Algebra of Fields and Weinberg's Second Sum Rule

In realistic $\mathrm{SU}\left(3\right)\mathrm{}\times \mathrm{SU}\left(3\right)\mathrm{}$ field-algebra Lagrangians, in which the unrenormalized masses of the spin-1 multiplets are split, nonminimal couplings are necessary. It is shown that when nonminimal couplings are allowed, Weinberg's second sum rule, relating spin-1 chiral partners, may be violated in both the $\mathrm{SU}\left(2\right)\mathrm{}\times \mathrm{SU}\left(2\right)\mathrm{}$ and $\mathrm{SU}\left(3\right)\mathrm{}\times \mathrm{SU}\left(3\right)\mathrm{}$ algebras even when all currents are conserved.