  Using particle simulations of the uniform shear flow of a rough dilute
granular gas, we show that the translational and rotational velocities are
strongly correlated in direction, but there is no orientational
correlation-induced singularity at perfectly smooth ($\beta=-1$) and rough
($\beta=1$) limits for elastic collisions ($e=1$); both the translational and
rotational velocity distribution functions remain close to a Gaussian for these
two limiting cases. Away from these two limits, the orientational as well as
spatial velocity correlations are responsible for the emergence of non-Gaussian
high velocity tails. The tails of both distribution functions follow stretched
exponentials, with the exponents depending on normal ($e$) and tangential
($\beta$) restitution coefficients.
