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arXiv · 0901.4614

Auxiliary field method for the square root potential

Bernard Silvestre-Brac·Claude Semay·Fabien Buisseret
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Abstract

Using the auxiliary field method, we give an analytical expression for the eigenenergies of a system composed of two non-relativistic particles interacting via a potential of type $\sqrt{a^2 r^2 + b}$. This situation is usual in the case of hybrid mesons in which the quark-antiquark pair evolves in an excited gluonic field. Asymptotic expressions are proposed and the approximate results are compared to the exact ones. It is shown that the accuracy is excellent.

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Bernard Silvestre-Brac, Claude Semay, Fabien Buisseret. 2009-01-29. Auxiliary field method for the square root potential. https://arxiv.org/abs/0901.4614

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