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The mass spectra and wave functions for the doubly heavy baryons are computed under the picture that the two heavy quarks inside a doubly heavy baryon, such as two $c$-quarks in $\Xi_{cc}$, combine into a heavy `diquark core' in color anti-triplet firstly, then the diquark core turns into a color-less doubly heavy baryon via combining the light $q$-quark inside the baryon.
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