Sum Rules and a Scalar Unitary Singlet
Abstract
The sum rules relating the axialvector coupling constant to ππ and πN total cross sections are derived using the commutation relations between the chiral currents χ^{+}(t) and χ^{3}(t). The sum rules obtained are the same as those obtained by other authors using the commutation relation between χ^{+}(t) and χ^{}(t). It is also shown that the assumption of the existence of the σ meson as a scalar unitary singlet helps in saturating the ππ and KK̄ sum rules. A definite conclusion cannot be arrived at about the existence of σ meson from the ππ sum rule, since the sum rule can equally well be saturated by postulating a large lowenergy ππ scattering in I=0 state, but the KK̄ sum rule does seem to require the presence of a particle with properties similar to those of the σ meson. SU(3) symmetry is assumed in the latter case.
 Publication:

Physical Review
 Pub Date:
 October 1966
 DOI:
 10.1103/PhysRev.150.1392
 Bibcode:
 1966PhRv..150.1392K