Consistency of parity-violating pion-nucleon couplings extracted from measurements in 18F and 133Cs

Abstract

The recent measurement of the nuclear anapole moment of ${}^{133}$Cs has been interpreted to yield a value of the weak pion-nucleon coupling ${H}_{\ensuremath{\pi}}^{1}$ which contradicts the upper limit from the ${}^{18}$F experiments. We argue that because of the sensitivity of the anapole moment to ${H}_{\ensuremath{\rho}}^{0}$ in the odd proton nucleus ${}^{133}$Cs, there is a combination of weak meson-nucleon couplings which satisfies both experiments and which is (barely) in agreement with theory. In addition, the anapole moment measurement in ${}^{205}$Tl gives a constraint which is inconsistent with the value from ${}^{133}$Cs, calling into question the theory of nuclear anapole moments. We argue that measurements of directional asymmetry in $\stackrel{\ensuremath{\rightarrow}}{n}+\stackrel{\ensuremath{\rightarrow}}{p}d+\ensuremath{\gamma}$ and in the photodisintegration of the deuteron by circularly polarized photons, combined with results from $\mathrm{pp}$ scattering, would determine ${H}_{\ensuremath{\pi}}^{1}$ and several other weak meson-nucleon couplings in a model-independent way.