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Next-to-Leading-Order QCD Predictions for the $Σ$ Dirac Form Factors

Bo-Xuan Shi, Hui-Xin Yu, Xue-Chen Zhao

TL;DR

This paper advances the perturbative QCD description of Sigma hyperon electromagnetic structure by performing a complete next-to-leading-order (NLO) analysis of the leading-power hard-gluon-exchange contribution to the Dirac form factor $F_1(Q^2)$ within the hard-collinear factorization framework. The authors analytically extract the short-distance coefficient $H_Σ$ from seven-point partonic amplitudes at ${\cal O}(\alpha_s^3)$, implementing a rigorous treatment of UV renormalization and IR subtraction and addressing the scheme dependence introduced by evanescent operators. They then combine these perturbative hard kernels with nonperturbative twist-3 Sigma distribution amplitudes obtained from lattice QCD, employing a conformal expansion to organize the input and providing numerical predictions for $F_1(Q^2)$ with NLO and NLL resummation. The numerical analysis, using LAT25 lattice inputs converted to the chosen evanescent scheme, shows sizable NLO corrections in the $Q^2$ range $20$–$50\,\mathrm{GeV}^2$, which are reduced by 20–30% when NLL resummation is included, yielding more stable predictions. This work delivers state-of-the-art theoretical predictions for Sigma form factors and lays the groundwork for future two-loop evolution and timelike analyses.

Abstract

In this work, we compute the next-to-leading-order QCD corrections to the Dirac electromagnetic form factors of the $Σ$ hyperons within the hard-collinear factorization framework at leading power. The corresponding short-distance coefficient functions are extracted from the relevant seven-point partonic correlation functions. We find that the one-loop radiative corrections to the leading-twist hard-scattering contributions are numerically significant over a broad range of momentum transfer. Combining the perturbatively calculated hard kernels with nonperturbative $Σ$ distribution amplitudes determined from lattice QCD, we present state-of-the-art theoretical predictions for the $Σ$ hyperon electromagnetic form factors.

Next-to-Leading-Order QCD Predictions for the $Σ$ Dirac Form Factors

TL;DR

This paper advances the perturbative QCD description of Sigma hyperon electromagnetic structure by performing a complete next-to-leading-order (NLO) analysis of the leading-power hard-gluon-exchange contribution to the Dirac form factor within the hard-collinear factorization framework. The authors analytically extract the short-distance coefficient from seven-point partonic amplitudes at , implementing a rigorous treatment of UV renormalization and IR subtraction and addressing the scheme dependence introduced by evanescent operators. They then combine these perturbative hard kernels with nonperturbative twist-3 Sigma distribution amplitudes obtained from lattice QCD, employing a conformal expansion to organize the input and providing numerical predictions for with NLO and NLL resummation. The numerical analysis, using LAT25 lattice inputs converted to the chosen evanescent scheme, shows sizable NLO corrections in the range –, which are reduced by 20–30% when NLL resummation is included, yielding more stable predictions. This work delivers state-of-the-art theoretical predictions for Sigma form factors and lays the groundwork for future two-loop evolution and timelike analyses.

Abstract

In this work, we compute the next-to-leading-order QCD corrections to the Dirac electromagnetic form factors of the hyperons within the hard-collinear factorization framework at leading power. The corresponding short-distance coefficient functions are extracted from the relevant seven-point partonic correlation functions. We find that the one-loop radiative corrections to the leading-twist hard-scattering contributions are numerically significant over a broad range of momentum transfer. Combining the perturbatively calculated hard kernels with nonperturbative distribution amplitudes determined from lattice QCD, we present state-of-the-art theoretical predictions for the hyperon electromagnetic form factors.
Paper Structure (8 sections, 25 equations, 2 figures, 1 table)

This paper contains 8 sections, 25 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Electromagnetic Hyperon Form Factors
  3. Factorization Formalism
  4. Extraction of short-distance coefficients
  5. Scheme dependence of short-distance coefficients
  6. Next-to-Leading-Order QCD Computations
  7. Numerical Analysis
  8. Conclusions

Figures (2)

  • Figure 1: Independent tree-level diagrams contributing to the QCD amplitude $\Pi_\mu$.
  • Figure 2: Predictions for the leading power hard-gluon-exchange contributions to the Dirac form factors of the $\Sigma^+$ (upper panel) and $\Sigma^-$ (lower panel) at LL, NLO, LL$^\prime$, and NLL accuracy, based on the LAT25 hyperon distribution amplitude. The colored bands represent perturbative uncertainties from scale variations $\nu^2 = \mu_F^2 = \langle x \rangle Q^2$ with $1/6 \le \langle x \rangle \le 1/2$.