  Two scenarios for cluster production have since long been discussed in the
literature: i) direct emission of the clusters from a (grand canonical) thermal
source or ii) subsequent formation of the clusters by coalescence of single
nucleons. While both approaches have been successfully applied in the past it
has not yet been clarified which of the two mechanisms dominates the cluster
production. We propose to use recently developed event-by-event techniques to
study particle multiplicity fluctuations on nuclear clusters and employ this
analysis to the deuteron number fluctuations to disentangle the two production
mechanisms. We argue that for a grand canonical cluster formation, the cluster
fluctuations will follow Poisson distribution, while for the coalescence
scenario, the fluctuations will strongly deviate from the Poisson expectation.
We estimate the effect to be 10% for the variance and up to a factor of 5 for
the kurtosis of the deuteron number multiplicity distribution. Our prediction
can be tested in the beam energy scan program at RHIC as well as experiments at
the FAIR and NICA facilities.
