Isospin splittings in baryons with two heavy quarks

Abstract

Isospin splittings in baryons with two heavy quarks and a $u$ or $d$ quark are calculated using simple methods proposed previously by the authors. The results are $M({\Xi }_{cc}^{++})-M({\Xi }_{cc}^{+})=1.41\pm 0.12^{+0.76}$ MeV, $M({\Xi }_{bb}^0)-M({\Xi }_{bb}^{-})=-4.78\pm 0.06^{+0.03}$ MeV, and $M({\Xi }_{bc}^{+})-M({\Xi }_{bc}^0)=-1.69\pm 0.07^{+0.39}$ MeV, where the statistical errors reflect uncertainties in input mass splittings, and the systematic errors are associated with the choice of constituent-quark masses.

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