Johan Bijnens, Lisa Carloni
Leading Logarithms in the Massive O(N) Nonlinear Sigma Model
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.
LU TP 09-26