Formation of deuterons by coalescence: Consequences for deuteron number fluctuations

Two scenarios for cluster production have 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 the BNL Relativistic Heavy Ion Collider as well as experiments at the GSI Facility for Antiproton and Ion Research and the Nuclotron-based Ion Collider Facility.

Figure 1

Model parameter $B$ for model A (black squares) and resulting proton (in blue) and deuteron (in red) multiplicities as functions of energy. The resulting deuteron multiplicity is compared to the thermal fit (red line) input to our model.

Figure 2

Fluctuation of the deuteron number for Au+Au collisions at $\sqrt{s_{NN}}=2.6$ GeV beam energy in comparison to the Poisson distribution. The parameters of the distributions are for model A: ${\sigma }^2/\langle n_d\rangle =1.609,S\sigma =2.218,\kappa {\sigma }^2=6.915$; model B: ${\sigma }^2/\langle n_d\rangle =1.308,S\sigma =1.616,\kappa {\sigma }^2=3.422$.

Figure 3

Energy dependence of the moments ${\sigma }^2/\langle n_d\rangle ,s\sigma$, and $k{\sigma }^2$ of the deuteron distribution obtained from model A compared to the Poisson expectation.

Figure 4

Energy dependence of the moments ${\sigma }^2/\langle n_d\rangle ,s\sigma$, and $k{\sigma }^2$ of the deuteron distribution in the coalescence model assuming independent proton and neutron fluctuations (model B) compared to the Poisson expectation.

Figure 5

Energy dependence of the correlation coefficients between proton number and deuteron number in the case of coalescence with strongly correlated proton and neutron fluctuations (model A) and in the case of coalescence with independent proton and neutron fluctuations (model B).