A Lagrangian approach to dual pion amplitudes

A simple Lagrangian is constructed, which in the tree approximation produces a ππ scattering amplitude possessing (i) the correct iso-spin structure with no exotic resonances (ii) Regge asymptotic behavior Sαρ(t) and (iii) duality and satisfies (iv) the Adler condition. The last condition is satisfied without any restriction on the Regge-trajectory intercept. However, if one sets αρ(mπ2)=1/2, the present model produces all the terms in the one of Lovelace-Veneziano plus a satellite term of 0(p2/mρ2) where p is the momentum of the off-shell pion. The ratio of I=0 to I=2 S-wave scattering lengths is a00/a02≈-2 and thus lies between the Schwinger value of -3/2 and the Weinberg value of -7/2

Duke Scholars

Author Morton Friedman Biomedical Engineering