Thermal and geometric normal modes of spectral fluctuations in heavy-ion collisions

TL;DR

This paper decomposes spectral fluctuations in heavy-ion collisions into thermal and geometric modes using principal component analysis, revealing their physical significance and impact on observed flow patterns.

Contribution

It introduces a novel interpretation of principal component modes as thermal and geometric vibrations, linking spectral fluctuations to initial state physics in heavy-ion collisions.

Findings

Thermal mode explains the measured $v_0(p_T)$.

Geometric mode accounts for the low-$p_T$ sign change in $v_{02}(p_T)$.

First physical interpretation of principal component modes in heavy-ion collisions.

Abstract

The transverse momentum spectrum of charged particles in ultra-relativistic heavy-ion collisions fluctuates event-by-event, encoding signatures of underlying collective dynamics. Such fluctuations originate from a combined effect of thermal and geometric fluctuations in the initial state. We present a direct decomposition of these spectral fluctuations through principal component analysis performed on the joint covariance structure of normalized spectrum, mean transverse momentum and elliptic flow squared. The first two leading modes explain 99.5\% of the total variance, and are orthogonally rotated by imposing physical constraints motivated by the initial state thermal and geometric response. The resulting thermal and geometric modes bear direct analogy with the vibrational normal modes of a linear triatomic molecule. The thermal mode entirely drives the experimentally measured $v_0(p_T)$, while the geometric mode contributes substantially to $v_{02}(p_T)$ in non-central collisions, providing a transparent explanation of its characteristic low-$p_T$ sign change. The study establishes the first physically motivated interpretation of principal component modes in the field of heavy-ion collisions and provides an experimental window into the thermo-geometric structure of the QGP initial state.