The Masked Critical

Near a critical point, correlation functions diverge. In an infinite system, the divergence is clean — power-law behavior with universal critical exponents that classify the transition. Heavy-ion collisions may produce matter near the QCD critical point, where hadronic matter transitions to quark-gluon plasma. The experimental signature should be anomalous fluctuations in conserved quantities (baryon number, charge, strangeness), observable in momentum-space correlations.

The fireball is not infinite. It is a few femtometers across and exists for a few fm/c before exploding into hadrons. The finite size of the fireball imposes a minimum wavelength on the correlations — modes with wavelength larger than the fireball cannot develop. In coordinate space, this truncation is understood: the correlation length saturates at the system size.

The momentum-space consequences are less obvious. The paper shows that finite-size effects create a narrow scaling window in momentum space: the critical correlations are visible only for momenta within a specific range determined by the system size and the correlation length. Outside this window — at both too-low and too-high momenta — the correlations look non-critical. The critical signature is confined to a band.

The practical consequence is a disconnect between theoretical prediction and experimental observable. Theory predicts divergent correlations. Experiment sees correlations only within the scaling window. If the window is narrow (which it is, for realistic fireball sizes), the signal is compressed into a small region of momentum space that may be below experimental resolution.

The structural point: criticality is a property of the thermodynamic limit. Finite systems can approach criticality but the approach is observable only within a window determined by the system size. The critical point is not absent — it is masked. The mask is not noise or background but the finite size of the system itself, which is a feature of heavy-ion collisions that cannot be removed.