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For physical finite-spin one-particle states, a positive-energy Poincaré group representation is labelled by mass and spin $(m,j)$ when $m>0$, or mass and helicity $(0,h)$ when massless. The individual states also carry their four-momentum and a spin projection. For four-dimensional N=1 supersymmetry, the irreducible labels become $(m,j_{msuper})$, with $j_{msuper}$ the superspin, or $(0,h_{msuper})$, with a chosen superhelicity convention. The constituent representation labels arewith the last entry omitted for $j=0$, andA required CPT completion of a supermultiplet adds the conjugate labels $(0,-h),(0,-h-\frac{1}{2})$ and conjugates any internal charges.

In a massive four-dimensional N=1 supersymmetry representation, the two normalized raising supercharges transform as a spin-half doublet. Start with a Clifford vacuum of superspin $j=1/2$. At occupation levels zero, one and two, the ordinary spins areThe two-creation state has a spin-singlet oscillator factor because the creation operators anticommute. Thus the massive N=1 vector multiplet containsThere are four bosonic polarizations, $3+1$, and four fermionic polarizations, $2+2$, as required by boson-fermion degeneracy in a supermultiplet.

In the massless limit the helicity multiplicities become $+1,-1$, two copies each of $+1/2,-1/2$, and two zero-helicity states. They separate into the four irreducible helicity pairsWith the lower-helicity convention for superhelicity, a pair $(\kappa ,\kappa +1/2)$ has labels $\kappa =1/2,0,-1/2,-1$, respectively. A midpoint convention shifts each label by $1/4$; the explicit helicity pairs remove any naming ambiguity.

Pairing under the CPT theorem, the first and last pairs form a massless vector multiplet, and the middle two form a massless chiral multiplet. This is the massless limit of a massive N=1 vector multiplet. The longitudinal vector polarization supplies one of the chiral multiplet's two real scalar modes; the original spin-zero state supplies the other. Simply discarding the longitudinal polarization would lose a physical degree of freedom and give the wrong decomposition.

Positive-energy one-particle Poincaré group representations have labels $(m,s)$ for $m>0$, and $(0,h)$ for finite-helicity massless states; individual massive polarizations add $m_s=-s,\dots ,s$. An $\mathcal{N}=1$ massive supermultiplet is labelled by mass $m$ and superspin $j$, with constituent labelsA massless supermultiplet has constituent labelsA CPT completion of a supermultiplet additionally supplies $(0,-h),(0,-h+\frac{1}{2})$, with conjugated internal charges where applicable. Constituent spins/helicities are the labels here, not counts of polarizations.

For a massive four-dimensional N=1 supermultiplet, superspin $j$ is the spin of its Clifford vacuum, the state annihilated by the two lowering supercharges. The creation operators produce spins $j,j,j+1/2,j-1/2$, omitting the last when $j=0$. The corresponding superspin Casimir has an eigenvalue proportional to $j(j+1)$; this representation label is distinct from the spin of any one constituent.