Nuclear Science and Techniques

Fluctuations of conserved quantities, such as baryon, electric charge, and strangeness number, are sensitive observables in relativistic heavy-ion collisions to probe the QCD phase transition and search for the QCD critical point. In this paper, we review the experimental measurements of the cumulants (up to fourth order) of event-by-event net-proton (proxy for net-baryon), net-charge and net-kaon (proxy for net-strangeness) multiplicity distributions in Au+Au collisions at $$\sqrt{{s}_{\text{NN}}}=7.7, 11.5, 14.5, 19.6, 27, 39, 62.4, 200$$  GeV from the first phase of beam energy scan program at the relativistic heavy-ion collider (RHIC). We also summarize the data analysis methods of suppressing the volume fluctuations, auto-correlations, and the unified description of efficiency correction and error estimation. Based on theoretical and model calculations, we will discuss the characteristic signatures of critical point as well as backgrounds for the fluctuation observables in heavy-ion collisions. The physics implications and the future second phase of the beam energy scan (2019–2020) at RHIC will also be discussed.