Unquenching the Quark-Antiquark Green's Function

Peter Watson; Wolfgang Cassing

doi:10.1007/s00601-004-0063-1

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arXiv · hep-ph/0405287

Unquenching the Quark-Antiquark Green's Function

Peter Watson·Wolfgang Cassing

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Abstract

We propose a nonperturbative resummation scheme for the four-point connected quark-antiquark Green's function $G^4$ that shows how the Bethe-Salpeter equation may be `unquenched' with respect to quark-antiquark loops. This mechanism allows to dynamically account for hadronic meson decays and multiquark structures whilst respecting the underlying symmetries. An initial approximation to the four-point Schwinger-Dyson equation -- suitable for phenomenological application -- is examined numerically in a couple of aspects. It is demonstrated that this approximation explicitly maintains the correct asymptotic limits and contains the physical resonance structures in the near timelike region in the quark-antiquark channel whereas no resonances are found in the diquark channel, respectively.

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Peter Watson, Wolfgang Cassing. 2004-05-28. Unquenching the Quark-Antiquark Green's Function. https://doi.org/10.1007/s00601-004-0063-1

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