Quark--Antiquark Bethe--Salpeter Equation in QCD
Abstract
We review our recent results \cite{bsult} on the derivation of a B-S equation in QCD in a Wilson loop context. We work in a second order formalism, use the Feynman--Schwinger path integral representation for a quark in external field and obtain a similar expression for a quark--antiquark amplitude in which the gauge fields appears only through the Wilson loop integral $W$. A $ q \bar{q}$ B-S equation is obtained starting from this expression under the assumption, already used in the derivation of heavy quark potential, that $i \ln W$ can be expressed as the sum of a perturbative contribution and an area term. The intrinsically nonperturbative derivation method is first discussed on the simpler case of two spinless particles interacting through a scalar field. The $q \bar{q}$ semirelativistic potential is reobtained in the large quark mass limit.
- Publication:
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arXiv e-prints
- Pub Date:
- October 1995
- DOI:
- 10.48550/arXiv.hep-ph/9510214
- arXiv:
- arXiv:hep-ph/9510214
- Bibcode:
- 1995hep.ph...10214B
- Keywords:
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- High Energy Physics - Phenomenology
- E-Print:
- 16 pages, latex