Nucleon matrix elements of twist – 3 and 4 operators from the instanton vacuum †

The spin–dependent twist–3 and 4 nucleon matrix elements d (2) and f (2) describing power corrections to the Bjorken and Ellis–Jaffe sum rules are computed in the instanton vacuum. A systematic expansion in the small packing fraction of the instanton medium, ¯ ρ/ ¯ R ≪ 1, is performed. We find that the twist–3 matrix element d (2) is suppressed [of order (¯ ρ/ ¯ R) 4 ], while the twist–4 matrix element f (2) is of order unity. Numerically, d (2) ≪ f (2). The small value of d (2) ∼ 10 −3 obtained from instantons is consistent with the recent E143 measurements of the structure function g 2 , where d (2) enters at the same level as the twist–2 contribution.