Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Massive O(N) Non-linear Sigma Model at High Orders   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.

15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga