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NLO corrections for the dipole factorization of DIS structure functions at low x

Guillaume Beuf

TL;DR

This work develops the NLO generalization of the dipole factorization for DIS structure functions at low $x$ using light-front perturbation theory in mixed space. It derives the quark-antiquark-gluon components of virtual-photon light-front wavefunctions and constructs NLO photon impact factors for longitudinal and transverse polarization, enabling a factorized expression for the photon-target cross sections $\sigma^{\gamma}_{T,L}$ with explicit LO and NLO contributions. A systematic subtraction of high-energy leading logs via a $k^+$ (or $z_f$) cutoff and the associated B-JIMWLK evolution yields a practical, phenomenology-ready framework that marries NLO accuracy with gluon-saturation dynamics. The results illuminate recoil and formation-time kinematics in mixed space and lay the groundwork for future Fourier transforms to momentum space and applications to mass effects and broader DIS observables. Overall, the paper advances the theoretical toolkit for quantitative, small-$x$ QCD calculations applicable to DIS and related processes within the CGC paradigm.

Abstract

The NLO generalization of the dipole factorization formula for the structure functions F_2 and F_L at low x is calculated using light front perturbation theory. That result gives some interesting insight into the kinematics of initial state parton showers in mixed space.

NLO corrections for the dipole factorization of DIS structure functions at low x

TL;DR

This work develops the NLO generalization of the dipole factorization for DIS structure functions at low using light-front perturbation theory in mixed space. It derives the quark-antiquark-gluon components of virtual-photon light-front wavefunctions and constructs NLO photon impact factors for longitudinal and transverse polarization, enabling a factorized expression for the photon-target cross sections with explicit LO and NLO contributions. A systematic subtraction of high-energy leading logs via a (or ) cutoff and the associated B-JIMWLK evolution yields a practical, phenomenology-ready framework that marries NLO accuracy with gluon-saturation dynamics. The results illuminate recoil and formation-time kinematics in mixed space and lay the groundwork for future Fourier transforms to momentum space and applications to mass effects and broader DIS observables. Overall, the paper advances the theoretical toolkit for quantitative, small- QCD calculations applicable to DIS and related processes within the CGC paradigm.

Abstract

The NLO generalization of the dipole factorization formula for the structure functions F_2 and F_L at low x is calculated using light front perturbation theory. That result gives some interesting insight into the kinematics of initial state parton showers in mixed space.

Paper Structure

This paper contains 18 sections, 79 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Virtual photon wave-functions
  3. Quark-antiquark components at LO
  4. Quark-antiquark-gluon components in the NLO wave-functions
  5. Some comments about kinematical effects in the results
  6. Recoil effects
  7. Formation time of multi-parton fluctuations
  8. Virtual corrections
  9. Photon cross sections and impact factors at NLO
  10. From wave-functions to cross sections
  11. Subtracting high energy leading logs
  12. Conclusion
  13. Light-front perturbation theory for DIS at low $x$
  14. Eikonal scattering and total cross section of a dilute projectile on a Color Glass Condensate
  15. Light-front wave-function of the projectile in perturbation theory
  16. ...and 3 more sections

Figures (4)

  • Figure 1: LO diagram for the transverse photon wave function.
  • Figure 2: Diagrams for the quark-antiquark-gluon component the transverse photon wave function at NLO. Each diagram is ordered along $x^+$, from $x^+\rightarrow -\infty$ on the left to $x^+=0$ on the right.
  • Figure 3: Geometric picture for the recoil effects found for the diagram \ref{['Fig:DiagNLOT']}(a) in mixed space.
  • Figure 4: The two possible topologies (A) and (B) for diagrams without instantaneous interactions leading to a $4$-partons Fock state.