Nonlinear response of flow harmonics in Gubser flow with participant-reaction planes mismatch

TL;DR

This paper analytically explores the nonlinear relationship between flow harmonics and initial eccentricities in Gubser flow, highlighting the impact of participant-reaction plane mismatch on nonlinear response coefficients.

Contribution

It extends Gubser flow solutions to derive analytic nonlinear response relations and examines how participant-plane mismatch influences these coefficients.

Findings

Reproduces the $v_4/v_2^2 o 1/2$ limit at high $p_T$.

Shows participant-plane mismatch modifies nonlinear response coefficients.

Identifies the sensitivity of response coefficients to initial nuclear configurations.

Abstract

We investigate the nonlinear response of flow harmonics $v_2,v_4$ to initial-state eccentricities $\epsilon_2,\epsilon_4$ within the Gubser-flow framework. By extending the perturbative solutions of Gubser flow, we derive analytic nonlinear response relations connecting the eccentricities $\epsilon_2,\epsilon_4$ to the flow harmonics $v_2,v_4$. Our results reproduce the well-known result $v_4/v_2^2 \to 1/2$ in large transverse momentum $p_T$ limit. Furthermore, we study the effects of a mismatch between the participant and reaction planes. We find that the conventional nonlinear response coefficients acquire an additional factor determined by the participant-plane angles, which is often approximated as statistical noise driven by event-by-event fluctuations. This factor can modify both the strength but even the sign of the effective nonlinear response coefficient, making it sensitive to the initial configuration of the colliding nuclei. Our study provides new analytical insight into the origin of collective phenomena in relativistic heavy-ion collisions.