Deuteron production from phase-space coalescence in the UrQMD approach

Ultrarelativistic quantum molecular dynamics phase-space coalescence calculations for the production of deuterons are compared with available data for various reactions from the Facility for Antiproton and Ion Research energy regime energy regime over the CERN Super Proton Synchrotron–Relativistic Heavy Ion Collider Beam Energy Scan region up to CERN Large Hadron Collider energies. It is found that the production process of deuterons, as reflected in their rapidity and transverse-momentum distributions in $p+p$, $p+A$, and $A+A$ collisions in the mentioned energy regime, are in good agreement with experimental data. We further explore the energy and centrality dependence of the $d$/$p$ and $\overline{d}/\overline{p}$ ratios and compare with thermal model results. Finally, we discuss antideuteron production for selected systems. Overall, a good description of the experimental data is observed. Most importantly this good description is based only on a single set of coalescence parameters that is independent of energy and system size and can also be applied for antideuterons.

Figure 1

Rapidity distributions of protons and deuterons in minimum bias $p$+Be (left) and $p$+Au (right) collisions at a beam energy of $14.6\mathrm{A}$ GeV from the UrQMD model (lines) compared to experimental E802 data (symbols) [18].

Figure 2

Energy dependence of $d/p$ and $\overline{d}$/ $\overline{p}$ ratios in $p+p$ collisions with $\left|y\right|<0.5$ at $\sqrt{s_{\mathit{NN}}}=53,900,2760$, and 7000 GeV. The open symbols represent UrQMD model results. The solid symbols denote the result from ISR (star) [19, 20, 21] and ALICE (circle and triangle) [22].

Figure 3

The $dN/d{y}^{\left(0\right)}$ distributions of deuterons, protons and ${\pi }^{-}$ for Ni+Ni collisions with $b\le 1.8$ fm at beam energies $1.93A\mathrm{GeV}$, $1.45A\mathrm{GeV}$, and $1.06A\mathrm{GeV}$ from our UrQMD simulation (lines) compared to the FOPI experimental data (symbols) [23].

Figure 4

Rapidity distributions of protons and deuterons (times 5) in Au+Au collisions at a beam energy of $10.8A\mathrm{GeV}$ with $b=3$ fm. Results of the present UrQMD study (dashed lines) are compared to data from the E917 collaboration [24].

Figure 5

Invariant yields of deuterons at $p_t=0$ as a function of rapidity in central (left) and minimum-bias (right) Au+Au collisions at a beam energy of $10.8A\mathrm{GeV}$. Data from the E878 Experiment [25] are shown as symbols and the model calculations as lines.

Figure 6

Rapidity distributions of protons and deuterons in Si+Au collisions at a beam energy of $14.6A\mathrm{GeV}$ with impact parameter $b=2$ fm comparing UrQMD results (lines) to data of E802 (symbols) [26].

Figure 7

Invariant yields of deuterons at $p_t=0$ as a function of rapidity in central (left) and minimum-bias (right) Si+Pb collisions at a beam energy of $14.6A\mathrm{GeV}$. Data of the E814 Experiment [28] are shown as symbols and the model calculations as lines.

Figure 8

Invariant yields of deuterons as a function of $m_t-m$ in central Si+Al, Si+Cu, and Si+Au collisions at a beam energy of $14.6A\mathrm{GeV}$. The rapidity interval is $y=0.5$ to 1.5 with $\mathrm{\Delta }y=0.2$. Each successive spectrum is divided by 100 for visual clarity. The symbols denote data of the E802 collaboration [26].

Figure 9

Deuteron yields as a function of rapidity in Pb+Pb collisions at a beam energy of $20A$ GeV for different centralities. The symbols denote data of the NA49 experiment [27].

Figure 10

Rapidity dependence of deuteron yields for various beam energies in Pb+Pb collisions for different centralities. The symbols denote data of the NA49 experiment [27], the lines show the calculations. Each spectrum is successively divided by a factor of 10.

Figure 11

Ratio of deuteron to protons+antiprotons in Pb+Pb collisions at $\sqrt{s_{\mathit{NN}}}=2.76$ TeV as a function of the charged particle multiplicity. In addition the values for proton-proton reaction at various energies are also indicated on the left part of the figure. The UrQMD results are compare to ALICE data [22, 39].

Figure 12

Invariant yields of antideuterons ($\overline{d}$) and antiprotons ($\overline{p}$) at $p_t=0$ as a function of rapidity in minimum-bias Si+Au collisions at a beam energy of $14.6A$ GeV. The symbols denote data of the experiments E814 [35] and E858 [38] and the histograms show results from the UrQMD model.

Figure 13

Energy dependence of the deuteron to proton ratio in Au+Au collisions with $b\le 4.6$ fm and $\left|y\right|<0.3$ at $\sqrt{s_{\mathit{NN}}}=2,5,7.7,11.5,14.5,17$, and 19.6 GeV. The solid lines represent UrQMD model results, the dotted lines denote the thermal model fit [31] and the symbols denote experimental data from various collaborations (down-triangle: SIS [30], hexagon: E802 [33], up-triangles: PHENIX [34], blue diamonds: NA49 [27], circles: STAR [32], pentagon: ALICE [29], square: E814 [35]). The blue horizontal line represents the UrQMD+hydro result on the $d$/$p$ ratio at 2.76 TeV and the green horizontal line represents the UrQMD result of the $\overline{d}/\overline{p}$ ratio in Si+Au collisions at $E_{\mathrm{lab}}=14.6A$ GeV.