Elliptic Anisotropy from Quantum Diffraction

Abstract

The surprising manifestation of collectivity in small collision systems, such as nucleon-nucleon and nucleon-nucleus collisions, is perhaps even more striking when discussed at higher momenta. In larger systems, high-$p_T$ elliptic anisotropy is understood as a selection bias effect due to the smaller energy loss experienced along the shorter direction that aligns with the event plane. However, in small systems the amount of energy loss appears insufficient to reproduce the sizable angular anisotropy observed experimentally. In this work, we explore a new mechanism generating preferred orientations for energetic particles without the need of energy loss. We exploit a simple model that is based on two basic although inalienable ingredients: geometry and quantum mechanics. Our findings suggest that this sum-over-paths mechanism can provide a relevant contribution to so-called flow coefficients of energetic particles traversing deconfined media of any size.

Figures (5)

• Figure 1: Sum‑over‑paths sketch illustrating the difference in in-medium phase accumulation between trajectories exiting along the short (lower curvature $\kappa$) and long (higher curvature $\kappa$) directions of the ellipse. The amount of paths explored is proportional to the particle wavelength $\lambda$. Sizes are not drawn to scale: the medium (in blue) is only a few femtometers across, whereas the detector (dashed grey line) is located meters away.
• Figure 2: Results for $v_2$ versus momentum $k_o>V=1$ GeV using the event plane method, as a function of centrality, for three different "nucleus" sizes: $R=0.5$ fm in the left, $R=1$ fm in the center and $R=2$ fm in the right. Dashed lines correspond to the SPA solution $v_2^S$ (identical in all three panels) while solid lines show the exact solution using Mathieu functions $v_2^M$.
• Figure 3: Ratio of the transmitted wave norm (with $V\neq0$) divided by the source norm (or setting $V=0$) versus momentum $k_o>V$, as a function of centrality, for different values of the potential $V$ and fixed "nucleus" size $R=1$ fm. The solid black line represents the centrality-averaged result, and the dashed line simply shows the curve for $1-e^{-k_o/V}$.
• Figure 4: Example of a specific configuration depicting the relevant quantities involved in the determination of the stationary points via Eq. \ref{['eq:snellnum']}. The detector angle is $\phi=\pi/4$, with $k_o=2$ GeV and $V=1$ GeV. The source location, $\bm{z}$, is at the red dot. The particle trajectory inside the medium, $\hat{\bm{u}}$, is shown in yellow, and the one outside, $\hat{\bm{e}}$, in purple. The tangent vector to the trajectory ($\hat{\bm{t}}$, green), the ellipse normal ($\hat{\bm{n}}$, red), the incident angle $\theta_i$ (blue), and the outgoing angle $\theta_o$ (orange) are drawn at the boundary exit point satisfying the stationary solution condition, $\bm{s}^*$.
• Figure 5: Results for $v_2$ using the SPA as a function of centrality (as defined in Section \ref{['sec:res']}) with $V=1$ GeV. We compare $v_2^S$ for a central source (red), $v_2^S$ averaged over 60 random sources (dashed blue) and the analytic approximation for a central source $v_2^A$ (black points).