Long multiplets in supersymmetric mechanics

The "long" indecomposable N=2, d=1 multiplet (2, 4, 2) defined in arXiv:1503.05537 [hep-th] as a deformation of the pair of chiral multiplets (2, 2, 0) and (0, 2, 2) by a number of the mass-dimension parameters is described in the superfield approach. We present its most general superfield and component actions, as well as a generalization to the case with the superfields of the opposite Grassmann parities and dimensionless deformation parameter. We show that the long N=2, d=1 multiplets are naturally embedded into the chiral SU(2|1), d=1 superfields having nonzero external spins with respect to SU(2) \subset SU(2|1). A superfield with spin s contains 2s long multiplets and two short multiplets (2, 2, 0) and (0, 2, 2). Two possible N=4, d=1 generalizations of the N=2 long multiplet in the superfield approach are also proposed.
Comment: 1 + 19 pages, new comments added, typos corrected, published version