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Dijet production in DIS off a large nucleus at next-to-eikonal accuracy in a Gaussian model within the CGC framework

Pedro Agostini, Tolga Altinoluk, Néstor Armesto, Guillaume Beuf, Florian Cougoulic, Swaleha Mulani

TL;DR

This work addresses next-to-eikonal corrections in DIS dijet production within the CGC framework by constructing a Gaussian model to compute decorated Wilson-line operators. It develops a general method for evaluating NEik operators with one decorated Wilson line and applies it to explicit NEik dipole, quadrupole, and 3-point structures, providing results that are ready for numerical implementation. A key finding is that, in the Gaussian model, NEik corrections to DIS dijet production arise only from NEik type-1 operators and from three-point correlators, while NEik type-2 contributions cancel and type-3 operators vanish. The framework is general and extensible to other processes and to including quark-exchange NEik corrections in the future, paving the way for quantitative NEik phenomenology at small x in DIS and high-energy pA collisions, with potential applications to the EIC.

Abstract

We develop a Gaussian model to evaluate the decorated dipole and quadrupole operators that arise beyond the eikonal approximation in the Color Glass Condensate framework. While the method is general and applicable to arbitrary beyond-eikonal Wilson line structures, we employ it for dijet production in deep inelastic scattering at next-to-eikonal accuracy. After validating the model at the eikonal level, we compute all next-to-eikonal operator structures entering the dijet cross section. We show that some of them do not contribute to this observable, while others vanish identically. Therefore, in the Gaussian model next-to-eikonal corrections to dijet production in deep inelastic scattering originate solely from a given type of operators and from next-to-eikonal three-point correlators. The resulting expressions are provided in a form suitable for numerical implementation.

Dijet production in DIS off a large nucleus at next-to-eikonal accuracy in a Gaussian model within the CGC framework

TL;DR

This work addresses next-to-eikonal corrections in DIS dijet production within the CGC framework by constructing a Gaussian model to compute decorated Wilson-line operators. It develops a general method for evaluating NEik operators with one decorated Wilson line and applies it to explicit NEik dipole, quadrupole, and 3-point structures, providing results that are ready for numerical implementation. A key finding is that, in the Gaussian model, NEik corrections to DIS dijet production arise only from NEik type-1 operators and from three-point correlators, while NEik type-2 contributions cancel and type-3 operators vanish. The framework is general and extensible to other processes and to including quark-exchange NEik corrections in the future, paving the way for quantitative NEik phenomenology at small x in DIS and high-energy pA collisions, with potential applications to the EIC.

Abstract

We develop a Gaussian model to evaluate the decorated dipole and quadrupole operators that arise beyond the eikonal approximation in the Color Glass Condensate framework. While the method is general and applicable to arbitrary beyond-eikonal Wilson line structures, we employ it for dijet production in deep inelastic scattering at next-to-eikonal accuracy. After validating the model at the eikonal level, we compute all next-to-eikonal operator structures entering the dijet cross section. We show that some of them do not contribute to this observable, while others vanish identically. Therefore, in the Gaussian model next-to-eikonal corrections to dijet production in deep inelastic scattering originate solely from a given type of operators and from next-to-eikonal three-point correlators. The resulting expressions are provided in a form suitable for numerical implementation.

Paper Structure

This paper contains 30 sections, 200 equations, 11 figures.

Table of Contents

  1. Introduction
  2. DIS dijet production at next-to-eikonal accuracy
  3. Wilson line operators at eikonal order within a Gaussian model
  4. Monopole operator
  5. Dipole operator
  6. Quadrupole operator
  7. Wilson line operators at next-to-eikonal order within a Gaussian model
  8. Next-to-eikonal dipole involving the $\langle A^jA^-\rangle$ interaction
  9. Generalization to any next-to-eikonal operators
  10. Next-to-eikonal operators of type 1
  11. NEik type-1 dipole operator.
  12. NEik type-1 quadrupole operator.
  13. Next-to-eikonal operators of type 2
  14. NEik type-2 dipole operator.
  15. NEik type-2 quadrupole operator.
  16. ...and 15 more sections

Figures (11)

  • Figure 1: Diagrammatic representation of $T_a$ contracted with $A^{-}_{a}(z^+, {\mathbf z})$.
  • Figure 2: Diagrammatic representation of 2-point correlator.
  • Figure 3: A tadpole contribution that is resummed into the expectation value of the operator $\langle {\mathcal{U}}_{[x^+,y^+]} \rangle$.
  • Figure 4: Diagram showing the interaction between quark or antiquark lines in the dipole.
  • Figure 5: Diagrammatic representation of the Fierz identity.
  • ...and 6 more figures