The Massive O(N) Non-linear Sigma Model at High Orders

Details The Massive O(N) Non-linear Sigma Model at High Orders The Massive O(N) Non-linear Sigma Model at High Orders

2010-08-20

arxiv.org/abs/1008.3499v1

Nucl.Phys.B843:55-83,2011

Physics

High Energy Physics

High Energy Physics - Phenomenology

39 pages

Scientific paper

10.1016/j.nuclphysb.2010.09.019

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.

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