Chirality selection rules and the U(1) problem

The conventional theory for the lack of U(1) chirality invariance in the presence of topological charge v fails to resolve the U(1) problem: it involves selection rules which forbid chirality changes ± 2 needed to generate the charged-pion decay constant F_π. Possible remedies are considered; if they work. F²_π is proportional to the average value of v² per unit Euclidean volume.