD the dominant role is played by the lowest nontrivial two-point correlator (Gaussian dominance). Lattice measurements of field correlators are discussed. Important for the formalism theoretical tools, such as nonabelian Stokes theorem, background perturbation theory, cluster expansion, as well as phenomenological applications to the heavy quarkonium dynamics and QCD phase transition are reviewed.

Baryon Sum Rules and Chiral Symmetry Breaking

Abstract In an SVZ-type approach sum rules for baryonic currents have been investigated, without radiative QCD corrections but with the inclusion of non-perturbative terms due to the non-vanishing vacuum expectation value of the quark-antiquark condensate. We give upper bounds for baryon masses, which allow a choice of optimal interpolating operators for low-lying baryon states. The results show that the mentioned vacuum expectation value not only sets the scale for parity splitting but also for the masses of the baryons directly. The alternative way of explicit symmetry breaking by quark masses has also been investigated in the same technical framework.

QCD sum rules in the effective heavy quark theory

We derive sum rules for the leptonic decay constant of a heavy-light meson in the effective heavy quark theory. We show that the summation of logarithms in the heavy quark mass by the renormalization group technique enhances considerably radiative corrections. Our result for the decay constant in the static limit agrees well with recent lattice calculations. Finite quark mass corrections are estimated.

Baryon masses and flavour symmetry breaking of chiral condensates

Abstract The masses of the baryon octet and decuplet are reproduced with a (10–20)% accuracy by ratios of exponential moment QCD spectral sum rules, obeying the τ (sum rule variable) stability criterion. The onset of the QCD continuum is determined by consistency with the lowest dimensional finite energy sum rule. The N-Δ mass splitting is mainly controlled by the size of the mixed 〈 ψ σGψ〉 condensate. The observed masses of the strange baryons can only be reproduced if there is a large breaking of the chiral condensates 〈 ψ ψ〉 and 〈 ψ σGψ〉. This result is independent of the choice of the nucleon current.

Direct extraction of the chiral quark condensate and bounds on the light quark masses

Abstract We select sum rules from which one can extract directly reliable limits on the size of the chiral symmetry breaking light quark condensate 〈 ψ ψ〉 . Combined results from the nucleon and B ∗ -B mass-splitting sum rules give a result compatible with the standard value: 〈 ψ ψ〉 (1 GeV) ≃(−229 MeV ) 3 , through the determinations of the quark-gluon mixed condensate. The vector form factor of the D→K ∗ lν semi-leptonic decay leads to the range 0.6≤〈 ψ ψ〉/(−229 MeV ) 3 ≤1.5 . The upper limit combined with the Gell-Mann-Oakes-Renner (GMOR) relation implies the interesting lower bound on the sum of light quark masses:(mu+md)(1 GeV)≥ 9.4 MeV, which combined with the ratio of light quark masses from chiral perturbation theory leads to ms(1 GeV)≥(121±12) MeV. The lower limit combined with the positivity of the mq2 contribution to the GMOR relation leads to the upper bound : (mu+md)(1 GeV)≤ 15.7 MeV, which is independent on the nature of chiral symmetry breaking.

Composite hadrons in non-Abelian lattice gauge theories

Abstract Euclidean non-Abelian gauge theories are quantized on a (finite) lattice using functional integration. From the general from of the 2 m -point Schwinger function for the fundamental fermions fields, dynamical consequences for composite meson and fermion fields are investigated. The Okubo-Zweig-Iizuka rule is derived and an analogy to non-relativistic potentials for the quark-antiquark and the 3-quark system is exhibited.

Chiral symmetry breaking condensates from baryonic sum rules

We analyse baryonic sum rules in order to determine chiral symmetry breaking condensates. We especially investigate the influence of the choice of the interpolating field and of the factorization hypothesis for the four quark condensate. Our results are consistent with those obtained from pseudoscalar sum rules and PCAC.