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The massive O(N) non-linear sigma model at high orders

Bijnens, Johan LU and Carloni, Lisa LU (2011) In Nuclear Physics, Section B 843(1). p.55-83
Abstract
We extend our earlier work on the massive O(N) non-linear sigma model to other observables. We derive expressions at leading order in the large N expansion at all orders in the loop expansion for the decay constant, vacuum expectation value, meson meson scattering and the scalar and vector form factors. This is done using cactus diagram resummation using a generalized gap equation and other recursion relations. For general N we derive the expressions for the n-th-loop-order leading logarithms (M-2/F-2 log(mu(2)/M-2))(n), up to five loops for the decay constant and vacuum expectation value (VEV) and up to four loops for meson-meson scattering, the scalar and vector form factors. We also quote our earlier result for the mass. The large N... (More)
We extend our earlier work on the massive O(N) non-linear sigma model to other observables. We derive expressions at leading order in the large N expansion at all orders in the loop expansion for the decay constant, vacuum expectation value, meson meson scattering and the scalar and vector form factors. This is done using cactus diagram resummation using a generalized gap equation and other recursion relations. For general N we derive the expressions for the n-th-loop-order leading logarithms (M-2/F-2 log(mu(2)/M-2))(n), up to five loops for the decay constant and vacuum expectation value (VEV) and up to four loops for meson-meson scattering, the scalar and vector form factors. We also quote our earlier result for the mass. The large N results do not give a good approximation for the case N = 3. We use our results to study the convergence of the perturbative series and compare with elastic unitarity. (C) 2010 Elsevier B.V. All rights reserved. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Spontaneous and radiative, 1/N expansions), numbers of components (e.g., Renormalization group evolution of parameters, Expansions for large, symmetry breaking, Chiral Lagrangians
in
Nuclear Physics, Section B
volume
843
issue
1
pages
55 - 83
publisher
Elsevier
external identifiers
  • wos:000285024100003
  • scopus:78049461142
ISSN
0550-3213
DOI
10.1016/j.nuclphysb.2010.09.019
language
English
LU publication?
yes
id
65feaba2-0220-4a26-9b7a-78e92ee27ea6 (old id 1774162)
date added to LUP
2011-02-01 09:59:45
date last changed
2017-08-13 04:10:21
@article{65feaba2-0220-4a26-9b7a-78e92ee27ea6,
  abstract     = {We extend our earlier work on the massive O(N) non-linear sigma model to other observables. We derive expressions at leading order in the large N expansion at all orders in the loop expansion for the decay constant, vacuum expectation value, meson meson scattering and the scalar and vector form factors. This is done using cactus diagram resummation using a generalized gap equation and other recursion relations. For general N we derive the expressions for the n-th-loop-order leading logarithms (M-2/F-2 log(mu(2)/M-2))(n), up to five loops for the decay constant and vacuum expectation value (VEV) and up to four loops for meson-meson scattering, the scalar and vector form factors. We also quote our earlier result for the mass. The large N results do not give a good approximation for the case N = 3. We use our results to study the convergence of the perturbative series and compare with elastic unitarity. (C) 2010 Elsevier B.V. All rights reserved.},
  author       = {Bijnens, Johan and Carloni, Lisa},
  issn         = {0550-3213},
  keyword      = {Spontaneous and radiative,1/N expansions),numbers of components (e.g.,Renormalization group evolution of parameters,Expansions for large,symmetry breaking,Chiral Lagrangians},
  language     = {eng},
  number       = {1},
  pages        = {55--83},
  publisher    = {Elsevier},
  series       = {Nuclear Physics, Section B},
  title        = {The massive O(N) non-linear sigma model at high orders},
  url          = {http://dx.doi.org/10.1016/j.nuclphysb.2010.09.019},
  volume       = {843},
  year         = {2011},
}