Veneziano amplitude, current algebra, and vertex functions

The possibility is examined of extending the ππ→ππ and πA1→ππ Veneziano amplitudes to the case of one or two mesons off the mass shell in a fashion consistent with chiral current algebra, partial conservation of axial-vector current, and conserved vector current. Soft-pion formulas for the pion-vector form factor and the σ-commutator vertex are deduced. The hard-meson analysis shows that if one wishes to maintain Veneziano form with two mesons off the mass shell, some of the πA1→ππ amplitudes must develop poles in one of the off-shell momenta at p2=0. The soft- pion vertex function equations are seen to be a consequence of removing the leading part of this singularity at the soft-pion point pμ=0. However, the resultant amplitudes are still singular at p2=o, pμ≠0 for a continuum of s, t, and u. The fixed poles implied by the presence of form factors (when two mesons are off shell) are seen to occur only in those amplitudes orthogonal to the A1 polarization vector and do not affect the amplitudes that make nonzero contributions for πA1→ππ scattering on the mass shell

Duke Scholars

Author Morton Friedman Biomedical Engineering