Finite size effects on critical correlations in momentum space

TL;DR

This paper analyzes how finite size effects influence the momentum-space correlations near the QCD critical point, revealing that finite system size alters observable critical scaling in heavy-ion collision experiments.

Contribution

It provides a theoretical framework for understanding finite size modifications of critical correlations in momentum space relevant to heavy-ion collision experiments.

Findings

Finite size effects modify the critical scaling behavior in momentum space.

An effective scaling exponent emerges due to finite size constraints.

The true critical scaling is recovered only within a specific momentum range.

Abstract

The search for the QCD critical end point (CEP) is a major objective of contemporary heavy-ion physics, motivating the study of fluctuation observables that are sensitive to critical dynamics. In particular, baryon-number fluctuations provide a natural probe because the net-baryon density can serve as an effective order parameter in the vicinity of the CEP. Near criticality, long-range correlations and power-law scaling are expected to emerge in the real-space two-point function of the baryon density, yet the finite size and finite lifetime of the fireball created in heavy-ion collisions impose intrinsic cutoffs that regulate the growth of the correlation length. These finite-size constraints significantly modify the observable structure of fluctuations, especially in momentum space, where experiments perform measurements. In this work we present a theoretical analysis of the momentum-space two-point correlation function for a system of finite spatial extent. We show that finite size effects lead to an effective scaling exponent which coincides with that of the infinitely extended system only in a prescribed scaling region within the experimentally accessible momentum range.