Johan Bijnens, Lisa Carloni
Leading Logarithms in the Massive O(N) Nonlinear Sigma Model
Preprint series: ESI preprints

MSC:

81T17 Renormalization group methods

81R40 Symmetry breaking

81V05 Strong interaction, including quantum chromodynamics

PACS: 11.10.Hi,11.15.Pg,11.30.Qc,12.39.Fe
Abstract: We review B\"uchler 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.