Acceptance dependence of fluctuation measures near the QCD critical point

TL;DR

This paper analyzes how the acceptance range in momentum space affects fluctuation measures near the QCD critical point, emphasizing the importance of rapidity correlation length and proposing that increased rapidity coverage enhances critical fluctuation signals.

Contribution

It provides a theoretical framework linking acceptance dependence of fluctuation measures to momentum space correlations, highlighting the impact of rapidity coverage on detecting critical point signatures.

Findings

Acceptance dependence is governed by the correlation range in rapidity.

Cumulants scale linearly with acceptance when acceptance is large.

Extending rapidity coverage can significantly boost critical fluctuation signals.

Abstract

We argue that a crucial determinant of the acceptance dependence of fluctuation measures in heavy-ion collisions is the range of correlations in the momentum space, e.g., in rapidity, $\Delta y_{\rm corr}$. The value of $\Delta y_{\rm corr}\sim1$ for critical thermal fluctuations is determined by the thermal rapidity spread of the particles at freezeout, and has little to do with position space correlations, even near the critical point where the spatial correlation length $\xi$ becomes as large as $2-3$ fm (this is in contrast to the magnitudes of the cumulants, which are sensitive to $\xi$). When the acceptance window is large, $\Delta y\gg\Delta y_{\rm corr}$, the cumulants of a given particle multiplicity, $\kappa_k$, scale linearly with $\Delta y$, or mean multiplicity in acceptance, $\langle N\rangle$, and cumulant ratios are acceptance independent. While in the opposite regime, $\Delta y\ll\Delta y_{\rm corr}$, the factorial cumulants, $\hat\kappa_k$, scale as $(\Delta y)^k$, or $\langle N\rangle^k$. We demonstrate this general behavior quantitatively in a model for critical point fluctuations, which also shows that the dependence on transverse momentum acceptance is very significant. We conclude that extension of rapidity coverage proposed by STAR should significantly increase the magnitude of the critical point fluctuation signatures.