Twist – 4 quark – quark correlations in the pion from the instanton vacuum

The second moment of the isospin–2 structure function of the pion, F π+ 2 +F π− 2 −2F π 0 2 , is determined by the pion matrix element of a four–quark operator of twist 4. This isospin–2 operator cannot mix with lower–dimensional operators, and thus provides a clean probe of the quark–quark correlations in the pion. We calculate the matrix element in the effective chiral theory based on the instanton vacuum. We find a surprisingly small value, A I=2 ≈ 0.14 F 2 π = (35 MeV) 2 , in good agreement with recent lattice results. The order of magnitude of the result is explained by the diluteness of the instanton medium, ¯ ρ/ ¯ R ≈ 1/3.