Probing colored glass via $q\bar{q}$ photoproduction

TL;DR

The work presents a first-principles calculation of qqbar photoproduction in peripheral heavy-ion collisions within the Color Glass Condensate framework. By coupling the electromagnetic probe to the classical color field of one nucleus and treating the color field of the other nucleus nonperturbatively, the authors connect the production rate to a Wilson-line correlator C(k_perp) that encodes gluon saturation through the saturation scale Q_s. They show that the transverse-momentum spectrum d_sigma_T/dydk_perp exhibits a maximum near k_perp ~ Q_s, providing a potential experimental handle to measure Q_s in heavy-ion collisions. The study also derives large- and small-mass limits of the integrated cross-section and discusses the dependence on nuclear size, impact parameter, and photon flux, highlighting the observable signatures of color glass condensate dynamics.

Abstract

In this paper, we calculate the cross-section for the photoproduction of quark-antiquark pairs in the peripheral collision of ultra-relativistic nuclei, by treating the color field of the nuclei within the Color Glass Condensate model. We find that this cross-section is sensitive to the saturation scale $Q_s^2$ that characterizes the model. In particular, the transverse momentum spectrum of the produced pairs could be used to measure the properties of the color glass condensate.

Figures (4)

• Figure 1: Prototype of the diagrams contributing to the photoproduction of a $q\bar{q}$ pair in $AA$ collisions.
• Figure 2: Plot of $d\sigma_{_{T}}/dy dk_\perp$ as a function of $k_\perp/\Lambda_{_{QCD}}$, in arbitrary units (only the $k_\perp$ dependent factors of Eq. (\ref{['eq:kt-spectrum']}) have been plotted). The value of $Q_s/\Lambda_{_{QCD}}$ is set to $10$. The dotted curves are based on a numerical evaluation of the full $C({\fam\imbf k}_\perp)$ as predicted in the color glass condensate model. The continuous curves have been obtained with the asymptotic form $C({\fam\imbf k}_\perp)=2Q_s^2/k_\perp^4$, which is the lowest order in $Q_s^2$. Open dots and solid curve: $m/\Lambda_{_{QCD}}=23$ (bottom), filled dots and dashed curve: $m/\Lambda_{_{QCD}}=8$ (charm), with $\Lambda_{_{QCD}}\approx 0.2$GeV.
• Figure 3: Plot of $d\sigma_{_{T}}/dy$ as a function of $m/\Lambda_{_{QCD}}$. In this plot, $Q_s/\Lambda_{_{QCD}}=10$. We use $R=6$fm and $\gamma=3000$. The open dots are a numerical evaluation of the integral in Eq. (\ref{['eq:nbar-final']}), while the solid curve is the asymptotic formula of Eq. (\ref{['eq:sigma-large-m']}), in which we have replaced $\ln(m/\Lambda_{_{QCD}})$ by $\ln(m/\Lambda_{_{QCD}})+0.92$ (the additive constant has been adjusted so that it fits at large values of $m$). We have circled the points corresponding to the mass of the charm and bottom quarks, assuming $\Lambda_{_{QCD}}\approx 0.2$GeV.
• Figure 4: Value of $C(k_\perp)$ as a function of $k_\perp/\Lambda_{_{QCD}}$ for $Q_s/\Lambda_{_{QCD}}=10$. The open circles are the result of a numerical evaluation, and the solid line is the asymptotic formula given in Eq. (\ref{['eq:Ck-asympt']}). The shaded area indicates the region where $k_\perp\le \Lambda_{_{QCD}}$. One can see on the numerical curve the onset of saturation at low values of $k_\perp$. In the upper right corner, we have plotted the same data for the quantity $k_\perp^4 C(k_\perp)/2Q_s^2$, which allows for an easier reading for large values of $k_\perp$.