Constraints on Weak Meson-Nucleon Coupling from Parity Nonconservation inF19

The parity-nonconservation asymmetry $A_{\gamma }$ in the decay of polarized ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}_{}^{*}{}_{}{}^{}$ (110-keV) nuclei has been measured to high precision and is found to be $A_{\gamma }=-(6.8\mathrm{}\pm 1.8)\times {10}^{-5\mathrm{}}$. Absolute uncertainties have been largely removed. This new value for $A_{\gamma }$ together with recent nuclear structure calculations provides severe constraints on the weak meson-nucleon coupling constants, in particular on $f_{\pi }$ and $h_{\rho }^0$.