Supersymmetrization of horizontality condition: nilpotent symmetries for a free spinning relativistic particle

We clearly and consistently supersymmetrize the celebrated horizontality condition to derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the supersymmetric system of a free spinning relativistic particle within the framework of superfield approach to BRST formalism. For the precise determination of the proper (anti-) BRST symmetry transformations for all the bosonic and fermionic dynamical variables of our system, we consider the present theory on a (1, 2)-dimensional supermanifold parameterized by an even (bosonic) variable (tau) and a pair of odd (fermionic) variables theta and (theta) over bar (with theta(2) = (theta) over bar (2) = 0, theta(theta) over bar + (theta) over bar theta = 0) of the Grassmann algebra. One of the most important and novel features of our present investigation is the derivation of (anti-) BRST invariant CurciFerrari type restriction which turns out to be responsible for the absolute anticommutativity of the (anti-) BRST transformations and existence of the coupled (but equivalent) Lagrangians for the present theory of a supersymmetric system. These observations are completely new results for this model.