Right invariant metrics on SU(3) and one loop divergences in chiral perturbation theory

Jul, 1990
39 pages
Published in:
  • Z.Phys.C 50 (1991) 255-274
Report number:
  • CPT-90-P-2363

Citations per year

19911999200720152023012345
Abstract: (Springer)
In the framework of chiral perturbation theory, we compute the one-loop divergences of the effective Lagrangian describing strong and non-leptonic weak interactions of pseudoscalar mesons. We use the background field method and the heat-kernel expansion, and underline the geometrical meaning of the different terms, showing how the right-invariance of the metrics onSU(3) allows to clarify and simplify the calculations. Our results are given in terms of a minimal set of independent counterterms, and shorten previous ones of the literature, in the particular case where the electromagnetic fild is the only external source which is considered. We also show that a geometrical construction of the effective Lagrangian at orderO(p4) allows to derive some relations between thefinite parts of the coupling constants. These relations do not depend on the scale μ used to renormalize.
  • perturbation theory: chiral
  • effective Lagrangian
  • sigma model
  • symmetry: SU(3) x SU(3)/SU(3)
  • renormalization
  • differential geometry: SU(3)
  • background field
  • expansion: heat kernel
  • pseudoscalar meson: strong interaction
  • strong interaction: pseudoscalar meson