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Johan Bijnens, Lisa Carloni
The Massive O(N) Non-linear 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, 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.
LU TP 10-21
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