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Leading-order analysis of the twist-3 space- and time-like cut vertices in QCD

A. V. Belitsky

TL;DR

This work develops a comprehensive leading-order framework for the scale evolution of twist-3 space-like and time-like cut vertices in QCD, emphasizing the construction and renormalization of three-parton correlators and their mixing. By employing light-cone gauge techniques and both Abelian and non-Abelian analyses, it derives evolution equations for twist-3 distributions (g2, e, hL) and their fragmentation counterparts, including the relation between position- and momentum-space kernels and the large-Nc simplifications that yield tractable solutions. A key finding is the breaking of Gribov-Lipatov reciprocity for twist-3 quantities, contrasted with the more familiar twist-2 case, alongside practical diagonalization approaches in the large-Nc limit. The results provide a robust theoretical foundation for interpreting higher-twist observables in polarized DIS and fragmentation processes and guide future phenomenological explorations.

Abstract

We review the recent theoretical progress in the construction and solution of the evolution equations which govern the scale dependence for the twist-three structure and fragmentation functions of the nucleon.

Leading-order analysis of the twist-3 space- and time-like cut vertices in QCD

TL;DR

This work develops a comprehensive leading-order framework for the scale evolution of twist-3 space-like and time-like cut vertices in QCD, emphasizing the construction and renormalization of three-parton correlators and their mixing. By employing light-cone gauge techniques and both Abelian and non-Abelian analyses, it derives evolution equations for twist-3 distributions (g2, e, hL) and their fragmentation counterparts, including the relation between position- and momentum-space kernels and the large-Nc simplifications that yield tractable solutions. A key finding is the breaking of Gribov-Lipatov reciprocity for twist-3 quantities, contrasted with the more familiar twist-2 case, alongside practical diagonalization approaches in the large-Nc limit. The results provide a robust theoretical foundation for interpreting higher-twist observables in polarized DIS and fragmentation processes and guide future phenomenological explorations.

Abstract

We review the recent theoretical progress in the construction and solution of the evolution equations which govern the scale dependence for the twist-three structure and fragmentation functions of the nucleon.

Paper Structure

This paper contains 30 sections, 163 equations, 13 figures.

Table of Contents

  1. Introduction.
  2. Space-like cut vertices.
  3. Correlation functions of nonleading twist.
  4. $g_2(x)$.
  5. $e(x)$.
  6. $h_L(x)$.
  7. Construction of the evolution equations.
  8. Renormalization in the light-cone gauge.
  9. Difference between the PV and ML prescriptions.
  10. Evolution equations in the abelian gauge theory.
  11. QCD evolution of the twist-3 distributions.
  12. Evolution of the chiral-even distributions.
  13. Evolution of the chiral-odd distributions.
  14. Local anomalous dimensions.
  15. Relating the evolution kernels in the light-cone position and light-cone fraction re-pre-sen-ta-tions.
  16. ...and 15 more sections

Figures (13)

  • Figure 1: Ladder diagram for deep inelastic scattering.
  • Figure 2: One-loop radiative corrections to the two-particle correlators in the abelian gauge theory. The fermion propagator crossed with a bar on diagram (c) means the contraction of the corresponding line into the point.
  • Figure 3: The one-loop renormalization of the three-parton correlation functions. Self-energy insertions into external legs are implied.
  • Figure 4: The spectrum of the eigenvalues $\lambda^n_l$ for the evolution kernel $P^n_{\cal ZZ}$ defined in (\ref{['DefPZZ']}).
  • Figure 5: Graphical representation of the three-parton recombination functions.
  • ...and 8 more figures