N-point functions in chiral SU(3)xSU(3) current algebra

Hard-meson techniques are presented for calculating processes involving octets (nonets) of mesons under the assumptions of chiral SU(3)×SU(3) [U(3)×U(3)] current-algebra commutation relations, partial conservation of axial-vector current, conservation and partial conservation of vector currents, and single-meson saturation of intermediate sums. Using these conditions and the usual smoothness hypothesis, the general procedure for constructing the arbitrary N-point function is given. If, in addition, one assumes that the `σ commutators' (i.e., the commutators of the time components of the currents with the scalar fields) are single-particle dominated, it is inconsistent to assume only octets of particles. A consistent formalism involving nonets of particles can be constructed, however. The spin-zero mesons must then belong to the (3,3*)+(3*,3) representation. Hence the (3,3*)+(3*,3) symmetry-breaking condition is deduced from the current-algebra conditions when combined with pole dominance

Duke Scholars

Author Morton Friedman Biomedical Engineering