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Parton model contributions as next-to-eikonal corrections to the dipole factorization of DIS and SIDIS at low $x_{Bj}$

Tolga Altinoluk, Guillaume Beuf, Swaleha Mulani

TL;DR

This paper addresses NEik power corrections to inclusive DIS and SIDIS at small $x$ arising from $t$-channel quark exchanges (the quark background field) in the CGC framework. It develops SIDIS and DIS calculations, showing that NEik corrections for transverse photons link to the unpolarized quark PDF/TMD with explicit $1/W^2$ suppression, while longitudinal-photon NEik vanish at leading order, and that DIS structure functions reproduce the standard parton-model forms at this order. The results reproduce the low-$x$ expansion of parton-model expressions and identify quark-background NEik terms as the first beyond-dipole corrections at low $x$, setting the stage for matching to collinear factorization in future work. Overall, the study clarifies the role and size of quark-background NEik contributions relative to dipole-factorization NEik terms and provides a route toward a more complete high-energy QCD description beyond the eikonal limit.

Abstract

We compute the next-to-eikonal (NEik) power corrections to inclusive deep inelastic scattering (DIS) and semi-inclusive deep inelastic scattering (SIDIS) at low $x$ beyond dipole factorization, which represent the eikonal result. The analysis is restricted to contributions arising from t-channel quark exchanges, thereby probing the quark background field of the target. For a transversely polarized virtual photon, the NEik corrections to inclusive DIS are expressed in terms of quark and antiquark collinear parton distribution functions (PDFs), while the corresponding corrections to SIDIS are formulated in terms of the unpolarized quark transverse-momentum-dependent distribution (TMD). In contrast, for a longitudinally polarized photon, the NEik corrections to both inclusive DIS and SIDIS vanish at lowest order in $α_{s}$.

Parton model contributions as next-to-eikonal corrections to the dipole factorization of DIS and SIDIS at low $x_{Bj}$

TL;DR

This paper addresses NEik power corrections to inclusive DIS and SIDIS at small arising from -channel quark exchanges (the quark background field) in the CGC framework. It develops SIDIS and DIS calculations, showing that NEik corrections for transverse photons link to the unpolarized quark PDF/TMD with explicit suppression, while longitudinal-photon NEik vanish at leading order, and that DIS structure functions reproduce the standard parton-model forms at this order. The results reproduce the low- expansion of parton-model expressions and identify quark-background NEik terms as the first beyond-dipole corrections at low , setting the stage for matching to collinear factorization in future work. Overall, the study clarifies the role and size of quark-background NEik contributions relative to dipole-factorization NEik terms and provides a route toward a more complete high-energy QCD description beyond the eikonal limit.

Abstract

We compute the next-to-eikonal (NEik) power corrections to inclusive deep inelastic scattering (DIS) and semi-inclusive deep inelastic scattering (SIDIS) at low beyond dipole factorization, which represent the eikonal result. The analysis is restricted to contributions arising from t-channel quark exchanges, thereby probing the quark background field of the target. For a transversely polarized virtual photon, the NEik corrections to inclusive DIS are expressed in terms of quark and antiquark collinear parton distribution functions (PDFs), while the corresponding corrections to SIDIS are formulated in terms of the unpolarized quark transverse-momentum-dependent distribution (TMD). In contrast, for a longitudinally polarized photon, the NEik corrections to both inclusive DIS and SIDIS vanish at lowest order in .
Paper Structure (6 sections, 74 equations, 3 figures)

This paper contains 6 sections, 74 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Quark background field contribution to SIDIS
  3. Quark background field contribution to DIS structure functions
  4. Discussion: dipole versus quark background field contributions to DIS and SIDIS
  5. Summary
  6. Calculation of the antiquark contribution to DIS structure functions.

Figures (3)

  • Figure 1: Semi-inclusive deep inelastic scattering (SIDIS) diagram: quark production from quark background field
  • Figure 2: Semi-inclusive deep inelastic scattering (SIDIS) diagram: antiquark production from quark background field
  • Figure 3: Quark background field contributions to the photon-target elastic scattering amplitude, and to inclusive DIS via the optical theorem