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We consider a generalization of the $SO(2)$ gauged $O(3)$ Skyrme model in$2+1$ dimensions in the presence of a Skyrme--Chern-Simons (SCS) term, which isdefined in terms of $SO(2)\times SO(2)$ gauge fields together with an auxiliary$O(5)$ Skyrme scalar. Several different truncations of the general model areconsidered, with the aim to reveal to what extent the properties found inmodels with a (usual) Chern-Simons (CS) term are present also for the case of aSCS term. The results in this work show that qualitatively a similar pictureemerges, with $e.g.$ the presence of negative slopes in the $(E,Q)$ and$(E,J)$-curves. However, the deformation of the "baryon number" observed in theCS case (with a suitable potential function of the Skyrme scalar) is absent.

The effect of Skyrme--Chern-Simons dynamics on gauged Skyrmions in $2+1$ dimensions