Spectra of Baryons Containing Two Heavy Quarks

The spectra of baryons containing two heavy quarks test the form of the QQ potential through the spin-averaged masses and hyperfine splittings. The mass splittings in these spectra are calculated in a nonrelativistic potential model and the effects of varying the potential studied. The simple description in terms of light quark and pointlike diquark is not yet valid for realistic heavy quark masses. It is well-known that the quarkonium (Ψ and Υ) spectra test the QCD potential between quark and antiquark. In this case, a phenomenological flavor-independent potential and a QCD-derived hyperfine interaction can be used to describe the masses and splittings of the cc̄ and bb̄ mesons [1]. Furthermore, such models allow predictions to be made for the unobserved states in the spectra [2] and for theBc system [3]. In the same way, the doubly-heavy baryons (those containing ccq or bbq) test the potential between two quarks. The one-gluon-exchange potential between heavy quarks differs from the quark-antiquark potential by a relative color factor 2. This relation does not hold at higher orders: the one-loop corrections to the QQ and QQ potentials are not equal [4]. The confining potential, which is determined phenomenologically, should be studied for QQ interactions as it has been for QQ. Tests of the QQ potential can be implemented not only in the spin-averaged spectra of the doubly-heavy baryons, but also by studying the hyperfine splittings of these particles. This is surprising, as the hyperfine interactions contain two types of terms: those describing the spin-spin interaction between the heavy quarks (∼ 1/m2Q), which depend on the QQ potential analogously to the quarkonium case, and those describing the spin-spin interactions between heavy and light quarks (∼ 1/mQmq), which might be thought to depend on the light-heavy quark interaction and not significantly on the heavy-heavy quark potential. Nevertheless, the wave function of the light quark depends sufficiently on the heavy quark pair to provide information on the QQ binding. Baryon spectroscopy with non-relativistic potential models is relatively accurate, although not perfect. The method is clearly limited by its use of a non-relativistic treatment of the light quarks. Nonetheless, such models provide a relatively good description of the baryon spectra and stable predictions for the hyperfine splittings Σ∗Q−ΣQ and ΣQ−ΛQ for the baryons containing one heavy quark [7]. One potential choice which provides a good fit to the observed baryon spectrum is the power-law form [8]: