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Gross-Llewellyn Smith sum rule with analytic coupling

I. R. Gabdrakhmanov, N. A Gramotkov, A. V. Kotikov, O. V. Teryaev, D. A. Volkova, I. A. Zemlyakov

TL;DR

The paper tackles the GLS sum rule in QCD at low $Q^2$ by comparing experimental data, lattice QCD, and perturbative QCD predictions under both conventional and analytic formulations. It employs the operator-product expansion with a leading twist $3\,(1-D(Q^2))$ and higher-twist terms, including a massive twist-four representation, while incorporating heavy-quark corrections and, in the analytic approach, recasting the coupling via analytic derivatives $\tilde{A}^{(k)}_{\nu}$. The main finding is that conventional PT fails to describe the data, especially at higher orders, whereas analytic QCD with the massive twist-four term provides good agreement with both experiment and lattice QCD, and clarifies the relation to the Bjorken sum rule. The work demonstrates the value of analytic couplings for probing the nonperturbative regime and informs the linking of GLS with BSR at moderate-to-high $Q^2$ for potential determinations of the strong coupling constant $\alpha_s$.

Abstract

We investigate the Gross-Llewellyn Smith sum rule within the framework of analytic QCD. A comparison is performed between experimental data, lattice calculations, and perturbative QCD based on conventional and analytic versions of perturbation theory with different parametrizations for the twist-four contribution. We show that conventional perturbation theory fails to reproduce the data, while the analytic version demonstrates good agreement with experiment and lattice calculations. We also discuss the relation between the Gross-Llewellyn Smith sum rule and the Bjorken sum rule.

Gross-Llewellyn Smith sum rule with analytic coupling

TL;DR

The paper tackles the GLS sum rule in QCD at low by comparing experimental data, lattice QCD, and perturbative QCD predictions under both conventional and analytic formulations. It employs the operator-product expansion with a leading twist and higher-twist terms, including a massive twist-four representation, while incorporating heavy-quark corrections and, in the analytic approach, recasting the coupling via analytic derivatives . The main finding is that conventional PT fails to describe the data, especially at higher orders, whereas analytic QCD with the massive twist-four term provides good agreement with both experiment and lattice QCD, and clarifies the relation to the Bjorken sum rule. The work demonstrates the value of analytic couplings for probing the nonperturbative regime and informs the linking of GLS with BSR at moderate-to-high for potential determinations of the strong coupling constant .

Abstract

We investigate the Gross-Llewellyn Smith sum rule within the framework of analytic QCD. A comparison is performed between experimental data, lattice calculations, and perturbative QCD based on conventional and analytic versions of perturbation theory with different parametrizations for the twist-four contribution. We show that conventional perturbation theory fails to reproduce the data, while the analytic version demonstrates good agreement with experiment and lattice calculations. We also discuss the relation between the Gross-Llewellyn Smith sum rule and the Bjorken sum rule.
Paper Structure (5 sections, 30 equations, 7 figures, 3 tables)

This paper contains 5 sections, 30 equations, 7 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Gross-Llewellyn Smith sum rule
  3. Bjorken sum rule
  4. Results
  5. Conclusions

Figures (7)

  • Figure 1: The results (\ref{['Gpn.OPEab']}) with $\mu_{2n}=0$ for $n\geq3$ in the first three orders of PT.
  • Figure 2: As in Fig. \ref{['fig:PT1']} but for the massive twist-four case (\ref{['Gpn.mOPEa']}).
  • Figure 3: As in Fig. \ref{['fig:PT1']} but for the APT result (\ref{['Gpn.MAab']})
  • Figure 4: As in Fig. \ref{['fig:PT2']} but for the APT result (\ref{['Gpn.MAa']})
  • Figure 5: As in Fig. \ref{['fig:PT2']} but with lattice data.
  • ...and 2 more figures