Narrow Results

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.

Diquarks, or metastable clusters of two quarks inside baryons, are shown to be produced by angular momentum excitation. In baryons with a light quark and two heavy quarks with large angular momentum (L>2), the centrifugal barrier that appears in the rotation frame of the two heavy quarks prevents the light quark from passing freely between the two heavy quarks. The light quark must tunnelize through this potential barrier, which gives rise to the clusters of a light and a heavy quark.

Quark interactions inside baryons depend on the spin states of the quarks. We investigated the contribution of the spin–spin interactions of quarks in comparison with other factors necessary for diquark formation in baryons, concluding that the effects of spin–spin interactions are correlated with the state of angular momentum excitation.