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Nucleon matrix elements of higher-twist operators from the instanton vacuum

J. Balla, M. V. Polyakov, C. Weiss

TL;DR

This work analyzes nonperturbative power corrections to deep-inelastic scattering using the instanton vacuum, modeling the nucleon as a chiral soliton within an effective theory. By fermionizing QCD gluonic operators and employing a 1/N_c expansion, the authors compute nucleon matrix elements for twist-3 and twist-4 operators, uncovering a hierarchy where twist-4 contributions are order-unity while twist-3 are suppressed by the instanton packing fraction. The leading higher-twist elements are f^{(2)}_{ m NS} and c^{(2)}_{ m S}, with d^{(2)}_{ m NS} significantly smaller, a pattern supported by comparisons to QCD sum rules and experimental data. The results demonstrate that instantons provide a clear, testable picture of nonperturbative gluonic effects in DIS and offer a framework for evaluating a wide range of higher-twist matrix elements.

Abstract

We compute the nucleon matrix elements of QCD operators of twist 3 and 4 in the instanton vacuum. We consider the operators determining 1/Q^2-power corrections to the Bjorken, Ellis-Jaffe and Gross-Llewellyn-Smith sum rules. The nucleon is described as a soliton of the effective chiral theory derived from instantons in the 1/N_c-expansion. QCD operators involving the gluon field are systematically represented by effective operators in the effective chiral theory. We find that twist-3 matrix elements are suppressed relative to twist-4 by a power of the packing fraction of the instanton medium. Numerical results for the spin-dependent (d^(2), f^(2)) and spin-independent twist-3 and 4 matrix elements are compared with results of other approaches and with experimental estimates of power corrections. The methods developed can be used to evaluate a wide range of matrix elements relevant to DIS.

Nucleon matrix elements of higher-twist operators from the instanton vacuum

TL;DR

This work analyzes nonperturbative power corrections to deep-inelastic scattering using the instanton vacuum, modeling the nucleon as a chiral soliton within an effective theory. By fermionizing QCD gluonic operators and employing a 1/N_c expansion, the authors compute nucleon matrix elements for twist-3 and twist-4 operators, uncovering a hierarchy where twist-4 contributions are order-unity while twist-3 are suppressed by the instanton packing fraction. The leading higher-twist elements are f^{(2)}_{ m NS} and c^{(2)}_{ m S}, with d^{(2)}_{ m NS} significantly smaller, a pattern supported by comparisons to QCD sum rules and experimental data. The results demonstrate that instantons provide a clear, testable picture of nonperturbative gluonic effects in DIS and offer a framework for evaluating a wide range of higher-twist matrix elements.

Abstract

We compute the nucleon matrix elements of QCD operators of twist 3 and 4 in the instanton vacuum. We consider the operators determining 1/Q^2-power corrections to the Bjorken, Ellis-Jaffe and Gross-Llewellyn-Smith sum rules. The nucleon is described as a soliton of the effective chiral theory derived from instantons in the 1/N_c-expansion. QCD operators involving the gluon field are systematically represented by effective operators in the effective chiral theory. We find that twist-3 matrix elements are suppressed relative to twist-4 by a power of the packing fraction of the instanton medium. Numerical results for the spin-dependent (d^(2), f^(2)) and spin-independent twist-3 and 4 matrix elements are compared with results of other approaches and with experimental estimates of power corrections. The methods developed can be used to evaluate a wide range of matrix elements relevant to DIS.

Paper Structure

This paper contains 15 sections, 142 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Power corrections to DIS
  3. From QCD to the effective chiral theory
  4. Effective chiral theory from the instanton vacuum
  5. Effective gluon operators
  6. Matrix elements of higher--twist operators in quark states
  7. The QCD equation of motion
  8. Non-leading vs. leading twist
  9. Nucleon matrix elements of higher--twist operators
  10. The nucleon in the effective chiral theory
  11. Nucleon matrix elements of effective gluon operators
  12. Higher--twist matrix elements in the naive quark model
  13. The leading higher--twist matrix elements in the large--$N_c$ limit
  14. Results and discussion
  15. Conclusions and outlook

Figures (2)

  • Figure 1: (a) The effective operator, eq.(\ref{['effop_novev']}), in the case of one quark flavor, $N_f = 1$. (b) Diagrams contributing to the matrix element of the effective operator in quark states.
  • Figure 2: Feynman diagrams contributing to the nucleon matrix element of the effective operator. (i) "Valence quark" contribution, eq.(\ref{['me_i']}) (ii) "Sea quark" contribution, eq.(\ref{['me_ii']}). (iii) Interaction contribution, eq.(\ref{['me_iii']}).