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

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 1 π which contradicts the upper limit from the 18 F experiments. We argue that because of the sensitivity of the anapole moment to H 0 ρ 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 n + p → d + γ and in the photo-disintegration of the deuteron by circularly polarized photons, combined with results from pp scattering, would determine H 1 π and several other weak meson-nucleon couplings in a model-independent way.