On the (anti-)BRST invariant Lagrangian densities of the Abelian 2-form gauge theory

We demonstrate that the known off-shell nilpotent (i.e. s(a)b = 0) and anticommuting (i.e. sbsab + sabsb = 0) Becchi-Rouet-Stora-Tyutin (BRST) transformations (sb) and anti-BRST transformations (sab) are the symmetry transformations of the appropriate Lagrangian densities of a four (3 + 1)-dimensional (4D) free Abelian 2-form gauge theory which do not explicitly incorporate a very specific constrained field condition through a Lagrange multiplier 4D vector field. The above condition, which is the analogue of the Curci-Ferrari restriction of the non-Abelian 1-form gauge theory, emerges from the Euler-Lagrange equations of motion of the theory and ensures the anticommutativity of the transformations s(a)b. PACS numbers: 11.15.-q, 12.20.-m, 03.70.+k