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The masses of excited states of mixed orbital symmetry of nonstrange andstrange baryons belonging to the lowest $[{\bf 70},1^-]$ multiplet arecalculated in the $1/N_c$ expansion to order $1/N_c$ with a new method whichallows to considerably reduce the number of linearly independent operatorsentering the mass formula. This study represents an extension to SU(6) of ourwork on nonstrange baryons, the framework of which was SU(4). The conclusionregarding the role of the flavor operator, neglected in previous SU(6) studies,is reinforced. Namely, both the flavor and spin operators contribute dominantlyto the flavor-spin breaking.

SU(6) $[{\bf 70},1^-]$ baryon multiplet in the $1/N_c$ expansion