To bin or not to bin: does binning in multiplicity reliably suppress unwanted volume fluctuations?

Abstract

In this study, we examine the effect of the so-called Centrality Bin Width Correction (CBWC) on the measurement of (net-)proton number cumulants in nucleus-nucleus collisions. We present an analytically tractable model, which includes correlations between multiplicity and proton number similar to those generated by the decay of baryon resonances. Within this model, we analyze the circumstances under which the CBWC method correctly removes the undesired effects of volume or impact parameter fluctuations. Additionally, we explore situations where the method fails and produces misleading results.

Figures (3)

• Figure 1: The probability distribution for $N$\ref{['eq:model_joint_dist']} for fixed $M= 80,\,100,\,120,\,140$ and $160$. Also shown are the original distribution, without volume fluctuations \ref{['eq:bivariate-poisson']} (filled in yellow) as well as the full distribution, which includes volume fluctuations \ref{['eq:model_joint_dist']}, both summed over all $M$. The parameters employed here are $k=50,\,\lambda=100,\,\nu=30,\,\mu=20$.
• Figure 2: Ratio of CBWC cumulants to their true values, $\kappa_n^{CBWC}/\kappa_n^{true}$ as a function of the correlation strength. Top left: For protons (corresponding to 7.7 GeV collisions). Top right: For net-protons at $\mu_B>0$ (corresponding to 39 GeV collisions). Bottom: For net-protons at $\mu_B=0$ (corresponding to LHC energy collisions).
• Figure 3: Ratio of CBWC cumulants to their true values, $\kappa_n^{CBWC}/\kappa_n^{true}$, as functions of charged particle multiplicity, $\mu$. Left: For protons. Right: For net protons at $\mu_B>0$.