SUM RULES FROM CHARGE-CHARGE-DENSITY AND CHARGE-CHARGE COMMUTATORS

The spectral-function approach to the broken-SU(3)-symmetry sum rules has two difficulties. One is the ambiguity with respect to the Schwinger terms, and the other is the derivation of the so-called second sum rules, which are not acceptable. By using commutators involving a charge operator, our approach is free of the first difficulty. In computation, we make the following approximation for the operator VK [which is an SU(3) raising or lowering operator in the symmetry limit]: In the broken symmetry the operator VK still acts as a generator, to a good approximation, in an appropriately chosen infinite-momenta limit. For the vector meson →l+l̄ couplings, we are able to derive sum rules which are essentially equivalent to the first spectral-function sum rules but not to the second ones. Instead, we obtain other sum rules which enable us to determine the first-order ω-φ mixing angle from the rates of V→l+l̄ decays. A sum rule for the ω→3π, φ→3π, and K*→Kππ couplings is also obtained. We also derive in our approach the Gell-Mann-Zachariasen relation and its K* analog which favors the existence of the κ meson. © 1968 The American Physical Society.