Higher twists in polarized DIS and the size of the constituent quark

The spontaneous breaking of chiral symmetry implies the presence of a short-distance scale in the QCD vacuum, which phenomenologically may be associated with the size of the constituent quark, ρ≈0.3 fm. We discuss the role of this scale in the matrix elements of the twist-4 and 3 quark-gluon operators determining the leading power (1/Q²)-corrections to the moments of the nucleon spin structure functions. We argue that the flavor-nonsinglet twist-4 matrix element, f₂^u-d, has a sizable negative value of the order ρ^-2, due to the presence of sea quarks with virtualities ~ρ^-2 in the proton wave function. The twist-3 matrix element, d₂, is not related to the scale ρ^-2. Our arguments support the results of previous calculations of the matrix elements in the instanton vacuum model. We show that this qualitative picture is in agreement with the phenomenological higher-twist correction extracted from an NLO QCD fit to the world data on g₁ᵖ and g₁ⁿ, which include recent data from the Jefferson Lab Hall A and COMPASS experiments. We comment on the implications of the short-distance scale ρ for quark-hadron duality and the x-dependence of higher-twist contributions.