Doubly Heavy Baryons in the Born–Oppenheimer Approximation

Abstract

The Born–Oppenheimer approximation, used to calculate the binding energy in the positively-charged molecular hydrogen ion, is applied for calculating the mass spectrum of doubly-heavy baryons. To find the ion binding energy, the perturbation theory is used within the non-relativistic quantum mechanics. When the protons are static, the approach is known as the Born–Oppenheimer approximation. The Hamiltonian average for the molecular hydrogen ion is found by applying the Ritz variational method. Similar method is used for calculation of a binding energy in a doubly-heavy baryon with heavy quarks of the same flavor. The binding energy of this baryon is found with account of additional interquark-potential-energy terms due to the quark confinement. The doubly charmed \(\Xi_{cc}^{++}\) baryon with the color-antitriplet doubly charmed diquark is studied as an example. Its binding energy is numerically studied in dependence on the distance between the charmed quarks and found to be a growing function without local minima.