The Role of Baryon Number Conservation in Measurements of Fluctuations

Abstract

I discuss the role and impact of net-baryon number conservation in measurements of net proton fluctuations in heavy-ion collisions. I show that the magnitude of the fluctuations is entirely determined by the strength of two particle correlations. At LHC and top RHIC energy, this implies the fluctuations are proportional to the integral of the balance function (BF), $B^{p\bar p}$ of protons and anti-protons, while in the context of the RHIC beam energy scan (BES), one must also account for correlations of "stopped" protons. The integral of $B^{p\bar p}$ measured in a $4π$ detector depends on the relative cross-sections of processes yielding $p\bar p$ and those balancing the proton baryon number via the production of other anti-baryons. The accepted integral of $B^{p\bar p}$ further depends on the shape and width of the BF relative to the width of the acceptance. The magnitude of the measured second order cumulant of net proton fluctuations thus has much less to do with QCD susceptibilities than with the creation/transport of baryons and anti-baryons in heavy-ion collisions, and most particularly the impact of radial flow on the width of the BF. I thus advocate that net-proton fluctuations should be studied by means of differential BF measurements rather integral correlators.