  We extend our earlier work on the massive $O(N)$ nonlinear sigma model to
other observables. We derive expressions at leading order in the large $N$
expansion at all orders in the loop expansion for the decay constant, vacuum
expectation value, meson-meson scattering and the scalar and vector form
factors. This is done using cactus diagram resummation using a generalized gap
equation and other recursion relations. For general $N$ we derive the
expressions for the $n$-th loop order leading logarithms
$\left(M^2/F^2\log(\mu^2/M^2)\right)^n$, up to five-loops for the decay
constant and vacuum expectation value (VEV) and up to four-loops for
meson-meson scattering, the scalar and vector form factors. We also quote our
earlier result for the mass. The large $N$ results do not give a good
approximation for the case $N=3$. We use our results to study the convergence
of the perturbative series and compare with elastic unitarity.
