Acceptance corrections to net baryon and net charge cumulants

TL;DR

This paper investigates how finite acceptance affects the measurement of net-baryon and net-charge cumulants, deriving formulas to relate true and measured values, and discusses implications for probing the QCD phase diagram.

Contribution

The authors derive general formulas connecting true and measured cumulants under finite acceptance modeled by a binomial distribution, highlighting additional moments needed for accurate interpretation.

Findings

Measured cumulant ratios converge quickly if acceptance probability p < 1/2.

Finite acceptance significantly complicates the interpretation of net-baryon cumulants.

Net-charge cumulants may provide more reliable signals for the QCD phase diagram.

Abstract

We show that the effect of finite acceptance drastically influences the net-baryon and net-charge cumulants, which are believed to be sensitive probes of the QCD phase diagram. We derive the general formulae that relate the true cumulants K_{n} which reflect the full dynamics of the system with the actually measured cumulants c_{n} for a given acceptance, modeled by a binomial probability parameter p. We find that this relation involves additional moments which cannot be expressed by cumulants and should be measured in order to extract any potential information about the QCD critical point. We demonstrate that for a wide range of the true cumulant ratios K_{n}/K_{m} the measured ratios c_{n}/c_{m} quickly converge if p < 1/2, which makes the interpretation of the data very challenging, especially in case of the net-proton cumulants. Our study further suggests that the measurement of net-charge cumulants may be more advantageous for the investigation of the QCD phase diagram.