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

TL;DR

This paper calculates the nucleon matrix elements for twist-3 and 4 operators using the instanton vacuum model, revealing a suppressed twist-3 and a significant twist-4 contribution, aligning with experimental data.

Contribution

It provides a systematic calculation of twist-3 and 4 nucleon matrix elements in the instanton vacuum, highlighting their relative magnitudes and consistency with recent measurements.

Findings

Twist-3 matrix element d^(2) is highly suppressed (~(rho/R)^4).

Twist-4 matrix element f^(2) is of order unity.

Numerical value of d^(2) aligns with experimental g_2 data.

Abstract

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, rho / R << 1, is performed. We find that the twist-3 matrix element d^(2) is suppressed [of order (rho / 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) \sim 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.