Unitary Padé approximants in strong coupling field theory and application to the calculation of the ρ- and f0-meson regge trajectories View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

1968-03

AUTHORS

D. Bessis, M. Pusteria

ABSTRACT

We show that the unitary Padé approximants, which are well suited for absorbing the essential singularities atg=0 in Lagrangian field theory, have in the case of a LagrangianL1=−g/4(ϕαϕα)2, where ϕα is the π field, the following nice features: 1) they are built up from the perturbativeS-matrix expansion, coinciding with it up to fourth order in our case; 2) they are rigorously unitary (elastic) and contain also inelastic unitarity (4π) (the modulus of the diagonalizedS-matrix is smaller than 1 all over the inelastic cut); 3) they have correct analytic properties in the energy variable; 4) there are no difficulties in extending them to complex values of the angular momentum; 5) they satisfy the right requirements between the number of inelastic channels open and the precision required on the crossing symmetry; 6) the complete equivalence between unitary Padé approximants and the approximations derived from the Lippmann-Schwinger variational principle is proved at all orders (using the Cini-Fubini «ansatz»). We have computed the complete fourth-order renormalized, including 2π and 4π contributions both in the direct and crossed channels. The main results we obtain are the mass of the ρ and f0 mesons and their Regge trajectories within 15% in agreement with experiment, in terms of only one parameter, the value ofg (∼6). The imaginary parts of Regge trajectories are found instable, so the widths are sensitive to the 6π and forces: in our model, the ρ and f0 mesons appear as narrow objects. More... »

PAGES

243-294

References to SciGraph publications

  • 1954-02. Non perturbation treatment of scattering in quantum field theory in IL NUOVO CIMENTO (1943-1954)
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    http://scigraph.springernature.com/pub.10.1007/bf02743788

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    http://dx.doi.org/10.1007/bf02743788

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