Absence of diquarks in S-wave baryons

We analyze the dynamics of diquark formation in baryons containing one light and two heavy quarks. Due to the slower motion of the heavy quarks, we consider the motion of the light quark in a reference frame fixed in the two heavy ones. The potential of the light quark interacting with the two heavy quarks is derived from the quark-antiquark potential in mesons. This potential has a repulsive barrier between the two heavy quarks. A variational approach similar to that used in the study of the hydrogen molecule is applied to determine the two lowest energy eigenvalues and eigenfunctions of the light quark. The time-dependent wave function obtained describes the oscillation of the light quark along the direction defined by the two heavy quarks. We observe that the energy of this oscillating state is higher than the repulsive barrier between the two heavy quarks. There is no tunneling in the oscillation of the light quark, so we conclude that there is not formation of clusters or metastable states of a heavy and a light quark in this kind of baryons.