Spectra of doubly heavy quark baryons

Abstract

Baryons containing two heavy quarks are treated in the Born-Oppenheimer approximation. The Schr\"odinger equation for the two-center Coulomb plus harmonic oscillator potential is solved by the method of the ethalon equation at large intercenter separations. Asymptotical expansions for the energy term and wave function are obtained in analytical form. Using those formulas, the energy spectra of doubly heavy baryons with various quark compositions are calculated analytically.