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$γ^*γ^*$ total cross-section in the dipole picture of BFKL dynamics

M. Boonekamp, A. De Roeck, C. Royon, S. Wallon

TL;DR

The paper analyzes high-energy γ*γ* scattering using the color-dipole picture to derive LO BFKL cross-sections and compares them with 2-gluon exchange and DLL–DGLAP backgrounds. It demonstrates that while DLL–DGLAP is subdominant in the studied phase space, the 2-gluon background can be sizeable, and that LO BFKL signals are strongly affected by large NLO corrections. The authors implement a phenomenological treatment of NLO effects via rapidity-scale variation and an effective coupling, showing that the BFKL/2-gluon ratio can be reduced to around 2–4, though the Y-dependence may still reveal BFKL dynamics under realistic collider conditions. The work highlights the observational challenges of isolating BFKL effects in γ*γ* scattering and emphasizes the need to account for substantial higher-order corrections in phenomenological analyses. Overall, it maps the prospects for testing BFKL dynamics at LEP and future linear colliders and outlines strategies to disentangle signal from background.

Abstract

The total $γ^*γ^*$ cross-section is derived in the Leading Order QCD dipole picture of BFKL dynamics, and compared with the one from 2-gluon exchange. The Double Leading Logarithm approximation of the DGLAP cross-section is found to be small in the phase space studied. Cross sections are calculated for realistic data samples at the $e^+e^-$ collider LEP and a future high energy linear collider. Next to Leading order corrections to the BFKL evolution have been determined phenomenologically, and are found to give very large corrections to the BFKL cross-section, leading to a reduced sensitivity for observing BFKL.

$γ^*γ^*$ total cross-section in the dipole picture of BFKL dynamics

TL;DR

The paper analyzes high-energy γ*γ* scattering using the color-dipole picture to derive LO BFKL cross-sections and compares them with 2-gluon exchange and DLL–DGLAP backgrounds. It demonstrates that while DLL–DGLAP is subdominant in the studied phase space, the 2-gluon background can be sizeable, and that LO BFKL signals are strongly affected by large NLO corrections. The authors implement a phenomenological treatment of NLO effects via rapidity-scale variation and an effective coupling, showing that the BFKL/2-gluon ratio can be reduced to around 2–4, though the Y-dependence may still reveal BFKL dynamics under realistic collider conditions. The work highlights the observational challenges of isolating BFKL effects in γ*γ* scattering and emphasizes the need to account for substantial higher-order corrections in phenomenological analyses. Overall, it maps the prospects for testing BFKL dynamics at LEP and future linear colliders and outlines strategies to disentangle signal from background.

Abstract

The total cross-section is derived in the Leading Order QCD dipole picture of BFKL dynamics, and compared with the one from 2-gluon exchange. The Double Leading Logarithm approximation of the DGLAP cross-section is found to be small in the phase space studied. Cross sections are calculated for realistic data samples at the collider LEP and a future high energy linear collider. Next to Leading order corrections to the BFKL evolution have been determined phenomenologically, and are found to give very large corrections to the BFKL cross-section, leading to a reduced sensitivity for observing BFKL.

Paper Structure

This paper contains 14 sections, 60 equations, 4 figures, 9 tables.

Table of Contents

  1. Introduction
  2. $\gamma^*\gamma^*$ total cross-section in the dipole picture of BFKL dynamics
  3. BFKL cross-section
  4. Double Leading Log and 2-gluon cross-sections
  5. Numerical Results in the Leading Log Approximation
  6. Kinematical constraints
  7. BFKL and DGLAP differential cross-sections
  8. Integrated cross-sections
  9. Phenomenological approach of NLO effects in BFKL equation
  10. Variation of the scale for rapidity
  11. Effective value for $\alpha_S$
  12. Conclusion
  13. Acknowledgements
  14. References

Figures (4)

  • Figure 1: 2-gluon exchange for the $\gamma^*\gamma^*$ subprocess in $e^+e^- \to e^+e^-+ X$ collisions.
  • Figure 2: Differential cross-sections vs. $\ln Q^{2}_{1}/Q^{2}_{2}$, for different values of $Y$. Exact values are shown as well as saddle-point approximations. The dashed vertical line on the left hand side is the value $Q^{2}_{1}/Q^{2}_{2}=2$.
  • Figure 3: Integrated BFKL and 2-gluon cross-sections, at LEP and the LC. Leptons are tagged from $E_{tag}$ up to the beam energy. We take $\theta_{tag}>33\hbox{$\,{\mathrm{mrad}} \,$}$ at LEP, $\theta_{tag}>40\hbox{$\,{\mathrm{mrad}} \,$}$ at the LC.
  • Figure 4: Integrated BFKL and 2-gluon cross-sections at the LC, for various acceptances. Leptons are tagged between 50 and 250 GeV.