A chiral Lagrangian for excited pions

Details A chiral Lagrangian for excited pions A chiral Lagrangian for excited pions

1996-08-16

arxiv.org/abs/hep-ph/9608347v1

Phys.Rev. D56 (1997) 221-229

Physics

High Energy Physics

High Energy Physics - Phenomenology

19 pages, LaTeX, 3 Postscript figures included using epsf

Scientific paper

10.1103/PhysRevD.56.221

We construct a chiral Lagrangian containing besides the usual pion field (pi) also its first radial excitation (pi'). The Lagrangian is derived by bosonization of a Nambu--Jona-Lasinio quark model with separable non-local interactions, with form factors corresponding to 3-dimensional ground and excited state wave functions. Chiral symmetry breaking is governed by the NJL gap equation. The effective Lagrangian for pi- and pi'-mesons shows the decoupling of the Goldstone pion and the vanishing of the pi' leptonic decay constant, f_pi', in the chiral limit, as required by axial current conservation. We derive the excited states' contribution to the axial current of the model using Noether's theorem. For finite pion mass and pi' masses in the range of 750 MeV -- 1300 MeV, f_pi' / f_pi is found to be of the order of 1 percent.

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