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Double diffractive rho-production in gamma^* gamma^* collisions

B. Pire, L. Szymanowski, S. Wallon

TL;DR

The paper provides a Born-order, perturbative QCD estimate for exclusive double rho production in high-energy $\gamma^*\gamma^*$ collisions, using an impact-factor framework with longitudinal polarizations and a collinear vector-meson distribution amplitude. It derives analytic results in the forward limit and develops a conformal-inversion-based method to handle the non-forward massive integrals, complemented by numerical integration over meson momentum fractions. The authors find sizable cross sections for photon virtualities of a few GeV$^2$, suggesting measurability at future $e^+e^-$ linear colliders, and outline plans to include $\text{BFKL}$ evolution, transverse-photon contributions, and possible Odderon interference in future work.

Abstract

We present a first estimate of the cross-section for the exclusive process gamma^*_L (Q_1^2) gamma^*_L(Q_2^2) -> rho^0_L rho^0_L, which will be studied in the future high energy e^+ e^- linear collider. As a first step, we calculate the Born order approximation of the amplitude for longitudinally polarized virtual photons and mesons, in the kinematical region s >> -t, Q_1^2, Q_2^2. This process is completely calculable in the hard region Q_1^2, Q_2^2 >> Lambda^2_{QCD}. We perform most of the steps in an analytical way. The resulting cross-section turns out to be large enough for this process to be measurable with foreseen luminosity and energy, for Q_1^2 and Q_2^2 in the range of a few GeV^2.

Double diffractive rho-production in gamma^* gamma^* collisions

TL;DR

The paper provides a Born-order, perturbative QCD estimate for exclusive double rho production in high-energy collisions, using an impact-factor framework with longitudinal polarizations and a collinear vector-meson distribution amplitude. It derives analytic results in the forward limit and develops a conformal-inversion-based method to handle the non-forward massive integrals, complemented by numerical integration over meson momentum fractions. The authors find sizable cross sections for photon virtualities of a few GeV, suggesting measurability at future linear colliders, and outline plans to include evolution, transverse-photon contributions, and possible Odderon interference in future work.

Abstract

We present a first estimate of the cross-section for the exclusive process gamma^*_L (Q_1^2) gamma^*_L(Q_2^2) -> rho^0_L rho^0_L, which will be studied in the future high energy e^+ e^- linear collider. As a first step, we calculate the Born order approximation of the amplitude for longitudinally polarized virtual photons and mesons, in the kinematical region s >> -t, Q_1^2, Q_2^2. This process is completely calculable in the hard region Q_1^2, Q_2^2 >> Lambda^2_{QCD}. We perform most of the steps in an analytical way. The resulting cross-section turns out to be large enough for this process to be measurable with foreseen luminosity and energy, for Q_1^2 and Q_2^2 in the range of a few GeV^2.

Paper Structure

This paper contains 12 sections, 94 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Kinematics
  3. Impact representation
  4. Cross section at Born order
  5. Forward case
  6. Non forward case
  7. Results
  8. Conclusion
  9. Appendices
  10. Computation of the amplitude at $t=t_{min}$
  11. Computation of the amplitude at $t=t_{min}$ in the partonic approach
  12. Integrals

Figures (5)

  • Figure 1: Amplitude for the process $\gamma^*_L\gamma^*_L \to \rho^0_L\rho^0_L$ in the impact representation. The blobs denote the vector meson distribution amplitudes.
  • Figure 2: Amplitude for the process $\gamma^*_L\gamma^*_L \to \rho^0_L\rho^0_L$ at Born order. The $t$-channel gluons are attached to the quark lines in all possible ways.
  • Figure 3: Differential cross-section for the process $\gamma^*_L\gamma^*_L \to \rho^0_L\rho^0_L$ at Born order, at the threshold $t=t_{min},$ as a function of $Q_2^2/Q_1^2.$ The dots represents the value of the cross-section at the special point $Q_1=Q_2,$ as given by the analytical formula (\ref{['amplitudeR1']}). The asymptotical curves are valid for large $Q_2^2/Q_1^2,$ as predicted by the asymptotical form (\ref{['amplitudeparton']})
  • Figure 4: Differential cross-section for the process $\gamma^*_L\gamma^*_L \to \rho^0_L\rho^0_L$ at Born order, as a function of $t,$ for different values of $Q = Q_1=Q_2.$
  • Figure 5: The integrated cross-section for the process $\gamma^*_L\gamma^*_L \to \rho^0_L\rho^0_L$ at Born order as a function of $Q_1^2=Q_2^2.$