Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1999-05-12
Physics
High Energy Physics
High Energy Physics - Phenomenology
7 pages, World Scientific style file. Talk given by R. Alkofer at the Workshop "Understanding Deconfinement in QCD", ECT*, Tre
Scientific paper
A closed system of equations for the propagators of Landau gauge QCD is obtained in a truncation scheme for their Dyson-Schwinger equations which implements the Slavnov-Taylor identities for the 3-point vertex functions while neglecting contributions from irreducible 4-point correlations. In the pure gauge theory without quarks, non-perturbative solutions for the gluon and ghost propagators are available in an approximation which allows for an analytic discussion of their behavior in the infrared: The gluon propagator vanishes for small spacelike momenta, whereas the ghost propagator is found to be infrared enhanced. The running coupling of the non-perturbative subtraction scheme approaches the finite value $\alpha_c \simeq 9.5$ at an infrared fixed point. The gluon propagator entails a violation of positivity for transverse gluon states implying their absence from a positive subspace expected for asymptotic hadronic states and thus confinement. Both propagators, obtained for gluons and ghosts in the present scheme, compare well with recent lattice calculations. In the quenched approximation, the quark propagator describes dynamical chiral symmetry breaking well, although the corresponding interaction in the gap equation for the quark self-energy is infrared suppressed. First results of a simultaneous solution to the coupled system of gluons, ghosts {\sl and} quarks indicate towards weak, and possibly negligible, vacuum polarisation effects of dynamical quarks on the gluon and ghost correlations in the infrared.
Ahlig Steven
Alkofer Reinhard
Smekal Lorenz von
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