
Johan Bijnens, Lisa Carloni
The Massive O(N) Nonlinear Sigma Model at High Orders
Abstract
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, mesonmeson 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 fiveloops for the decay
constant and vacuum expectation value (VEV) and up to fourloops for
mesonmeson 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.
LU TP 1021
