Chiral Lagrangian for excited pions
- Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna Head Post Office, P.O. Box 79, 101000 Moscow (Russia)
- Institut fuer Theoretische Physik II, Ruhr-Universitaet Bochum, D-44780 Bochum (Germany)
We construct a chiral Lagrangian containing, in addition to the usual pion field ({pi}), also its first radial excitation ({pi}{sup {prime}}). The Lagrangian is derived in the large-N{sub c} limit from a Nambu{endash}Jona-Lasinio (NJL) quark model with separable nonlocal interactions, with form factors corresponding to three-dimensional ground- and excited-state wave functions. Chiral symmetry breaking is governed by the NJL gap equation. The effective Lagrangian for {pi} and {pi}{sup {prime}} mesons shows the decoupling of the Goldstone pion and the vanishing of the {pi}{sup {prime}} leptonic decay constant f{sub {pi}{sup {prime}}} in the chiral limit, as required by axial-vector current conservation. We derive the excited-state contribution to the axial-vector current of the model using Noether{close_quote}s theorem. For a finite pion mass and {pi}{sup {prime}} masses in the range of 750{endash}1300 MeV, f{sub {pi}{sup {prime}}}/f{sub {pi}} is found to be of the order of 1{percent}. {copyright} {ital 1997} {ital The American Physical Society}
- OSTI ID:
- 531962
- Journal Information:
- Physical Review, D, Journal Name: Physical Review, D Journal Issue: 1 Vol. 56; ISSN PRVDAQ; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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