Electromagnetic tomography of radial flow in the quark-gluon plasma

Abstract

We present a novel multimessenger approach to extract the effective radial flow of the quark-gluon plasma (QGP) by jointly analyzing thermal photon and dilepton spectra in heavy-ion collisions. A key feature of this method is that it circumvents the need for a directly unmeasurable reference -- the photon temperature in the absence of flow -- by establishing, within a calibrated model framework, a stable, approximately linear correlation with the dilepton-inferred temperature. This construction defines an experimentally constructible quantity, $v_r^\mathrm{eff}$, which reflects early-time collectivity and exhibits a strong correlation with the spacetime-averaged radial velocity of the QGP. Together with previous results linking dilepton slopes to the initial QGP temperature, our work establishes a consistent framework for electromagnetic tomography of the QGP. Our framework quantifies the experimental precision target, thereby providing a concrete roadmap for future measurements at RHIC and the LHC and opening a new avenue to probe the early-time dynamics of hot QCD matter.

Figures (5)

• Figure 1: Effective temperatures (see text) at midrapidity extracted from dilepton invariant mass spectra ($T_{\ell\bar{\ell}}$, upper line) and photon transverse momentum spectra ($T_{\gamma}$, lower line), plotted against the photon effective temperature extracted from spectra without transverse flow ($T_{\gamma0}$) (see du_2026_18718103 for a table containing all data points; same for Fig. \ref{['fig2']}). Linear fits are shown for each set, excluding the gray points corresponding to $\sqrt{s_\mathrm{NN}}=7.7$ GeV. The dotted line indicates $y = x$.
• Figure 2: Comparison between the effective radial flow $v_r^\mathrm{eff}$ extracted from electromagnetic spectra and hydrodynamic flow benchmarks: $v_r^\mathrm{prefrz}$ (lower line), the spacetime-averaged radial velocity of fluid cells above the freezeout surface, and $v_r^\mathrm{frz}$ (upper cloud), the averaged flow velocity on the freezeout surface. Points at fixed beam energy but varying centrality are connected by gray lines to guide the eye. A linear fit to $v_r^\mathrm{eff}$ versus $v_r^\mathrm{prefrz}$ is also shown.
• Figure 3: Radial flow quantities at $\sqrt{s_\mathrm{NN}}=19.6$ and $200$ GeV: the effective flow $v_r^\mathrm{eff}$ extracted from electromagnetic spectra, the pre-freezeout average $v_r^\mathrm{prefrz}$ from hydrodynamics, the freezeout surface average $v_r^\mathrm{frz}$, and the kinetic freezeout velocity $v_r^\mathrm{kin}$ obtained from blast-wave fits to hadronic spectra. Error bars indicate fitting uncertainties for $v_r^\mathrm{eff}$ and $v_r^\mathrm{kin}$, while shaded boxes represent the spatial variations among fluid cells for $v_r^\mathrm{prefrz}$ and $v_r^\mathrm{frz}$.
• Figure S1: Time evolution of effective temperatures extracted from photon and dilepton spectra at $\sqrt{s_\mathrm{NN}} = 19.6$, $62.4$, and $200$ GeV (panels (a)–(c)). Each panel shows the photon temperature with ($T_{\gamma}$, red solid) and without transverse flow ($T_{\gamma0}$, green dashed), the dilepton-inferred temperature ($T_{\ell\bar{\ell}}$, blue dotted), and the hydrodynamic average temperature (gray curve) with its variation (gray band) in 20–30% Au+Au collisions at midrapidity. At each energy, $T_{\gamma0}$ and $T_{\ell\bar{\ell}}$ track each other closely throughout the evolution, separated by an approximately constant offset $\Delta T$.
• Figure S2: Comparison of effective radial flow extracted using true and proxy baselines for the no-flow photon temperature. For each beam energy shown in Fig. \ref{['app_fig1']}, the radial flow $v_r$ is computed from the blue-shift relation using the measured $T_{\gamma}$ and either the true $T_{\gamma0}$ (green dashed) or the proxy estimate $T_{\ell\bar{\ell}} - \Delta T$ (blue dotted, denoted as "photon+dilepton"). The gray curve shows the hydrodynamic average radial flow, and the gray band indicates its standard deviation, reflecting variations among fluid cells weighted as described in footnote \ref{['fn:avg']}.