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(corr). The value of Delta y(corr) similar to 1 for critical thermal fluctuations is determined by the thermal rapidity spread of the particles at freeze-out, 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 >> Delta y(corr), the cumulants of a given particle multiplicity, kappa(k), scale linearly with Delta y, or mean multiplicity in acceptance, , and cumulant ratios are acceptance independent. In the opposite regime, Delta y (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 the extension of rapidity coverage as proposed by the STAR Collaboration should significantly increase the magnitude of the critical point fluctuation signatures.
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