Finite size effects on critical correlations in momentum space
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.