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Probing colored glass via $q\bar{q}$ photoproduction II: diffraction

F. Gelis, A. Peshier

TL;DR

This work computes the diffractive photoproduction of $q\bar{q}$ pairs in peripheral heavy-ion collisions within the Colored Glass Condensate framework, emphasizing how the cross-section probes the saturation scale $Q_s$. By treating the color background to all orders and the EM coupling to leading order, the authors derive explicit expressions for the diffractive amplitude, the differential $p_\perp$ spectrum, and the integrated cross-section, showing a strong $Q_s$-dependence, especially for charm and bottom quarks. They establish a fundamental bound $P_1^{\rm diff} \le \tfrac{1}{2} P_1^{\rm incl}$ and discuss the black-disc limit $Q_s\to\infty$ where $P_1^{\rm diff}\to P_1^{\rm incl}/2$, along with unitarity considerations and possible Poisson unitarization. The results indicate that diffractive photoproduction offers a practical observable to measure the saturation scale in ultra-relativistic heavy-ion collisions, with clear predictions for RHIC/LHC energies and heavy-quark channels.

Abstract

In this paper, we consider the diffractive photoproduction of quark-antiquark pairs in peripheral heavy ion collisions. The color field of the nuclei is treated within the Colored Glass Condensate model. The cross-section turns out to be very sensitive to the value of the saturation scale.

Probing colored glass via $q\bar{q}$ photoproduction II: diffraction

TL;DR

This work computes the diffractive photoproduction of pairs in peripheral heavy-ion collisions within the Colored Glass Condensate framework, emphasizing how the cross-section probes the saturation scale . By treating the color background to all orders and the EM coupling to leading order, the authors derive explicit expressions for the diffractive amplitude, the differential spectrum, and the integrated cross-section, showing a strong -dependence, especially for charm and bottom quarks. They establish a fundamental bound and discuss the black-disc limit where , along with unitarity considerations and possible Poisson unitarization. The results indicate that diffractive photoproduction offers a practical observable to measure the saturation scale in ultra-relativistic heavy-ion collisions, with clear predictions for RHIC/LHC energies and heavy-quark channels.

Abstract

In this paper, we consider the diffractive photoproduction of quark-antiquark pairs in peripheral heavy ion collisions. The color field of the nuclei is treated within the Colored Glass Condensate model. The cross-section turns out to be very sensitive to the value of the saturation scale.

Paper Structure

This paper contains 14 sections, 47 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Reduction formulas for pair production
  3. $\overline{n}$ versus $P_1$
  4. Diffractive and inclusive quantities
  5. Expression of $P_1$ to order $(Z\alpha)^2$
  6. Pair production amplitude
  7. Equality of $P_1^{\rm incl}$ and $\overline{n}$ at order $(Z\alpha)^2$
  8. A useful inequality
  9. $p_\perp$ spectrum for diffraction
  10. Integrated diffractive cross-section
  11. Cross-section
  12. Unitarity and black-disc limit
  13. Summary
  14. Conclusions

Figures (6)

  • Figure 1: Prototype of the diagrams contributing to the diffractive photoproduction of a $q\bar{q}$ pair in $AA$ collisions.
  • Figure 2: Inclusive (left) vs. diffractive (right) photoproduction of $q\bar{q}$ pairs. The shaded blob represents the average over a hard color source. For the diffractive cross-section, one has to average the amplitude before squaring it.
  • Figure 3: The three diagrams contributing to ${\cal T}_F$ at lowest order in the electromagnetic coupling constant. The black dot denotes the time-ordered eikonal matrix $T_F$ that describes the interaction of a quark or antiquark with the colored glass condensate.
  • Figure 4: Differential diffractive cross-section as a function of the transverse momentum of the quark. The value of $Q_s/\Lambda_{_{QCD}}$ is set to $10$. Open circles: strange quarks. Filled squares: charm quark. Open squares: bottom quark. The differential cross-section is in units of mbarns$/\Lambda_{_{QCD}}$.
  • Figure 5: Diffractive cross-section in mbarns per unit of rapidity as a function of the saturation scale. Open circles: strange quarks. Filled squares: charm quarks. Open squares: bottom quarks.
  • ...and 1 more figures