  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.
