Some Difficulties with the Use of the Kemmer-Duffin Formalism for Pseudoscalar Mesons

Abstract

While the Kemmer-Duffin formalism for pseudoscalar mesons eliminates some difficulties in the analysis of $K_{l3\mathrm{}}$ form factors, it gives rise to difficulties in other areas. It is shown that this formalism leads to: (i) a linear Gell-Mann—Okubo mass formula for mesons; (ii) an incompatibility between SU(3)-symmetric meson-nucleon couplings and experiment; (iii) (3*,3) breaking of chiral symmetry ($H^{\prime }=u^0+c{u}^8$) leads to $c=-0.9\mathrm{}$ and $\frac{f_K}{f_{\pi }}={\left(\frac{m_{\pi }}{m_K}\right)}^{\frac{1}{2}}$.