Sum rules for charmed baryon masses.

The measured masses of the three charge states of the charmed Σc baryon are found to be in disagreement with a sum rule based on the quark model, but relying on no detailed assumptions about the form of the interaction. This poses a significant problem for the charmed baryon sector of the quark model. Other relations among charmed baryon masses are also discussed. PACS numbers: 12.40.Yx., 14.20.-c, 14.40.-n In recent years, measurements have been made[1] of the masses of the three charge states of the charmed Σc baryon. These measurements can be applied to sum rules[2] that were derived some time ago using fairly minimal assumptions within the quark model. The sum rules depend on standard quark model assumptions, and the additional assumption that the interaction energy of a pair of quarks in a particular spin state does not depend on which baryon the pair of quarks is in. No assumptions are made about the type of potential, and no internal symmetry is assumed. The Σ sum rule relates electromagnetic mass differences of the Σc baryon with corresponding mass differences of the Σ and Σ[2] Duu +Ddd − 2Dud = Σ + + Σ− − 2Σ = 1.7± 0.2 (1) = Σ + Σ∗− − 2Σ = 2.6± 2.1 (2) = Σ c + Σ 0 c − 2Σ + c = −2.1± 1.3. (3) The baryon symbol has been used as its mass, and the Dij represent the two body interaction energies between pairs of quarks in states of spin one. The