  We discuss several points that may help to clarify some questions that remain
about the anomaly puzzle in supersymmetric theories. In particular, we consider
a general N=1 supersymmetric Yang-Mills theory. The anomaly puzzle concerns the
question of whether there is a consistent way to put the R-current and the
stress tensor in a single supercurrent, even though in the classical theory
they are in the same supermultiplet. As is well known, the classically
conserved supercurrent bifurcates into two supercurrents having different
anomalies in the quantum regime. The most interesting result we obtain is an
explicit expression for the lowest component of one of the two supercurrents in
4-dimensional spacetime, namely the supercurrent that has the energy-momentum
tensor as one of its components. This expression for the lowest component is an
energy-dependent linear combination of two chiral currents, which itself does
not correspond to a classically conserved chiral current. The lowest component
of the other supercurrent, namely, the R-current, satisfies the Adler-Bardeen
theorem. The lowest component of the first supercurrent has an anomaly that we
show is consistent with the anomaly of the trace of the energy-momentum tensor.
Therefore, we conclude that there is no consistent way to put the R-current and
the stress tensor in a single supercurrent in the quantized theory. We also
discuss and try to clarify some technical points in the derivations of the
two-supercurrents in the literature. These latter points concern the
significance of infrared contributions to the NSVZ beta-function and the role
of the equations of motion in deriving the two supercurrents.
