A multipole expansion and the Casimir-Polder effect in quantum chromodynamics

Gyan Bhanot, Willy Fischler, Serge Rudaz

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A multipole expansion for correlation functions in quantum chromodynamics in the presence of a static quark-antiquark pair is described. We discover a retardation effect, analogous to the Casimir-Polder effect in atomic physics, which is proven to persist to all finite orders of perturbation theory. The correlation functions studied may be used to gain some insight into the total rates for decays of the form (QQ)n′l′ → (QQ)nl + hadrons among states of a heavy quark Q. We also derive the Casimir-Polder potential between heavy mesons.

Original languageEnglish (US)
Pages (from-to)208-236
Number of pages29
JournalNuclear Physics, Section B
Issue number1
StatePublished - Aug 13 1979

Bibliographical note

Funding Information:
Our present understanding of quantum chromodynamics (QCD) is that the true vacuum of the theory is very different from the perturbative vacuum. This is due to the large scale fluctuations of the fields which are not taken into account in the usual perturbative approach. However, if we restrict our attention to the physics of heavy QQ systems, these large scale fluctuations will occur only for the gluonic degrees of freedom. Indeed, the heavier one chooses the quark to be, the closer they will resemble static external sources. In this work, we will idealize the heavy QQ system by making the quarks truly static. This means that we will consider rectangular Wilson loops, tr P exp \[ig~AauTadx~\], where P denotes path ordering, ATa and Ir a are respectively the color gauge field and generators of the gauge group SU(3)c, and a is a color index (see fig. 1). For such a static system, we need concentrate only on the gluonic degrees of freedom of the * Work supported in part by the National Science Foundation (Cornell) and by the Department of energy (Los Alamos).


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