Alex Kalloniatis

CSSM, University of Adelaide, Adelaide, Australia

High energy behaviour and analytic confinement

Confinement, more than the absence of coloured particles in the physical spectrum, is the mechanism by which colourless hadronic bound states emerge from the quark-gluon fields of Quantum Chromodynamics with their particular properties, such as lying on Regge trajectories. The string model is one intuitive picture for this. Another is analytic confinement, whereby quark and gluon momentum space propagators are entire functions but hadronic correlators admit Regge-like particle fluctuations. One of the long-standing problems of this approach is that such propagators necessarily diverge in the high energy regime where quark-hadron duality should be manifested. With S.N. Nedelko, the four dimensional "virton model" of Efimov and Ganbold, which manifests analytic confinement of scalar bosonic fields with Regge-like bound states, was studied. A resummation of Feynman graphs enables correct high energy behaviour in the cross-section for e+e- annihilation to hadrons to be restored. The key ingredient is that decay widths, depending as they do on divergent-in-energy propagators, also grow in energy and are manifested in amplitudes via the resummation. This suffices to regulate the cross-section such that the OPE result correctly emerges asymptotically.

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