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

Bijnens, Johan LU and Carloni, Lisa LU (2010) In Nuclear Physics, Section B 827(1-2). p.237-255
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.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Expansions for large, Renormalization group evolution of parameters, numbers of components (e.g., 1/N expansions), Spontaneous and radiative, symmetry breaking, Chiral Lagrangians
in
Nuclear Physics, Section B
volume
827
issue
1-2
pages
237 - 255
publisher
Elsevier
external identifiers
  • wos:000272669900008
  • scopus:84859958580
ISSN
0550-3213
DOI
10.1016/j.nuclphysb.2009.10.028
language
English
LU publication?
yes
id
93866a94-f4d7-4161-906a-185f92d6aac6 (old id 1508718)
alternative location
http://arxiv.org/abs/0909.5086
date added to LUP
2009-11-23 22:14:52
date last changed
2018-05-29 11:12:18
@article{93866a94-f4d7-4161-906a-185f92d6aac6,
  abstract     = {We review Buchler and Colangelo's result<br/><br>
that leading divergences<br/><br>
at any loop order can be calculated using only one-loop calculations<br/><br>
and we provide an alternative proof.<br/><br>
We then use this method to calculate the leading divergences of<br/><br>
and thus the leading logarithmic corrections to the meson mass in<br/><br>
the massive $O(N)$<br/><br>
nonlinear sigma model to five-loop order.<br/><br>
We also calculate the all-loop result to leading order in the large $N$<br/><br>
expansion by showing that only cactus diagrams contribute and by summing<br/><br>
these via a generalized gap equation.},
  author       = {Bijnens, Johan and Carloni, Lisa},
  issn         = {0550-3213},
  keyword      = {Expansions for large,Renormalization group evolution of parameters,numbers of components (e.g.,1/N expansions),Spontaneous and radiative,symmetry breaking,Chiral Lagrangians},
  language     = {eng},
  number       = {1-2},
  pages        = {237--255},
  publisher    = {Elsevier},
  series       = {Nuclear Physics, Section B},
  title        = {Leading Logarithms in the Massive $O(N)$ Nonlinear Sigma Model},
  url          = {http://dx.doi.org/10.1016/j.nuclphysb.2009.10.028},
  volume       = {827},
  year         = {2010},
}