Sources of Radial Flow Fluctuations in the Quark-Gluon Plasma

Abstract

The differential radial flow fluctuation $v_0(p_{\mathrm{T}})$ has emerged as a new probe of the quark-gluon plasma. However, its characteristic rise-and-fall pattern with $p_{\mathrm{T}}$, resembling anisotropic flow, remains unexplained. I introduce a momentum rescaling framework that factorizes $v_0(p_{\mathrm{T}})$ into kinematic and dynamical components: $v_0(p_{\mathrm{T}})/v_0 = -[d\ln\langle n(p_{\mathrm{T}})\rangle/d\ln p_{\mathrm{T}} + 1] \times g(p_{\mathrm{T}})$. The first factor, determined by spectral shape, generates the rise-and-fall pattern as the spectra transition from exponential to power-law behavior. The dynamical component $g(p_{\mathrm{T}})$ isolates $p_{\mathrm{T}}$-dependent dynamics: $<1$ signals suppressed fluctuations, $>1$ indicates enhancement. Analysis of LHC data reveals $g(p_{\mathrm{T}})$ deviates from unity by 20-40% in central collisions. Predictions for RHIC show that spectral shape alone generates the rise-and-fall baseline pattern with substantial energy dependence. This framework enables tighter medium property constraints by separating kinematic from dynamical effects, with broad applications to anisotropic flow and higher-order radial flow fluctuations.

Figures (7)

• Figure 1: Cartoon illustration of the momentum rescaling model and its connection to $v_0(p_{\mathrm{T}})$. (a) Shows the global event-by-event fluctuation of fractional spectra yield, $\delta n(p_{\mathrm{T}})/\left\langle n(p_{\mathrm{T}})\right\rangle$ with $\int n(p_{\mathrm{T}})dp_{\mathrm{T}}=1$. The blue curve indicates the change of $n(p_{\mathrm{T}})$ in an event with large $[p_{\mathrm{T}}]$ from the average $\left\langle n(p_{\mathrm{T}})\right\rangle$ represented by the black curve. (b) Shows how these fluctuations can be mapped to the characteristic shape of the $v_0(p_{\mathrm{T}})$ATLAS:2025ztg, which typically rises from negative values, crosses zero, peaks, and then falls. (c) Depicts the core concept of our model: these fluctuations are interpreted as a rescaling of the $p_{\mathrm{T}}$-axis, $\Delta_{p_{\mathrm{T}}} (p_{\mathrm{T}})/p_{\mathrm{T}} = g(p_{\mathrm{T}}) \delta[p_{\mathrm{T}}]/\left\langle [p_{\mathrm{T}}]\right\rangle$. Our primary goal is to extract this effective $p_{\mathrm{T}}$-dependent momentum scaling factor, $g(p_{\mathrm{T}})$, from the experimentally measured $v_0(p_{\mathrm{T}})$ and average spectrum $\left\langle n(p_{\mathrm{T}})\right\rangle$.
• Figure 2: The $v_0(p_{\mathrm{T}})/v_0$ (a) and $v_0(p_{\mathrm{T}})/v_0^A$ (b) calculated from charged hadron spectra via Eq. \ref{['eq:5']} and Eq. \ref{['eq:9']}, respectively, assuming constant fractional momentum rescaling ($g(p_{\mathrm{T}})=1$). Results are shown for $pp$ and several centrality classes in Pb+Pb collisions at $\hbox{$\sqrt{s_{\mathrm{NN}}}$} = 5.02$ TeV. The spectral uncertainties influencing $v_0(p_{\mathrm{T}})/v_0$ are very small and hence not included.
• Figure 3: Extracting physics from ATLAS $v_0(p_{\mathrm{T}})$ data. (a) Calculated $v_0(p_{\mathrm{T}})/v_0^A$ (lines) after zero-crossing alignment (Eq. \ref{['eq:10']}), compared with ATLAS data (markers) for Pb+Pb centrality classes at $\hbox{$\sqrt{s_{\mathrm{NN}}}$}=5.02$ TeV. (b) Extracted $g(p_{\mathrm{T}})$ (markers) via Eq. \ref{['eq:11']}. The dashed line at $g(p_{\mathrm{T}})=1$ indicates global momentum rescaling. (c) Differential momentum rescaling factor $\Delta_{p_{\mathrm{T}}}(p_{\mathrm{T}})/p_{\mathrm{T}}$ from Eq. \ref{['eq:12']}.
• Figure 4: Predicted $v_0(p_{\mathrm{T}})/v_0$ at RHIC and LHC energies based on momentum rescaling model. The $v_0(p_{\mathrm{T}})/v_0$ calculated from charged hadron spectra via Eq. \ref{['eq:5']} for Pb+Pb collisions at $\hbox{$\sqrt{s_{\mathrm{NN}}}$} = 5.02$ TeV (solid lines, LHC) and Au+Au collisions at $\hbox{$\sqrt{s_{\mathrm{NN}}}$} = 0.2$ TeV (markers, RHIC). Panels show results normalized to $v_0$ calculated in different reference $p_{\mathrm{T}}$ ranges: (a) full $p_{\mathrm{T}}$ range, (b) $0.2 < p_{\mathrm{T}} < 10$ GeV range, (c) $0.2 < p_{\mathrm{T}} < 2$ GeV range, and (d) $0.5 < p_{\mathrm{T}} < 2$ GeV range.
• Figure 5: Acceptance factor versus momentum range boundaries. The acceptance factor $C_A = v_0^A/v_0$ (Eq. \ref{['eq:8']}) versus $p_{\mathrm{T}}^{\mathrm{max}}$ for different $p_{\mathrm{T}}^{\mathrm{min}}$ values (labeled). Results are shown for Pb+Pb at $\hbox{$\sqrt{s_{\mathrm{NN}}}$} = 5.02$ TeV (a) and Au+Au at $\hbox{$\sqrt{s_{\mathrm{NN}}}$} = 0.2$ TeV (b), with four centrality classes per group. The factor increases with $p_{\mathrm{T}}^{\mathrm{max}}$ and saturates differently at RHIC versus LHC due to spectral shape differences.