  Leading (large) logarithms in non-renormalizable theories have been
investigated in the recent past. Besides some general considerations, explicit
results for the expansion coefficients (in terms of leading logarithms) of
partial wave amplitudes and of scalar and vector form factors have been given.
Analyticity and unitarity constraints haven been used to obtain the expansion
coefficients of partial waves in massless theories, yielding form factors and
the scalar two-point function to five-loop order in the O(4)/O(3) model. Later,
the all order solutions for the partial waves in any O(N+1)/O(N) model were
found. Also, results up to four-loop order exist for massive theories. Here we
extend the implications of analyticity and unitarity constraints on the leading
logarithms to arbitrary loop order in massless theories. We explicitly obtain
the scalar and vector form factors as well as to the scalar two-point function
in any O(N) and SU(N) type models. We present relations between the expansion
coefficients of these quantities and those of of the relevant partial waves.
Our work offers a consistency check on the published results in the O(N) models
for form factors, and new results for the scalar two-point function. For the
SU(N) type models, we use the known expansion coefficients for partial waves to
obtain those for scalar and vector form factors as well as for the scalar
two-point function. Our results for the form factor offer a check for the known
and future results for massive O(N) and SU(N) type models when the massless
limit is taken. Mathematica notebooks which can be used to calculate the
expansion coefficients are provided as ancillary files.
