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

Summary, in English

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.

• Author: Johan Bijnens; Lisa Carloni
• Department/s: Theoretical Particle Physics - Has been reorganised
• Publishing year: 2010
• Language: English
• Pages: 237-255
• Publication/Series: Nuclear Physics, Section B
• Volume: 827
• Issue: 1-2
• Links: http://arxiv.org/abs/0909.5086; http://dx.doi.org/10.1016/j.nuclphysb.2009.10.028
• Document type: Journal article
• Publisher: North-Holland
• Topic: Subatomic Physics
• Keywords: Expansions for large; Renormalization group evolution of parameters; numbers of components (e.g.; 1/N expansions); Spontaneous and radiative; symmetry breaking; Chiral Lagrangians
• Status: Published
• ISBN/ISSN/Other: ISSN: 0550-3213