An extraordinary mass invariant and an obstruction in a massive superspin one half model made with a chiral dotted spinor superfield

An action for a complex irreducible massive superspin 12 multiplet can be constructed out of two chiral dotted spinor and two chiral undotted spinor superfields. To make this action a sensible one, additional ‘reality constraints’ are needed, and the notion of BRST recycling is needed to find the supersymmetry transformations of the theory with these additional constraints. This theory possesses three possible mass terms. An earlier paper examined the theory with the first mass term. This paper adds a second mass term and examines the consequences of that. This second mass invariant is ‘extraordinary’, which means that it is intrinsically dependent on the Zinn sources (‘antifields’) of the theory. This in turn implies that the action needs to be ‘completed’ so that it yields zero for the relevant Poisson Bracket. This ‘Completion’ meets an ‘Obstruction’, which is a ghost charge one object in the BRST cohomology space. Usually Obstructions arise from a one loop calculation, in which case they form anomalies of the theory. However this Obstruction arises at tree level from the completion. The coefficient of the Obstruction needs to be set to zero. This restores the complex irreducible massive superspin 12 multiplet to its usual structure, except that the mass is constructed out of the two mass parameters. The construction suggests interesting possibilities for related interacting theories.