  The main difficulty of statistical theories of fluid turbulence is the lack
of an obvious small parameter. In this paper we show that the formerly
established fusion rules can be employed to develop a theory in which
Kolmogorov's statistics of 1941 acts as the zero order, or background
statistics, and the anomalous corrections to the K41 scaling exponents
$\zeta_n$ of the $n$th order structure functions can be computed analytically.
The crux of the method consists of renormalizing a 4-point interaction
amplitude on the basis of the fusion rules. The novelty is that this amplitude
includes a small dimensionless parameter, which is shown to be of the order of
the anomaly of $\zeta_2$, $\delta_2= \zeta_2-2/3\approx 0.03$. Higher order
interaction amplitudes are shown to be even smaller. The corrections to K41 to
$O(\delta_2)$ result from standard logarithmically divergent ladder-diagrams in
which the 4-point interaction acts as a "rung". The theory allows a calculation
of the anomalous exponents $\zeta_n$ in powers of the small parameter
$\delta_2$. The $n$-dependence of the scaling exponents $\zeta_n$ stems from
pure combinatorics of the ladder diagrams. We calculate the exponents $\zeta_n$
up to $O(\delta_2^3)$. Previously derived bridge relations allow a calculation
of the anomalous exponents of correlations of the dissipation field and of
dynamical correlations in terms of the same parameter $\delta_2$. The actual
evaluation of the small parameter $\delta_2$ from first principles requires
additional developments that are outside the scope of this paper.

Chaotic Dynamics;Fluid Dynamics