Positivity constraints and flavor dependence of higher twists

The positivity bound for the transverse asymmetry A2 may be improved and applied for each quark flavor separately. We use it to test the consistency of twist-two approximation for the transverse spin-dependent (gT) and the longitudinal spin-averaged (FL) structure functions. While it is satisfied in the case of u quarks, it might be violated for d quarks in a region of moderate x because of its negative polarization. We attribute this inconsistency to a stronger twist-three contribution, whose existence found by the QCD sum rule method is a long-standing puzzle.