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Next-to-Leading Order corrections to the Next-to-Eikonal DIS structure functions

Tolga Altinoluk, Guillaume Beuf, Jules Favrel, Michael Fucilla

TL;DR

This work advances CGC-based DIS by deriving the NLO corrections to NEik (next-to-eikonal) contributions, including both quark and gluon target backgrounds. The authors systematically construct NEik building blocks (decorated Wilson lines and various propagators) and compute the NLO corrections to the NEik inclusive DIS cross section, separating and subtracting rapidity and UV divergences, and expressing results in terms of nonperturbative quark and gluon distributions. They find that NEik corrections to the longitudinal structure function are finite, while the transverse piece exhibits rapidity and UV divergences that are partially isolated and attributed to small-$x$ evolution; gluon-background contributions follow a similar pattern with appropriate replacements of distributions. Overall, the paper establishes the first combined NLO+NEik framework for DIS in CGC, paving the way for high-precision predictions at future facilities like the EIC and guiding extensions to SIDIS and double-log evolution analyses.

Abstract

We compute next-to-leading order (NLO) corrections to next-to-eikonal (NEik) quark background contributions to DIS structure functions. Among NEik corrections, $t$-channel quark exchanges provide the lowest order contributions in $α_s$, and can be represented as insertions of the quark background field of the target. At NLO, we compute NEik corrections induced by both quark and gluon background fields, and suppressed by an explicit factor of $α_s$. We show that the NLO corrections to the NEik longitudinal structure function are finite, while those to the NEik transverse structure function exhibit rapidity and UV divergences. These divergences are analyzed, and the finite contributions are extracted.

Next-to-Leading Order corrections to the Next-to-Eikonal DIS structure functions

TL;DR

This work advances CGC-based DIS by deriving the NLO corrections to NEik (next-to-eikonal) contributions, including both quark and gluon target backgrounds. The authors systematically construct NEik building blocks (decorated Wilson lines and various propagators) and compute the NLO corrections to the NEik inclusive DIS cross section, separating and subtracting rapidity and UV divergences, and expressing results in terms of nonperturbative quark and gluon distributions. They find that NEik corrections to the longitudinal structure function are finite, while the transverse piece exhibits rapidity and UV divergences that are partially isolated and attributed to small- evolution; gluon-background contributions follow a similar pattern with appropriate replacements of distributions. Overall, the paper establishes the first combined NLO+NEik framework for DIS in CGC, paving the way for high-precision predictions at future facilities like the EIC and guiding extensions to SIDIS and double-log evolution analyses.

Abstract

We compute next-to-leading order (NLO) corrections to next-to-eikonal (NEik) quark background contributions to DIS structure functions. Among NEik corrections, -channel quark exchanges provide the lowest order contributions in , and can be represented as insertions of the quark background field of the target. At NLO, we compute NEik corrections induced by both quark and gluon background fields, and suppressed by an explicit factor of . We show that the NLO corrections to the NEik longitudinal structure function are finite, while those to the NEik transverse structure function exhibit rapidity and UV divergences. These divergences are analyzed, and the finite contributions are extracted.

Paper Structure

This paper contains 20 sections, 184 equations, 4 figures.

Table of Contents

  1. Introduction
  2. CGC beyond eikonal accuracy and various parton propagators
  3. NEik DIS cross-section at the leading order
  4. NEik DIS cross-section at the next-to-leading order: Fermion background field contribution
  5. Quark background field contribution
  6. Analysis of the divergences and extraction of the finite contributions
  7. Isolating divergent and finite contributions: massless case
  8. Isolating divergent and finite contributions: massive case
  9. Antiquark background field contribution
  10. Total fermionic contribution
  11. NEik DIS cross-section at the next-to-leading order: Gluon background field contribution
  12. Contributions from the gluon background field within the static approximation
  13. Contributions from the gluon background field beyond the static approximation
  14. Total gluon contribution
  15. Summary and outlook
  16. ...and 5 more sections

Figures (4)

  • Figure 1: (a) Leading order contribution to DIS at the NEik accuracy from the quark background of the target. (b) Leading order contribution to DIS at the NEik accuracy from the antiquark background of the target.
  • Figure 2: (a) Next-to-leading order contribution to DIS at the NEik accuracy from the quark background of the target. (b) Next-to-leading order contribution to DIS at the NEik accuracy from the antiquark background of the target.
  • Figure 3: Next-to-leading order contribution to DIS at the NEik accuracy from the gluon background of the target.
  • Figure 4: All the NEik contributions from the gluon background of the target, considering the $x^+ > y^+$ configuration.