Introduction

Quantum chromodynamics (QCD) is the fundamental theory of strong interactions that governs the strong interactions between quarks and gluons and serves as the cornerstone for understanding QCD matter. One of the major goals of ultra-relativistic nuclear collisions is to explore the properties of the QCD phase diagram [1], which shows the possible phases of QCD matter under different temperatures and baryon density conditions. According to lattice QCD calculations, a deconfinement transition from hadronic matter to a new state of matter called quark-gluon plasma (QGP) has been predicted at high temperatures and low baryon densities [2]. QGP is a state in which quarks and gluons are no longer confined inside hadrons but can move freely in a hot and dense medium. The existence of QGP has been confirmed by various experimental signatures observed in heavy-ion collisions at ultra-relativistic energies, such as the suppression of high transverse momentum (p_T) hadrons owing to jet quenching [3, 4] and the large elliptic flow (v₂) for hadrons owing to collective expansion [5-10].

After the discovery of strongly coupled QGP, efforts have been made to vary the collision energy and explore the phase structure of hot and dense QCD matter, which can be represented by the $T-{\mu }_{\text{B}}$ plane (T: temperature, μ_B: baryon chemical potential) of the QCD phase diagram. One of the most powerful tools for probing QCD phase diagrams is hadron production, which reflects the system's thermodynamic conditions during a chemical freeze-out. Hadron yields were measured from the AGS to LHC energies and can be described by a thermal statistical model, assuming that chemical equilibrium is reached [11-15]. The temperature T_ch and μ_B at chemical equilibrium, which are also referred to as the chemical freeze-out parameters when all hadron abundances are fixed, are determined from experimental data fitting.

One of the remarkable findings of previous studies on LHC energy was that the chemical freeze-out temperature T_ch=156.5±1.5 MeV obtained from the thermal fit to the hadron and light nuclei yields [14] was consistent with the pseudo-critical temperature T_c = 154±9 MeV obtained from lattice QCD calculations [16] within a certain uncertainty. This suggests that chemical freeze-out occurred close to the phase boundary between the QGP and hadronic matter. The data used for the thermal fit were from ALICE Collaboration, which measured not only hadrons but also light nuclei, such as $d\left(\overline{d}\right)$, ${}^3\text{He}\left({}^3\overline{\text{He}}\right)$, ${}^4\text{He}\left({}^4\overline{\text{He}}\right)$, and hyper-triton ${}_{\text{Λ}}^3\text{H}$ [14]. Meanwhile, a T_ch of 167.8±4.2 MeV extracted via thermal fitting at the RHIC top energy was higher than the value at the LHC and T_c [12], while only hadron yields were included in the fitting. Additionally, the authors also reported that when the fit is limited to the yields of pions, kaons, and protons, the derived T_ch is approximately 10–15 MeV lower than that of fits that include the yields of hadrons with strange quarks. Furthermore, at the LHC energy, it was found that considering two distinct freeze-out temperatures for non-strange and strange hadrons could provide a better fit to the ALICE data [17]. Specifically, by analyzing energies ranging from 11.5 GeV to 5.02 TeV in Ref. [18], a light-flavor freeze-out temperature of T_L=150.2±6 MeV and a strange-flavor freeze-out temperature of T_s=165.1±2.7 MeV at vanishing μ_B were identified. These findings indicate that strange and non-strange hadrons are produced at distinct freeze-out hypersurfaces, which shows evidence of flavor-dependent chemical freeze-out temperatures, at least in the crossover region of the QCD phase diagram. However, these results do not fully account for the differences in T_ch between the RHIC top energy and LHC energy, as both fits include yields for both strange and non-strange hadrons. By comparing the particles used in the fits at RHIC and LHC, it appears that the yield of light nuclei may be the only factor that could account for the differences in the results. Therefore, this study aimed to investigate whether the inclusion of light nuclei yields in RHIC experiments leads to changes in T_ch, and whether light nuclei have their own distinct T_ch.

In relativistic heavy-ion collisions, the detailed mechanisms underlying the production of light nuclei are not fully understood [19-29]. A widely discussed theory suggests that light nuclei are formed by the coalescence of nucleons during the final stages of collisions [30, 31]. This scenario clearly implies that the production of light nuclei occurs later than that of other hadrons and, consequently, at a lower temperature than that at which other hadrons are formed. Additionally, the thermal model offers an alternative perspective [14, 32, 33] in which protons, neutrons, and light nuclei are considered to reach a state of chemical equilibrium. In this scenario, light nuclei and nucleons are presumed to be produced concurrently, suggesting that their freeze-out temperatures are identical or similar to those of light-flavor hadrons. One particular study highlighted in Ref. [21] demonstrated that the yield of (anti-)deuterons remained relatively stable throughout the system's evolution, given that it was thermally initialized at the LHC energy. The (anti-)deuteron can be destroyed and created through the reaction $\pi d\leftrightarrow \pi pn$, indicating that the thermal model, despite its different foundational assumptions, may yield similar (anti-)deuteron yields as the coalescence model. Therefore, studying the chemical freeze-out temperature of light nuclei can provide valuable insights into the light nuclei production mechanisms, aiding our understanding of the evolution of fireballs produced in relativistic heavy-ion collisions.

To study the effects of light nuclei on T_ch, we utilized the statistical thermal model Thermal-FIST to analyze the yields of hadrons [12], (anti-)deuterons [20], and tritons [34] at RHIC energies. We compared the extracted freeze-out parameters across various particle yield sets and discussed the underlying physics of the production of strange, light-flavor, and light nuclei. In Sect. 2, we provide a brief introduction to the employed Statistical Thermal Model and selected particle sets. Subsequently, in Sect. 3, we present and discuss the results. Finally, Sect. 4 summarizes our study and findings.

Model and Particle Sets

The chemical properties of bulk particle production can be treated within the framework of thermal statistical models using the Thermal-FIST package [35]. This package is designed for convenient general-purpose physics analysis and is well-suited for the family of hadron resonance gas (HRG) models. Notable features of this package include the treatment of fluctuations and correlations of conserved charges, the effects of probabilistic decay, chemical non-equilibrium, and the inclusion of van der Waals hadronic interactions. However, in our study, we opted for an ideal non-interacting gas of hadrons and resonances within a Grand Canonical Ensemble (GCE) for simplicity and focus on the fundamental aspects of particle production. In GCE, all conserved charges, such as the baryonic number B, electric charge Q, strangeness S, and charm C, are conserved on average. For the chemical equilibrium case, these average values are regulated by their corresponding chemical potentials, μB, μS, μQ, and μC. The chemical potential μi of hadron species i is determined as ${\mu }_i=B_i{\mu }_B+S_i{\mu }_S+Q_i{\mu }_Q+C_i{\mu }_C\mathrm{.}$ (1) The particle density of hadron species i can be parameterized as $n_i\left(T\mathrm{,}{\mu }_i\right)=g_i{\displaystyle \int }\frac{d^{3}p}{{\left(2\pi \right)}^3}{\left[{\gamma }_{\text{s}}^{-\left|{S^{\prime }}_i\right|}\exp \left(\frac{E_i-{\mu }_i}{T_{\text{ch}}}\right)+{\eta }_i\right]}^{-1}\mathrm{,}$ (2) where gi, $E_i=\sqrt{p^2+m_i^2}$, and mi are the spin degeneracy factor, energy, and mass of hadron species i, respectively,. ηi is +1 for fermions, -1 for bosons, and 0 for the Boltzmann approximation. The quantum statistic is considered only for mesons, that is, ${\eta }_i=-1$ for π^±and K^±, whereas ${\eta }_i=0$ for other particles. Finite resonance widths with a Breit-Wigner form mass distribution were considered in our fitting [36]. μQ and μS are determined in a unique manner to satisfy two conservation laws given by the initial conditions: the electric-to-baryon charge ratio of Q/B = 0.4 for Au+Au collisions and the vanishing net strangeness S = 0. γ_s is the strangeness undersaturation factor that regulates the deviation from the chemical equilibrium of strange quarks. ${S^{\prime }}_i$ is the number of strange and anti-strange valence quarks in particle i. γ_s=1 corresponds to the chemical equilibrium for strange quarks.

The hadron yield of π^±, K^±, $p\left(\overline{p}\right)$ [12, 37-39], $\text{Λ}\left(\overline{\text{Λ}}\right)$, ${\text{Ξ}}^{-}\left({\overline{\text{Ξ}}}^{+}\right)$[24, 40, 41] and light nuclei yield of $d\left(\overline{d}\right)$ [20], and t [34] for Au+Au collision at $\sqrt{s_{\text{NN}}}$ = 7.7–200 GeV were used in the analysis. The yields of $p\left(\overline{p}\right)$ are inclusive and are not corrected for the feed-down contribution from weak decay. The Thermal-FIST package allows the assignment of separate decay chains to each input. In the model, the total yield Ni of the i-th particle species is calculated as the sum of the primordial yield $N_i^{*}$ and the resonance decay contributions, as follows: $N_i=N_i^{*}+{\displaystyle \sum _j\text{B}{\text{.R}}_{ji}}\times N_j\mathrm{,}$ (3) where $\text{B}{\text{.R}}_{ji}$ denotes the branching ratio of the j-th to the i-th particle species. Therefore, it matched the specific feed-down corrections of a particular dataset. Four centralities, 0%–10%, 10%–20%, 20%–40%, and 40%–80%, were selected to maintain consistency with the triton analysis [34]. Data across various centralities were consolidated by averaging, allowing the determination of representative values for the defined centrality classes. Three different sets of particle yields are listed in Table 1. The first set is the same as that in Ref. [12], which includes the yields of π^±, K^±, $p\left(\overline{p}\right)$, $\text{Λ}\left(\overline{\text{Λ}}\right)$, and ${\text{Ξ}}^{-}\left({\overline{\text{Ξ}}}^{+}\right)$. The yields of light nuclei $d\left(\overline{d}\right)$ and t are included in the second particle set. In Particle Set III, we excluded all mesons and hadrons, meaning that only $d\left(\overline{d}\right)$ and t are included. The three particle sets are presented in Table 1. Therefore, only four parameters were fitted. For Particle Sets I and II, the fitting process involves four parameters: T_ch, the baryon chemical potential μ_B, the strangeness undersaturation factor γ_s, and the fireball radius V (the fireball volume is $V=4/3\pi R^3$). However, for Particle Set III, which does not include strange particles, the strangeness undersaturation factor γ_s is fixed at 1, resulting in only three parameters being fitted. Because there are only three particle yields for fitting in Particle Set III, a perfect fit with zero degrees of freedom is obtained; therefore, a ${\chi }^2/dof$ for the fit cannot be obtained.

Results

The detailed fitting outcomes for each energy, encompassing V and ${\chi }^2/dof$, are presented in Table 2 for collision energies $\sqrt{s_{\text{NN}}}$ = 200, 62.4, 39, and 27 GeV. The outcomes for lower collision energies, $\sqrt{s_{\text{NN}}}$ = 19.6, 14.5, 11.5, and 7.7 GeV, are presented in Table 3. It is wort noting that for Particle Set III, at 11.5 GeV of 40%–80% centrality and 7.7 GeV of all centralities, the experimental data for $\overline{d}$ is absent. Because of the lack of sufficient experimental data, specifically, with only two yield data points (d and t) for the three fitting parameters (T_ch, μ_B, V), it was impossible to accurately determine the chemical freeze-out parameters.

The upper panel of Fig. 1 shows a comparison between the particle yield per unit rapidity dN/dy and the Thermal-FIST package fitting results for Au+Au collisions at $\sqrt{s_{\text{NN}}}$=200 GeV within the 0%–10% centrality interval. The STAR experimental data are depicted by red circles, while the model data are represented by bars of different colors. Different freeze-out parameters were obtained for the two particle sets. When the light nuclei were not considered (magenta solid bars), T_ch was 163.5±3.8 MeV, which significantly decreased to 152.0±1.1 MeV after the light nuclei yield was included in the fitting (blue dashed bars). The inclusion of light nuclei resulted in a noticeably lower fitting temperature. Additionally, as presented in Table 2, if only the light nuclei yield is used for the fitting, the temperature is further reduced to 137.6±3.4 MeV. Similar to the conclusions in Ref. [18], we can speculate that not only do light and strange flavors have different freeze-out temperatures, but light nuclei also achieve lower freeze-out temperatures. Three experiments were conducted on different freeze-out surfaces. A possible reason for this is that light nuclei production occurs at a later collision stage, at least within the STAR energy region, where the light nuclei production mechanism occurs through coalescence. Because light nuclei originate from the recombination of nucleons in the coalescence model, we also investigated the effect of including the yields of $p\left(\overline{p}\right)$ in the fitting for Particle Set III. We found that T_ch increased by 1~2 MeV. For instance, in the 0%–10% central collisions at 200 GeV, the inclusion of yield $p\left(\overline{p}\right)$ resulted in a T_ch change from 137.6±3.4 to 138.4±1.9 MeV. Although there was an increase, this value remained significantly lower than the T_ch obtained from Particle Set II.

Fig. 1Full-screen View

Particle yield and predictions of the Thermal-FIST package. Upper panel: dN/dy values (red circles) from different hadrons and nuclei, measured at mid-rapidity, compared with the fit results from Particle Sets I (magenta solid bars) and II (blue dashed bars). The experimental data are from the STAR Collaboration for 0%–10% Au+Au collisions at $\sqrt{s_{\text{NN}}}=200$ GeV. Lower panel: standard deviation σ between the fit and experimental data

The μ_B values obtained from the two fittings remained consistent within error. The lower panel of Fig. 1 shows the standard deviations (Std. Dev.) for different particles in the two fittings. It is evident that the deviations of strange-flavor particles K^±, $\text{Λ}(\overline{\text{Λ}})$, and ${\text{Ξ}}^{\pm }$ significantly increased after the inclusion of light nuclei, whereas the deviations of light-flavor particles π^± and $p\left(\overline{p}\right)$ decreased. This can also be explained by our previous conclusions: because the freeze-out temperature difference between strange-flavor particles and light nuclei is significant and the difference between light-flavor particles and light nuclei is relatively small, the inclusion of light nuclei cannot fit the strange-flavor particles well but can improve the fitting for light-flavor particles.

Figure 2 shows a series of graphs displaying the centrality dependence of T_ch from the Thermal-FIST fit with the three different particle sets for Au+Au collisions at $\sqrt{s_{\text{NN}}}$ = 7.7–200 GeV. As can be seen, with an increase in centrality, that is, from central to peripheral collisions, for different collision energies and particle sets, T_ch exhibits a consistent trend, remaining independent of centrality within error. Additionally, it is evident that the three particle sets yield three distinct T_ch ranges in the fitting. When light nuclei were included in the fitting, as observed in the transition from Particle Set I to Particle Set II (solid circles to solid triangles in the figure), T_ch decreased. For instance, at $\sqrt{s_{\text{NN}}}$ = 200 GeV, the decrease is approximately 10 MeV, whereas at other collision energies, it is approximately 5 MeV. More notably, when considering only light nuclei, as in Particle Set III (open circles in the figure), T_ch decreases even further compared with Particle Set II, which includes all particles. For example, at $\sqrt{s_{\text{NN}}}$ = 200 GeV, this difference reaches approximately 14 MeV, and at a lower energy of 11.5 GeV, it is approximately 9 MeV. These differences clearly distinguish the open circles from the other two categories in the figure. This also indicates that light nuclei indeed reach chemical freeze-out at a different time than other particles and are produced later in the collision process.

Fig. 2Full-screen View

Centrality dependence of chemical freeze-out parameters T_ch from the Thermal-FIST fit with Particle Sets I (solid red circles), II (solid blue triangles), and III (open black circles) listed in Table 2 in Au+Au collisions at $\sqrt{s_{\text{NN}}}$ = 7.7–200 GeV

To systematically study the particle production stages, Figure 3 shows the variation in VT^3/2 with collision centrality for the different particle sets at various collision energies. According to the Sackur–Tetrode equation [42], under non-relativistic conditions, VT^3/2 is directly related to the entropy per nucleon (S/N) [43]. $\frac{S}{N}=\ln \frac{V{T}^{3/2}}{N}+\text{const}\mathrm{.}$ (4) After chemical freeze-out, the number of particles remains essentially constant; therefore, the magnitude of VT^3/2 essentially reflects the change in the entropy of the system. It is well known that the evolution of an isolated system always proceeds in the direction of increasing entropy. In other words, the magnitude of VT^3/2 can reflect the system's evolution process sequence; that is, for the same system, a smaller VT^3/2 indicates an earlier system evolution stage, whereas a larger VT^3/2 indicates a later system evolution stage. As shown in Fig. 3, when the yield of light nuclei is included, that is, when transitioning from Particle Set I to Particle Set II, the system's VT^3/2 increases. If only the yield of light nuclei is considered, an even larger VT^3/2 is obtained, which also indicates that at RHIC energies, light nuclei are likely to be produced later in the evolution, rather than at a slightly earlier strange hadron freeze-out time. Similarly, it can be observed that for a certain collision energy and a certain particle set, VT^3/2 is larger in central collisions, meaning that each particle carries more entropy and there is a higher disorder degree in central collisions. Additionally, for a certain collision centrality and a certain particle set, VT^3/2 decreases with a decrease in the collision energy, meaning that the entropy carried by each particle is smaller at lower energies than at higher energies, which is understandable.

Fig. 3Full-screen View

Centrality dependence of VT^3/2 calculated by the chemical freeze-out parameters from the Thermal-FIST fit with Particle Sets I (solid red circles), II (solid blue triangles), and III (open black circles) listed in Table 2 in Au+Au collisions at $\sqrt{s_{\text{NN}}}$ = 7.7–200 GeV

To provide a clear visual representation of the system's location in the two-dimensional $T-{\mu }_{\text{B}}$ phase diagram at chemical freeze-out, Figure 4 shows the chemical freeze-out parameters, T_ch and μ_B, as a function of collision energy in Au+Au collisions. For enhanced readability and mitigate the visual clutter that can result from overlapping data points, the results for collision energies of 62.4, 27, and 14.5 GeV were intentionally excluded. Additionally, the outcomes for different collision energies are delineated using elliptical dashed lines. It can be observed that, within the same particle set, T_ch decreases with decreasing collision energy. However, it is worth noting that for Particle Set III, which includes only light nuclei yields, this collision energy dependence is quite weak, remaining at T_ch≈140 MeV. In other words, the chemical freeze-out temperature for light nuclei, or their coalescence temperature, was approximately 140 MeV. This observation may potentially explain why the freeze-out temperatures derived from the top energy at RHIC [12] are higher than those obtained from the LHC results [14], as the LHC fits incorporate multiple light nuclei yields. As the collision energy decreases, μ_B increases. This is attributed to a decrease in antibaryon production, leading to an increased net baryon density, and consequently, an increase in μ_B. Furthermore, the different particle sets yielded consistent results for μ_B. Moreover, the three different particle sets clearly define three separate bands on the diagram, indicating that at RHIC energies, light nuclei and other hadrons are likely to exist on distinct freeze-out hypersurfaces.

Fig. 4Full-screen View

Chemical freeze-out parameters T_ch and μ_B as a function of collision energy in Au+Au collisions. Data points represent the results from the Thermal-FIST fit with particle sets I (solid red circles), II (solid blue triangles), and III (open black circles) listed in Table 2 in Au+Au collisions at $\sqrt{s_{\text{NN}}}$ = 200, 39, 19.6, 11.5, and 7.7 GeV. Elliptical dashed lines represent the results corresponding to different collision energies

Parameterization equations for the chemical freezing parameters T_ch and μ_B, using the collision energy $\sqrt{s_{\text{NN}}}$ as a variable, are detailed in Ref. [14]. The equations are as follows: $\begin{array}{ll}{T}_{\text{ch}}\hfill & =T_{\text{ch}}^{\text{lim}}\frac{1}{1+\exp \left\{a-\ln \left[\sqrt{s_{\text{NN}}}\left(\text{GeV}\right)\right]/b\right\}}\hfill \\ {\mu }_{\text{B}}\hfill & =\frac{c}{1+d\sqrt{s_{\text{NN}}}\left(\text{GeV}\right)}\hfill \end{array}$ (5) These parameterized equations utilize experimental fit data from both the STAR and LHC collaborations. The chemical freeze-out parameters for these experiments were fitted using various particle sets as previously discussed. It is evident from the previous discussion that incorporating light nuclei into the fitting process significantly influenced the derived chemical freeze-out temperatures. Therefore, determining the chemical freeze-out parameters of the different particle sets is crucial. Figure 5 presents the chemical freeze-out parameters, including T_ch and μ_B, obtained through fits with various particle sets in central Au+Au collisions. Detailed parameters are listed in Table 4. It is evident that the fitted parameters exhibit notable differences, particularly $T_{\text{ch}}^{\text{lim}}$, which indicates the highest temperature achievable during hadronic chemical freeze-out. This parameter also represents the maximum temperature at which the hadron resonance gas can exist before transitioning to quark–gluon plasma. For fits excluding light nuclei yields, such as in Particle Set I, this value is 161.8±3.6 MeV, which is higher than the value reported in Ref. [14]. When the light nuclei yield is incorporated into the fitting process, as in Particle Set II, the parameterized $T_{\text{ch}}^{\text{lim}}$ decreases to 153.5±1.4 MeV. Similarly, other parameters align with those obtained in Ref. [14], indicating that the results from the Particle Set II fit are consistent with the derived parameterized equations. However, when considering only light nuclei yields, as in Particle Set III, $T_{\text{ch}}^{\text{lim}}$ further decreases to 141.7±1.4 MeV, which is notably lower than that in the other two sets. This suggests that light nuclei and other hadrons are likely to exist on two distinct freeze-out hypersurfaces. Owing to the absence of fit results for 7.7 GeV in Particle Set III, we were unable to determine the behavior of T_ch at lower energies from the existing data. Additional experimental data encompassing a variety of light nuclei yields could enhance the characterization of this energy dependence.

Fig. 5Full-screen View

Chemical freeze-out parameters T_ch and μ_B as a function of the center-of-mass collision energy for Au+Au central collisions. The curves represent parametrizations for T_ch and μ_B from Eq. (5)

Using the energy-dependent relationship between the chemical freeze-out parameters T_ch and μ_B, we calculated the yields of various hadrons and plotted the chemical freeze-out line on a two-dimensional phase diagram at the RHIC energies. This line can provide information for determining the phase boundary from the hadronic matter to the quark-gluon plasma. Figure 6 shows the chemical freeze-out line. Because of insufficient light nuclei yield data at 7.7 GeV, for Particle Set III, we only show the region where μ_B < 320 MeV. It is evident that the chemical freeze-out lines differ for various particle sets. The lines for light nuclei (Particle Set III) and hadrons without light nuclei (Particle Set I) are distinctly separated, indicating that light nuclei and other hadrons freeze at different hypersurfaces. In conjunction with the results reported in Ref. [18], we can identify at least three different chemical freeze-out temperatures at the RHIC energies: the light-flavor freeze-out temperature T_L = 150.2±6 MeV, strange-flavor freeze-out temperature T_s = 165.1±2.7 MeV, and light-nuclei freeze-out temperature T_ln = 141.7±1.4 MeV. The fireball produced after the relativistic heavy-ion collisions exhibited three distinct freeze-out hypersurfaces. The first pertains to strange hadrons, which are expected to have relatively smaller hadronic interaction cross sections than light hadrons. Consequently, the primary yield of strangeness particles experiences little change from the phase-transition stage owing to hadronic interactions [44, 45]. As a result, they can carry temperature information from the quarks' chemical equilibrium, which is higher than the temperature at which light hadron chemical freeze-out occurs, and exhibit a clear chemical freeze-out sequence throughout the system's evolution. The light nuclei yields evolve as the system progresses, indicating that they reach chemical equilibrium much later; that is, they freeze out of the system at lower temperatures. This observation is crucial for understanding the complex particle production dynamics and thermodynamic evolution of the medium created in heavy-ion collisions.

Fig. 6Full-screen View

Chemical freeze-out temperature T_ch versus baryon chemical potential μ_B from central Au+Au collisions at $\sqrt{s_{\text{NN}}}$= 7.7–200 GeV. Data points represent the results from the Thermal-FIST fit with particle sets I (solid red circles), II (solid blue triangles), and III (open black circles) listed in Table 2. The curves represent parametrizations for T_ch and μB from Eq. (5)

It should be emphasized that our conclusions are based on existing experimental data from RHIC energies, indicating that our findings are reliable for RHIC energies. To verify whether our conclusions hold for the LHC energy, we repeated the fitting process using experimental data from the LHC. During the fitting process, we replicated the particle set in Ref. [14] and subsequently performed fits using particle sets I–III, as presented in this study. It is worth noting that owing to the absence of triton experimental data at the LHC, we utilized the yield data of ³He as a proxy for the triton yields in the fitting procedure. We also utilized all available light nuclei yield data from the LHC, including $d\mathrm{,}\overline{d}$, ³He, ${}^3\overline{\text{H}}\text{e}$, ⁴He, and ${}^4\overline{\text{H}}\text{e}$, for the fitting, which is labeled Particle Set IV. The final set, labeled as Particle Set V, includes the yields of hypertriton ${}_{\text{Λ}}^3\text{H}$ and its antiparticle ${}_{\overline{\text{Λ}}}^3\overline{\text{H}}$. Six particle sets were fitted and the results are presented in Table 5.

As can be seen in the table, in the LHC energy, specifically for Pb+Pb collisions at $\sqrt{s_{\text{NN}}}$ = 2.76 TeV, the inclusion or exclusion of light nuclei yields in the fitting process does not significantly affect the derived T_ch. Fitting using the yield of all particles (first row in the table), fitting without the light nuclei yield (particle set I), and fitting with the inclusion of d, $\overline{d}$, and ${}^3\text{He}$ yields (particle set II) result in chemical freeze-out temperatures T_ch that are consistent within error. Other chemical freeze-out parameters, such as μ_B, γ_s, and V, were found to be consistent within error. The primary difference is that fitting with more particles reduces the ${\chi }^2/dof$. More interestingly, when only the light nuclei yields are incorporated into the fitting process, a higher T_ch is obtained, approximately 158-159 MeV. Regardless of the light nuclei particle set, the resulting T_ch is consistent, and this temperature is higher than that of the other particles. This is in contrast to the conclusions drawn from the RHIC energies, where the chemical freeze-out temperature of light nuclei is approximately 10 MeV lower than that of light-flavor hadrons, whereas at the LHC $\sqrt{s_{\text{NN}}}$ = 2.76 TeV, the chemical freeze-out temperature of light nuclei is approximately 10 MeV higher than that of light-flavor hadrons. Given the difference in the experimental data errors between RHIC and LHC, we investigated the impact of these data errors on the fitting results by artificially reducing the original experimental errors by 50% for the 0%–10% central Au+Au collisions at $\sqrt{s_{\text{NN}}}=200$ GeV. The fitting results indicate that this adjustment did not alter the central values of the fitted parameters, but rather affected the magnitude of the errors. For instance, for Particle Set I, T_ch shifts from 163.5±3.8 to 163.5±1.9 MeV.

Recently, the ALICE Collaboration published thermodynamic fitting results for Pb+Pb collisions at 5.02 TeV, where it was found that a T_ch of 155±2 MeV provided an excellent fit to the experimental data at $\sqrt{s_{\text{NN}}}=5.02$ TeV [46]. This result is similar to that obtained using Particle Set II at 2.76 TeV. Additionally, the ALICE Collaboration published results on light nuclei yields [47]. To verify our findings at 5.02 TeV, we performed a similar fitting using these light nuclei yields by selecting the yields of four particles: d, $\overline{d}$, ${}^3\text{He}$, and ${}^3\overline{\text{H}}\text{e}$. We obtained a T_ch of 145.8±0.7 MeV, as listed in Table 6, which is lower than the result reported in the ALICE paper. Based on our results, we found that the ALICE Pb+Pb collisions at $\sqrt{s_{\text{NN}}}=2.76$ and 5.02 TeV yield opposite outcomes. At the LHC $\sqrt{s_{\text{NN}}}=2.76$ TeV, the chemical freeze-out temperature of light nuclei is higher than that of light- and strange-flavor hadrons. However, at the ALICE Pb+Pb $\sqrt{s_{\text{NN}}}=5.02$ TeV, the chemical freeze-out temperature of light nuclei is lower than that of light- and strange-flavor hadrons. These results are consistent with our conclusions for RHIC and aligns with the findings of Ref. [48], which indicates that deuterons and tritons chemically freeze out in the late hadronic stage.

The peculiarity of the results at 2.76 TeV might arise from two main factors. First, the light nuclei production mechanisms may differ at 2.76 TeV. However, there are no compelling reasons to suspect that the particle production mechanisms vary among the top energy at RHIC and the 2.76 and 5.02 TeV collisions at the LHC, all of which are high-energy collision systems. Second, energy-dependent effects may influence the collision dynamics and the resulting particle yields. However, based on our findings, we cannot provide a definitive answer, requiring further research to gain a deeper understanding of the processes underlying light nuclei production.

Summary

Thermodynamic statistical model fitting enables precise determination of chemical freeze-out parameters T_ch and μ_B during relativistic heavy-ion collisions. These parameters offer crucial insights into the phase transition from QGP to hadronic matter. In this study, we utilized the Thermal-FIST Grand Canonical Ensemble fit to analyze the experimental data from RHIC Au+Au collisions at collision energies of $\sqrt{s_{\text{NN}}}$ = 7.7–200 GeV. The chemical freeze-out parameters of the system were determined using various particle sets and collision centralities. Different particle sets yield different chemical freeze-out temperatures, with light nuclei achieving lower freeze-out temperatures. Additionally, we examined VT^3/2 for different particle sets, which reflected the entropy per particle (S/N) of the system. We found that when considering only light nuclei, VT^3/2 was larger, indicating higher entropy and suggesting that light nuclei are produced at a later system evolution stage. We also obtained the parameterized chemical freeze-out parameters T_ch and μ_B. Similar to the conclusions of previous studies, these findings indicate the existence of multiple chemical freeze-out hypersurfaces for different hadron types at RHIC energies. Concurrently, the experimental data indicate three distinct chemical freeze-out temperatures: a light-flavor freeze-out temperature T_L = 150.2±6 MeV, a strange-flavor freeze-out temperature T_s = 165.1±2.7 MeV, and a light-nuclei freeze-out temperature T_ln = 141.7±1.4 MeV. When applying our research methodology to LHC energies, we observed similar results for Pb+Pb 5.02 TeV, where the light-nuclei chemical freeze-out temperature was lower than that for light-flavor hadrons. However, at Pb+Pb 2.76 TeV, we did not observe a lower light-nuclei freeze-out temperature. By contrast, the light-nuclei chemical freeze-out temperature was approximately 10 MeV higher than that for light-flavor hadrons. This indicates that energy-dependent effects influence the collision dynamics and the resulting particle yields. We aim to address this issue in future work.