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

The recent measurement of the nuclear anapole moment of 133Cs has been interpreted to yield a value of the weak pion-nucleon coupling H_pi^1 which contradicts the upper limit from the 18F experiments. We argue that because of the sensitivity of the anapole moment to H_rho^0 in the odd proton nucleus 133Cs, 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 205Tl gives a constraint which is inconsistent with the value from 133Cs, calling into question the theory of nuclear anapole moments. We argue that measurements of directional asymmetry in n+p-->d+gamma and in the photo-disintegration of the deuteron by circularly polarized photons, combined with results from pp scattering, would determine H_pi^1 and several other weak meson-nucleon couplings in a model-independent way.