Leading Logarithms in the Massive O(N) Nonlinear Sigma Model

TL;DR

This paper reviews a method for calculating leading divergences in the massive O(N) nonlinear sigma model, extends it to five-loop order, and derives all-loop results in the large N limit, advancing understanding of quantum corrections in this model.

Contribution

It provides an alternative proof for calculating leading divergences and applies this to compute high-order loop corrections and large N results in the nonlinear sigma model.

Findings

Leading divergences can be computed from one-loop calculations.

Calculated five-loop order leading logarithmic corrections to meson mass.

Derived all-loop leading order results in the large N expansion.

Abstract

We review Buchler and Colangelo's result that leading divergences at any loop order can be calculated using only one-loop calculations and we provide an alternative proof. We then use this method to calculate the leading divergences of and thus the leading logarithmic corrections to the meson mass in the massive O(N) nonlinear sigma model to five-loop order. We also calculate the all-loop result to leading order in the large $N$ expansion by showing that only cactus diagrams contribute and by summing these via a generalized gap equation.