Auxiliary field method for the square root potential

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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• Semirelativistic Hamiltonians and the auxiliary field method