Abstract
We introduce the subensemble acceptance method 2.0 (SAM-2.0) -- a procedure to correct cumulants of a random number distribution inside a subsystem for the effect of exact global conservation of a conserved quantity to which this number is correlated, with applications to measurements of event-by-event fluctuations in heavy-ion collisions. The method expresses the corrected cumulants in terms of the cumulants inside and outside the subsystem that are not subject to the exact conservation. The derivation assumes that all probability distributions associated with the cumulants are peaked at the mean values but are otherwise of arbitrary shape. The formalism reduces to the original SAM [V. Vovchenko et al., Phys.Lett.B 811 (2020) 135868 [arXiv:2003.13905]] when applied to a coordinate space subvolume of a uniform thermal system. As the new method is restricted neither to the uniform systems nor to the coordinate space, it is applicable to fluctuations measured in heavy-ion collisions at various collision energies in different momentum space acceptances. The SAM-2.0 thus brings the experimental measurements and theoretical calculations of event-by-event fluctuations closer together, as the latter are typically performed without the account of exact global conservation.
Highlights
Event-by-event fluctuations are among the key observables for probing the QCD phase structure experimentally [1], with measurements performed at experiments in a broad collision energy range from HADES-GSI to ALICE-LHC [2,3,4,5,6]
This paper introduces the subensemble acceptance method (SAM)-2.0, which addresses the limitations of the original SAM
= α2β2δ(2B + δ) . exact B + δ − 2αβδ. It follows from Eq (69) that, for |δ| < B, the sign of (κ2C,Ein )SAM−2.0 − (κ2C,Ein )exact is determined by the sign of δ, the SAM-2.0 overestimates the effect of correlations to κ2C,Ein
Summary
Event-by-event fluctuations are among the key observables for probing the QCD phase structure experimentally [1], with measurements performed at experiments in a broad collision energy range from HADES-GSI to ALICE-LHC [2,3,4,5,6]. The method allows one to calculate the effect of exact global conservation on cumulants measured in an arbitrary subsystem, for instance in momentum space as appropriate for the experiment. The SAM-2.0 allows one to evaluate the effect of a global conservation law, such as that of net baryon number, on the cumulants of a nonconserved quantity like the net proton number. This is relevant for the experiment, where it is usually not possible to measure all particles contributing to a given conserved charge.
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