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Impact factor for high-energy two and three jets diffractive production

R. Boussarie, A. V. Grabovsky, L. Szymanowski, S. Wallon

TL;DR

This work furnishes the LO and general $\gamma^* \to q\bar{q}g$ impact factors within Balitsky's high-energy (shockwave) OPE framework, deriving them with no soft/collinear approximations for the emitted gluon. By expressing results in coordinate space via Wilson lines and in momentum space through Fourier transforms, the authors provide tools that naturally incorporate saturation effects and multi-gluon exchanges relevant to diffractive DIS and multi-jet production. They establish a dipole-based linearized regime and connect to established small-x evolution equations (BK/BFKL), enabling quantitative diffractive cross-section studies and saturation phenomenology. The findings pave the way for detailed comparisons with HERA data and future e-p/e-A colliders, and they suggest routes to include higher-twist effects and massive-quark extensions in subsequent work.

Abstract

We present the calculation of the impact factor for the gamma(*) -> q qb g transition within Balitsky's high energy operator expansion. We also rederive the impact factor for the gamma(*) -> q qb transition within the same framework. These results provide the necessary building blocks for further phenomenological studies of inclusive diffractive deep inelastic scattering as well as for two and three jets diffractive production which go beyond approximations discussed in the litterature.

Impact factor for high-energy two and three jets diffractive production

TL;DR

This work furnishes the LO and general impact factors within Balitsky's high-energy (shockwave) OPE framework, deriving them with no soft/collinear approximations for the emitted gluon. By expressing results in coordinate space via Wilson lines and in momentum space through Fourier transforms, the authors provide tools that naturally incorporate saturation effects and multi-gluon exchanges relevant to diffractive DIS and multi-jet production. They establish a dipole-based linearized regime and connect to established small-x evolution equations (BK/BFKL), enabling quantitative diffractive cross-section studies and saturation phenomenology. The findings pave the way for detailed comparisons with HERA data and future e-p/e-A colliders, and they suggest routes to include higher-twist effects and massive-quark extensions in subsequent work.

Abstract

We present the calculation of the impact factor for the gamma(*) -> q qb g transition within Balitsky's high energy operator expansion. We also rederive the impact factor for the gamma(*) -> q qb transition within the same framework. These results provide the necessary building blocks for further phenomenological studies of inclusive diffractive deep inelastic scattering as well as for two and three jets diffractive production which go beyond approximations discussed in the litterature.

Paper Structure

This paper contains 9 sections, 122 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Definitions and necessary intermediate results
  3. LO impact factor for $\gamma\rightarrow q\bar{q}$ transition
  4. General expression for $\gamma\rightarrow q\bar{q}g$ impact factor
  5. Diagrams with the gluon crossing the shockwave
  6. Diagrams without the gluon crossing the shockwave
  7. Impact factor for interaction with color dipole
  8. Impact factor in the momentum space and in the linear approximation
  9. Conclusions

Figures (2)

  • Figure 1: LO $\gamma\rightarrow q\bar{q}$ impact factor
  • Figure 2: Impact factor for 3 jet production. The grey ellipse stands for the shockwave at $z^{+}=0$. The lines crossing the ellipse are calculated in the shock wave background (\ref{['qpropinSW']}), (\ref{['uinSW']}--\ref{['einSW']}).