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Leading logarithms in N-flavour mesonic Chiral Perturbation Theory

Bijnens, Johan LU ; Kampf, Karol and Lanz, Stefan (2013) In Nuclear Physics, Section B 873(1). p.137-164
Abstract
We extend earlier work on leading logarithms in the massive nonlinear O(n) sigma model to the case of SU(N) x SU(N)/SU(N) which coincides with mesonic Chiral Perturbation Theory for N flavours of light quarks. We discuss the leading logarithms for the mass and decay constant to six loops and for the vacuum expectation value ((q) over barq) to seven loops. For dynamical quantities the expressions grow extremely large much faster such that we only quote the leading logarithms to five loops for the vector and scalar form factor and for meson-meson scattering. The last quantity we consider is the vector-vector to meson-meson amplitude where we quote results up to four loops for a subset of quantities, in particular for the pion... (More)
We extend earlier work on leading logarithms in the massive nonlinear O(n) sigma model to the case of SU(N) x SU(N)/SU(N) which coincides with mesonic Chiral Perturbation Theory for N flavours of light quarks. We discuss the leading logarithms for the mass and decay constant to six loops and for the vacuum expectation value ((q) over barq) to seven loops. For dynamical quantities the expressions grow extremely large much faster such that we only quote the leading logarithms to five loops for the vector and scalar form factor and for meson-meson scattering. The last quantity we consider is the vector-vector to meson-meson amplitude where we quote results up to four loops for a subset of quantities, in particular for the pion polarizabilities. As a side result we provide an elementary proof that the factors of N appearing at each loop order are odd or even depending on the order and the remaining traces over external flavours. (C) 2013 Published by Elsevier B.V. (Less)
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publication status
published
subject
keywords
Renormalization group evolution of parameters, Spontaneous and radiative, symmetry breaking, Chiral Lagrangians, Meson-meson interactions
in
Nuclear Physics, Section B
volume
873
issue
1
pages
137 - 164
publisher
North-Holland
external identifiers
  • wos:000319794000005
  • scopus:84877109848
ISSN
0550-3213
DOI
10.1016/j.nuclphysb.2013.04.012
language
English
LU publication?
yes
id
ec5e6b86-22b8-4bda-9711-85cf6c3c46ef (old id 3930508)
date added to LUP
2016-04-01 14:36:00
date last changed
2020-09-02 02:19:19
@article{ec5e6b86-22b8-4bda-9711-85cf6c3c46ef,
  abstract     = {We extend earlier work on leading logarithms in the massive nonlinear O(n) sigma model to the case of SU(N) x SU(N)/SU(N) which coincides with mesonic Chiral Perturbation Theory for N flavours of light quarks. We discuss the leading logarithms for the mass and decay constant to six loops and for the vacuum expectation value ((q) over barq) to seven loops. For dynamical quantities the expressions grow extremely large much faster such that we only quote the leading logarithms to five loops for the vector and scalar form factor and for meson-meson scattering. The last quantity we consider is the vector-vector to meson-meson amplitude where we quote results up to four loops for a subset of quantities, in particular for the pion polarizabilities. As a side result we provide an elementary proof that the factors of N appearing at each loop order are odd or even depending on the order and the remaining traces over external flavours. (C) 2013 Published by Elsevier B.V.},
  author       = {Bijnens, Johan and Kampf, Karol and Lanz, Stefan},
  issn         = {0550-3213},
  language     = {eng},
  number       = {1},
  pages        = {137--164},
  publisher    = {North-Holland},
  series       = {Nuclear Physics, Section B},
  title        = {Leading logarithms in N-flavour mesonic Chiral Perturbation Theory},
  url          = {http://dx.doi.org/10.1016/j.nuclphysb.2013.04.012},
  doi          = {10.1016/j.nuclphysb.2013.04.012},
  volume       = {873},
  year         = {2013},
}