Improved positivity bound for Deep Inelastic Scattering on transversely polarized nucleon

The positivity bound for the transverse asymmetry $A_2$ may be improved by making use of the fact, that the state of a photon and a nucleon with total spin 3/2, does not participate to the interference. The bound is therefore useful in the case of a longitudinal asymmetry small (say, at low $x$) or negative (like in the neuteron case).