A novel observation in the BRST approach to a free spinning relativistic particle

For the newly proposed coupled (but equivalent) Lagrangians for the supersymmetric (SUSY) system of a one (0 + 1)-dimensional spinning relativistic particle, we derive the Noether conserved charges corresponding to its (super)gauge, Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST and ghost-scale symmetry transformations. We deduce the underlying algebra amongst the continuous symmetry operators and corresponding conserved charges. We point out a novel observation that emerges, for this specific SUSY system, when we discuss it within the framework of BRST formalism. In particular, the requirement of the physicality criteria with the (anti-)BRST charges leads to a completely new observation because, as it turns out, one of the primary constraints does not annihilate the physical state of the theory. We have never come across this kind of result in the realm of BRST approach to usual gauge theories. We provide the physical and theoretical reasons behind the above observation.