Effect of the QCD equation of state and strange hadronic resonances on multiparticle correlations in heavy ion collisions

The QCD equation of state at zero baryon chemical potential is the only element of the standard dynamical framework to describe heavy ion collisions that can be directly determined from first principles. Continuum extrapolated lattice QCD equations of state have been computed using 2+1 quark flavors (up/down and strange) as well as 2+1+1 flavors to investigate the effect of thermalized charm quarks on QCD thermodynamics. Lattice results have also indicated the presence of new strange resonances that not only contribute to the equation of state of QCD matter but also affect hadronic afterburners used to model the later stages of heavy ion collisions. We investigate how these new developments obtained from first principles calculations affect multiparticle correlations in heavy ion collisions. We compare the commonly used equation of state S95n-v1, which was constructed using what are now considered outdated lattice results and hadron states, to the current state-of-the-art lattice QCD equations of state with 2+1 and 2+1+1 flavors coupled to the most up-to-date hadronic resonances and their decays. New hadronic resonances lead to an enhancement in the hadronic spectra at intermediate $p_T$. Using an outdated equation of state can directly affect the extraction of the shear viscosity to entropy density ratio, $\eta /s$, of the quark-gluon plasma and results for different flow observables. The effects of the QCD equation of state on multiparticle correlations of identified particles are determined for both AuAu $\sqrt{s_{\text{NN}}}=200$ GeV and PbPb $\sqrt{s_{\text{NN}}}=5.02$ TeV collisions. New insights into the $v_2\left\{2\right\}$ to $v_3\left\{2\right\}$ puzzle in ultracentral collisions are found. Flow observables of heavier particles exhibit more nonlinear behavior regardless of the assumptions about the equation of state, which may provide a new way to constrain the temperature dependence of $\eta /s$.

Figure 1

Trace anomaly of QCD with 2+1 and 2+1+1 flavors computed by the Wuppertal-Budapest Collaboration [3, 5] compared to the corresponding EoS constructed here.

Figure 2

Trace anomaly of the equation of state S95n-v1 [15] compared to results for the equations of state for 2+1 and 2+1+1 flavors constructed here using state-of-the-art lattice results by the Wuppertal-Budapest collaboration [3, 5].

Figure 3

(a) Pressure, (b) energy density, (c) entropy density, and (d) speed of sound of EoS S95n-v1 [15] compared to the corresponding quantities determined using the EoS constructed here for 2+1 and 2+1+1 flavors that employed state-of-the-art lattice results by the Wuppertal-Budapest collaboration [3, 5].

Figure 4

$v_2\left\{2\right\}$ and $v_3\left\{2\right\}$ results across centrality for AuAu $\sqrt{s_{\text{NN}}}=200$ GeV (a) and PbPb $\sqrt{s_{\text{NN}}}=5.02$ TeV (b) collisions for all charged particles for the S95n-v1 EoS from 2009 (red, dashed lines) [15], the 2+1 flavor WB EoS (black, full lines) [3], and the 2+1+1 WB EoS from 2016 (blue, dot-dashed lines) [5].

Figure 5

Spectra of $\pi$'s, $p$'s, and $K$'s in the centrality class $0-5\%$ for RHIC AuAu $\sqrt{s_{\text{NN}}}=200$ GeV (a) and the corresponding predictions for LHC PbPb $\sqrt{s_{\text{NN}}}=5.02$ TeV (b) collisions computed using the S95n-v1 EoS from 2009 [15], the 2+1 WB EoS from [3], and the 2+1+1 WB EoS from 2016 [5]. Experimental data points from PHENIX collaboration [66] (a).

Figure 6

$\langle p_T\rangle$ results for ${\pi }^{+}$'s, $K^{+}$'s and p's compared to AuAu $\sqrt{s_{\text{NN}}}=200$ GeV STAR data [68] (a) and our corresponding predictions for PbPb $\sqrt{s_{\text{NN}}}=5.02$ TeV collisions (b) computed using the S95n-v1 EoS from 2009 [15], the 2+1 WB EoS from [3], and the 2+1+1 WB EoS from 2016 [5].

Figure 7

Pearson coefficient results for $v_2$ of all charged particles for AuAu $\sqrt{s_{\text{NN}}}=200$ GeV collisions (a) and PbPb $\sqrt{s_{\text{NN}}}=5.02$ TeV collisions (b) computed using the S95n-v1 EoS from 2009 [15], the 2+1 WB EoS from [3], and the 2+1+1 WB EoS from 2016 [5].

Figure 8

Pearson coefficient results for $v_2$ of various identified particles in AuAu $\sqrt{s_{\text{NN}}}=200$ GeV collisions (a) and PbPb $\sqrt{s_{\text{NN}}}=5.02$ TeV collisions (b) computed using the 2+1+1 WB EoS [5].

Figure 9

$v_2\left\{2\right\}/v_3\left\{2\right\}$ results in AuAu $\sqrt{s_{\text{NN}}}=200$ GeV collisions (a) and PbPb $\sqrt{s_{\text{NN}}}=5.02$ TeV collisions (b) for all charged particles computed using the S95n-v1 EoS from 2009 [15], the 2+1 WB EoS from Ref. [3], and the 2+1+1 WB EoS from 2016 [5]. Experimental data for LHC $\sqrt{s_{\text{NN}}}=2.76$ TeV from CMS [80] are included for comparison (error propagation was implemented to obtain the error of the ratio, which was not originally presented by CMS).

Figure 10

$v_2\left\{4\right\}/v_2\left\{2\right\}$ (a), (b) and $v_3\left\{4\right\}/v_3\left\{2\right\}$ (c), (d) results for AuAu $\sqrt{s_{\text{NN}}}=200$ GeV collisions (a), (c) and PbPb $\sqrt{s_{\text{NN}}}=5.02$ TeV collisions (b), (d) for all charged particles computed using the S95n-v1 EoS from 2009 [15], the 2+1 WB EoS from Ref. [3], and the 2+1+1 WB EoS from 2016 [5]. The green dashed line is the calculation using ${\varepsilon }_n\left\{4\right\}/{\varepsilon }_n\left\{2\right\}$.

Figure 11

$v_2\left\{6\right\}/v_2\left\{4\right\}$ results for AuAu $\sqrt{s_{\text{NN}}}=200$ GeV collisions (a) and PbPb $\sqrt{s_{\text{NN}}}=5.02$ TeV collisions (b) for all charged particles computed using the S95n-v1 EoS from 2009 [15], the 2+1 WB EoS from [3], and the 2+1+1 WB EoS from 2016 [5]. The green dashed line is the calculation using ${\varepsilon }_2\left\{6\right\}/{\varepsilon }_2\left\{4\right\}$.

Figure 12

${\left(v_4\left\{4\right\}\right)}^4$ results for AuAu $\sqrt{s_{\text{NN}}}=200$ GeV collisions (a) and PbPb $\sqrt{s_{\text{NN}}}=5.02$ TeV collisions (b) for all charged particles computed using the S95n-v1 EoS from 2009 [15], the 2+1 WB EoS from Ref. [3], and the 2+1+1 WB EoS from 2016 [5].

Figure 13

$v_2\left\{4\right\}/v_2\left\{2\right\}$ for pions, kaons, and protons in AuAu $\sqrt{s_{\text{NN}}}=200$ GeV collisions (a) and PbPb $\sqrt{s_{\text{NN}}}=5.02$ TeV collisions (b) computed using the 2+1 WB EoS [3].

Figure 14

Symmetric cumulants results for all charged particles in AuAu $\sqrt{s_{\text{NN}}}=200$ GeV collisions (a), (b), (c) and PbPb $\sqrt{s_{\text{NN}}}=5.02$ TeV collisions (d), (e), (f) computed using the S95n-v1 EoS from 2009 [15], the 2+1 WB EoS from Ref. [3], and the 2+1+1 WB EoS from 2016 [5]. The green dashed line is the calculation using $\varepsilon \text{SC}(m,n)$.

Figure 15

Symmetric cumulants results with $v_6$ combinations for all charged particles in AuAu $\sqrt{s_{\text{NN}}}=200$ GeV collisions (a), (b), (c) and PbPb $\sqrt{s_{\text{NN}}}=5.02$ TeV collisions (d), (e), (f) computed using the S95n-v1 EoS from 2009 [15], the 2+1 WB EoS from Ref. [3], and the 2+1+1 WB EoS from 2016 [5].

Figure 16

Symmetric cumulants results for pions, kaons, and protons in AuAu $\sqrt{s_{\text{NN}}}=200$ GeV collisions (a), (b), (c) and PbPb $\sqrt{s_{\text{NN}}}=5.02$ TeV collisions (d), (e), (f) computed using the 2+1 WB EoS [3].

Figure 17

Pearson coefficient for the linear mapping between ${\varepsilon }_2$ and $v_2$ for all charged particles in AuAu $\sqrt{s_{\text{NN}}}=200$ GeV collisions compared to PbPb $\sqrt{s_{\text{NN}}}=5.02$ TeV collisions computed using the 2+1 WB EoS from Ref. [3]. Here we scale both by the centrality (a) and the number of participants (b).

Figure 18

$v_2\left\{4\right\}/v_2\left\{2\right\}$ results for all charged particles in AuAu $\sqrt{s_{\text{NN}}}=200$ GeV collisions compared to PbPb $\sqrt{s_{\text{NN}}}=5.02$ TeV collisions computed using the 2+1 WB EoS from Ref. [3]. Here we scale both by the centrality (a) and the number of participants (b).

Figure 19

${\varepsilon }_2\left\{4\right\}/{\varepsilon }_2\left\{2\right\}$ results for AuAu $\sqrt{s_{\text{NN}}}=200$ GeV collisions compared to PbPb $\sqrt{s_{\text{NN}}}=5.02$ TeV collisions.

Figure 20

Symmetric cumulant results for all charged particles in AuAu $\sqrt{s_{\text{NN}}}=200$ GeV collisions compared to PbPb $\sqrt{s_{\text{NN}}}=5.02$ TeV collisions computed using the 2+1 WB EoS from Ref. [3]. Here we scale both by the centrality (a), (b), (c) and the number of participants (d), (e), (f).

Figure 21

Trace anomaly of the equation of state with 2+1 flavors coupled to the PDG16 (***-**** states) and the PDG16 (*-**** states).

Figure 22

Spectra of $\pi$'s, $p$'s, and $K$'s in the centrality class $0–5\%$ for RHIC AuAu $\sqrt{s_{\text{NN}}}=200$ GeV (a) and the corresponding $\langle p_T\rangle$ (b) computed using the S95n-v1 EoS from 2009 [15], the 2+1 WB EoS with all *-**** resonances (PDG16+), and the 2+1 WB EoS with only ***-**** resonances (PDG16). Experimental data points from PHENIX collaboration [66] (b).

Figure 23

$v_2\left\{2\right\}$ and $v_3\left\{2\right\}$ results across centrality for AuAu $\sqrt{s_{\text{NN}}}=200$ GeV for all charged particles for the 2+1 flavor WB EoS coupled to all *-**** resonances (PDG16+) and to only ***-**** resonances (PDG16).