Massive 4D Abelian 2-Form Theory: Nilpotent Symmetries from the (Anti-)Chiral Superfield Approach

We derive the off-shell nilpotent (anti-)BRST symmetry transformations by exploiting the (anti-)chiral superfield approach (ACSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism for the four (3+1)-dimensional (4D) St$\ddot{u}$ckelberg-modified massive Abelian 2-form gauge theory. We perform exactly similar kind of exercise for the derivation of the off-shell nilpotent (anti-)co-BRST symmetry transformations, too. In the above derivations, the symmetry invariant restrictions on the superfields play very important and decisive roles. To prove the sanctity of the above nilpotent symmetries, we generalize our 4D ordinary theory (defined on the 4D flat Minkowskian spacetime manifold) to its counterparts (4,1)-dimensional (anti-)chiral super sub-manifolds of the (4,2)-dimensional supermanifold which is parameterized by the superspace coordinates $Z^{M} = (x^{\mu},\theta, \bar{\theta} ) $ where $x^\mu ( \mu = 0,1,2,3 )$ are the bosonic coordinates and a pair of Grassmannian variables $(\theta, \bar{\theta})$ are fermionic: ($\theta^{2} = \bar{\theta^{2}} = 0, \,\,\theta\,\bar{\theta} +\bar{\theta}\,\theta = 0$) in nature. One of the novel observations of our present endeavor is the derivation of the Curci-Ferrari (CF) type restrictions from the requirement of the symmetry invariance of the coupled (but equivalent) Lagrangian densities for our theory within the framework of ACSA to BRST formalism. We also exploit the standard techniques of ACSA to capture the off-shell nilpotency and absolute anticommutativity of the conserved (anti-)BRST as well as the (anti-)co-BRST charges. In a subtle manner, the proof of the absolute anticommutativity of the above conserved charges also implies the existence of the appropriate CF-type restrictions on our theory.