Effective field theory for double heavy baryons at strong coupling
Joan Soto, Jaume Tarrús Castellà
Abstract
We present an effective field theory for doubly heavy baryons that goes beyond the compact heavy diquark approximation. The heavy quark distance $r$ is only restricted to ${m}_{Q}\ensuremath{\gg}1/r\ensuremath{\gg}{E}_{\text{bin}}$, where ${m}_{Q}$ is the mass of the heavy quark and ${E}_{\text{bin}}$ the typical binding energy. This means that the size of the heavy diquark can be as large as the typical size of a light hadron. We start from nonrelativistic QCD, and build the effective field theory at next-to-leading order in the $1/{m}_{Q}$ expansion. At leading order the effective field theory reduces to the Born-Oppenheimer approximation. The Born-Oppenheimer potentials are obtained from available lattice QCD data. The spectrum for double charm baryons below threshold is compatible with most of the lattice QCD results. We present for the first time the full spin averaged double bottom baryon spectrum below threshold based on QCD. We also present model-independent formulas for the spin splittings.