We report the first measurements of cumulants, up to $4^{th}$ order, of deuteron number distributions and proton-deuteron correlations in Au+Au collisions recorded by the STAR experiment in phase-I of Beam Energy Scan (BES) program at the Relativistic Heavy Ion Collider. Deuteron cumulants, their ratios, and proton-deuteron mixed cumulants are presented for different collision centralities covering a range of center-of-mass energy per nucleon pair $\sqrt{s_{NN}}$~=~7.7 to 200~GeV. It is found that the cumulant ratios at lower collision energies favor a canonical ensemble over a grand canonical ensemble in thermal models. An anti-correlation between proton and deuteron multiplicity is observed across all collision energies and centralities, consistent with the expectation from global baryon number conservation. The UrQMD model coupled with a phase-space coalescence mechanism qualitatively reproduces the collision-energy dependence of cumulant ratios and proton-deuteron correlations.
Cumulants of the deuteron number distributions as a function of collision energy (from $\sqrt{s_{NN}}$ = 7.7 - 200 GeV) for most central (0 - 5$\%$), mid-central (30 - 40$\%$), and peripheral (70 - 80$\%$) Au+Au collisions. Cumulants are corrected for detector efficiency and centrality bin-width effect.
Cumulant ratios C2/C1, C3/C2, C4/C2 of deuteron number distributions and the Pearson correlation co-efficient between deuteron and proton distributions in 0-5$\%$ and 70-80$\%$ centralities in Au+Au collisions at nine energies from $\sqrt{s_{NN}}$ = 7.7 - 200 GeV.
Cumulant ratio C4/C2 of deuteron number distributions in 0-5$\%$ centrality in Au+Au collisions at nine energies from $\sqrt{s_{NN}}$ = 7.7 - 200 GeV.
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