Energy Dependence of Light Nuclei ($d$, $t$) Production at STAR

In high-energy nuclear collisions, the production of light nuclei is sensitive to the temperature and phase-space density of the system at freeze-out. In addition, the phase transition from QGP to the hadronic phase will lead to large baryon density fluctuation, which will be reflected in the light nuclei production. For example, the ratio of proton ($N(p)$) and triton ($N(t)$) to deuteron ($N(d)$) yields, which is defined as $N(t)$$\cdot$$N(p)$/$N^2(d)$, may be used as a sensitive observable to search for the QCD critical point. In this paper, we will report the energy dependence of light nuclei ($d$, $t$) production in Au+Au collisions at $\sqrt{s_{NN}}$ =7.7, 11.5, 14.5, 19.6, 27, 39, 62.4, and 200 GeV measured by the STAR experiment at RHIC. We will present the beam energy dependence for the coalescence parameter $B_2(d)$ and $B_3(t)$, particle ratios ($d/p$, $t/p$, and $t/d$), and the yield ratio of $N(t)$$\cdot$$N(p)$/$N^2(d)$. Their physics implications will be discussed.

In high-energy nuclear collisions, the production of light nuclei is sensitive to the temperature and phase-space density of the system at freeze-out. In addition, the phase transition from QGP to the hadronic phase will lead to large baryon density fluctuation, which will be reflected in the light nuclei production. For example, the ratio of proton (N (p)) and triton (N (t)) to deuteron (N (d)) yields, which is defined as N (t)·N (p)/N 2 (d), may be used as a sensitive observable to search for the QCD critical point. In this paper, we will report the energy dependence of light nuclei (d, t) production in Au+Au collisions at √ s N N =7. 7, 11.5, 14.5, 19.6, 27, 39, 62.4, and 200 GeV measured by the STAR experiment at RHIC. We will present the beam energy dependence for the coalescence parameter B 2 (d) and B 3 (t), particle ratios (d/p, t/p, and t/d), and the yield ratio of N (t)·N (p)/N 2 (d). Their physics implications will be discussed.

I. INTRODUCTION
In relativistic heavy-ion collisions, the most important goal is to study the properties of nuclear matter at high baryon density or temperature. The phase transition between the Quark-Gluon Plasma (QGP) and the hadronic matter is currently a topic of great interest [1]. Light nuclei are sensitive small binding energy, they are sensitive to the local nucleon density. Light nuclei production is described by coalescence [2] and thermodynamic models [3]. In the coalescence picture, the density of the cluster is proportional to the proton density times the probability of finding a neutron within a small sphere of radius around the proton momentum. Nucleon coalescence mechanism can be described as: where E p d 3 Np d 3 pp is the Lorentz-invariant momentum distribution of proton, A is the mass number, Z is the proton number, p A = Ap p . The coalescence parameter, B A , reflects the probability of nucleon coalescence, which is related to the local nucleon density [7].
Based on the coalescence picture, the yield ratio, N (t)·N (p)/N 2 (d), is sensitive to the neutron density fluctuation, ∆n= (δn) 2 / n 2 , at kinetic freeze-out in relativistic heavy-ion collisions, where n denotes the average value over space and δn denotes the fluctuation of neutron density from its average value n [9]. In this case, the yield ratio of light nuclei can be approximated as: In heavy-ion collisions, the created matter is expected to develop strong baryon density fluctuation [4]. When its evolution trajectory in the QCD phase diagram passes across the first-order phase transition line, a rapid increase of correlation length in the critical region has emerged as a results of the spinodal instability or approaches the CEP [9]. Therefore, light nuclei production at kinetic freeze-out in relativistic heavy-ion collisions may provide a unique probe to the critical endpoint in the QCD phase diagram.

II. RESULTS AND DISCUSSIONS
A. Transverse momentum spectra with increasing multiplicity/centrality [11]. The blast-wave fits are shown as dashed lines in Fig. 1.

B. Coalescence parameters
In the coalescence picture, the coalescence parameter, B A , reflects the probability of nucleon coalescence, which is related to the local nucleon density. The reference proton spectra for coalescence parameter extraction are from previous measurements by STAR [12]. In the left panel of

C. Integral yields and particle ratios
The yields of triton and deuteron are obtained by measured p T range and extrapolated to the unmeasured p T regions with various parameterizations. The extrapolation is done by the individual blast-wave fits [11]. We also show the yield ratios of d/p, t/p, and t/d as a function of collisions energy in 0-10% central Au+Au collision in Fig. 3. The proton yields are corrected for the feed-down contribution [12]. The dashed lines are the thermal model calculations, which employ parameters established from the analysis of light hadron production in relativistic nuclear collisions. The thermal model describes the ratios of d/p very well but overestimate the t/p and t/d particle ratios [8,13].

D. Neutron density fluctuation
The neutron density fluctuation, ∆n, extracted from yield of light nuclei is presented in Fig. 4.
A maximum around √ s NN = 20 GeV is found. This non-monotonic behavior indicates that the density fluctuations become the largest in collisions at this energy. When the evolution trajectory approaches the critical endpoint, the correlation length increases dramatically [10], and the density fluctuation enhances accordingly and reaches its maximum. The baryon density fluctuations are expected to be negligible if the phase transition from QGP to the hadronic matter is a crossover.
Therefore, nucleon density fluctuations at kinetic freeze-out in relativistic heavy-ion collisions may provide a unique probe to the critical endpoint in the QCD phase diagram, which need further studies, especially the precise measurements and theoretical understanding. and deuteron at the top RHIC energy. The d/p ratio can be reproduced by the thermal model but it cannot describe the triton production. We also measured the collision-energy dependence of neutron density fluctuation and a non-monotonic energy dependence with a peak at around 20 GeV was found, which may indicate that the thermodynamic evolution trajectories of the system pass through the critical region.