  Shearing granular materials induces non-affine displacements. Such non-affine
displacements have been studied extensively, and are known to correlate with
plasticity and other mechanical features of amorphous packings. A well known
example is shear transformation zones as captured by the local deviation from
affine deformation, $D^2_{min}$, and their relevance to failure and stress
fluctuations. We analyze sheared frictional athermal disk packings and show
that there exists at least one additional mesoscopic transport mechanism that
superimposes itself on top of local diffusive motion. We evidence this second
transport mechanism in a homogeneous system via a diffusion tensor analysis and
show that the trace of the diffusion tensor equals the classic $D^2_{min}$ when
this second mesoscopic transport is corrected for. The new transport mechanism
is consistently observed over a wide range of volume fractions and even for
particles with different friction coefficients and is consistently observed
also upon shear reversal, hinting at its relevance for memory effects.
