Role of baryon number conservation in measurements of fluctuations

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^pp of protons and antiprotons, while in the context of the RHIC beam energy scan (BES), one must also account for correlations of stopped protons. The integral of B^pp measured in a 4 detector depends on the relative cross sections of processes yielding pp and those balancing the proton baryon number via the production of other antibaryons. The accepted integral of B^pp 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 antibaryons 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 than with integral correlators. I also derive an expression of net-baryon fluctuations in terms of integrals of balance functions of identified baryon pairs and argue that measurements of such balance functions would enable a better understanding of the collision system expansion dynamics, the hadronization chemistry, and an experimental assessment of the strength of net-baryon fluctuations.