Higher Twist Distribution Amplitudes of the Nucleon in QCD

TL;DR

This work develops a systematic framework for higher-twist nucleon distribution amplitudes in QCD, identifying eight independent three-quark DAs that describe the valence state at small transverse separation. Using a conformal expansion, the authors organize these DAs by twist (3, 4, 5, 6) and provide explicit forms up to next-to-leading conformal spin, together with isospin and equation-of-motion constraints that reduce the parameter set to a manageable number. They express the higher-twist amplitudes in terms of a small set of nonperturbative parameters, most of which are estimated via QCD sum rules, yielding concrete normalizations (e.g., $f_N$, $\lambda_1$, $\lambda_2$) and a handful of correction parameters (e.g., $V_1^d$, $A_1^u$, $f_1^d$, $f_2^d$, $f_1^u$). The results indicate that higher-twist three-quark operators contribute sizable, genuine nonperturbative content, distinct from higher Fock-state gluon contributions, and provide the necessary input for hard-exclusive calculations (e.g., nucleon form factors and spin asymmetries) via light-cone sum rules at moderate $Q^2$. Overall, the paper furnishes a rigorous, quantifiable foundation for incorporating higher-twist nucleon effects into QCD predictions of exclusive processes.

Abstract

We present the first systematic study of higher-twist light-cone distribution amplitudes of the nucleon in QCD. We find that the valence three-quark state is described at small transverse separations by eight independent distribution amplitudes. One of them is leading twist-3, three distributions are twist-4 and twist-5, respectively, and one is twist-6. A complete set of distribution amplitudes is constructed, which satisfies equations of motion and constraints that follow from conformal expansion. Nonperturbative input parameters are estimated from QCD sum rules.

Figures (2)

• Figure 1: Twist-3 distribution amplitude $\Phi_3(x_i)$
• Figure 2: Twist-4 distribution amplitudes $\Phi_4(x_i)$ in the first line to the left, $\Psi_4(x_i)$ in the first line to the right, and $\Xi(x_i)$ in the second line