  An exact analysis is performed for the two-point correlation function C(r,t)
in dissipative Burgers turbulence with bounded initial data, in arbitrary
spatial dimension d. Contrary to the usual scaling hypothesis of a single
dynamic length scale, it is found that C contains two dynamic scales: a
diffusive scale l_{D} \sim t^{1/2} for very large r, and a super-diffusive
scale L(t) \sim t^{a} for r \ll l_{D}, where a = (d+1)/(d+2). The consequences
for conventional scaling theory are discussed. Finally, some simple scaling
arguments are presented within the `toy model' of disordered systems theory,
which may be exactly mapped onto the current problem.
