Pseudoscalar-meson decay constants, Goldberger-Treiman relations, and chiral SU(4) × SU(4) symmetry breaking

Abstract

A relation is obtained between pseudoscalar-meson decay constants, $F_{\pi }$, $F_K$, $F_D$, and $F_F$, and the corrections to the Goldberger-Treiman relations in SU(2) × SU(2), SU(3) × SU(3), and SU(4) × SU(4). From this the following model- independent inequality is derived: $\frac{F_F}{F_{\pi }}\gtrsim \frac{F_D}{F_{\pi }}>\frac{F_K}{F_{\pi }}>1\mathrm{}$. Predictions are then made for the corrections to Goldberger-Treiman relations in the charm sector using the three-point-function Veneziano model. These corrections turn out to be large, i.e., 70-85%, compared to those in SU(2) × SU(2) and SU(3) × SU(3). Also, values for the ratios $\frac{F_D}{F_{\pi }}$ and $\frac{F_F}{F_{\pi }}$ are predicted.