Influence of the hadronic phase on observables in ultrarelativistic heavy ion collisions

The hadronic phase in ultrarelativistic nuclear collisions has a large influence on final state observables like multiplicity, flow, and $p_t$ spectra, as studied in the UrQMD approach. In this model one assumes that a nonequilibrium decoupling phase follows a fluid dynamical description of the high density phase. Hadrons are produced assuming local thermal equilibrium and dynamically decouple during the hadronic rescattering until the particles are registered in the detectors. This rescattering of hadrons modifies every hadronic bulk observable. The apparent multiplicity of resonances is suppressed as compared to a chemical equilibrium freeze-out model, because the decay products rescatter. Therefore the resonances, which decay in the early hadronic phase, cannot be identified anymore by the invariant mass method. Stable and unstable particles change their momentum distribution by more than $30\%$ through rescattering and their multiplicity is modified by resonance production and annihilation on a similar magnitude. These findings show that it is all but trivial to conclude from the final state observables on the properties of the system at an earlier time where it may have been in local equilibrium.

Figure 1

Different total (elastic + inelastic) hadronic cross sections as implemented in UrQMD. We show the cross sections as function of the relative energy, i.e., we subtract the rest masses $\sqrt{s_0}$ of both hadrons from the total invariant mass.

Figure 2

Total number of different hadronic interactions occurring until the time $t$, during the hadronic phase of central collisions of Au+Au at $\sqrt{s_{NN}}=200$ GeV.

Figure 3

Reaction rates of different hadronic interactions during the hadronic phase of central collisions of Au+Au at $\sqrt{s_{NN}}=200$ GeV, as a function of the total system evolution time. The rates are normalized to the total number of the specific collisions to make different time dependencies visible.

Figure 4

Net gain rates of different hadronic resonances as a function of time and normalized to the initial yield at hadronization (Cooper-Frye). The results are for central collisions of Au+Au at $\sqrt{s_{NN}}=200$ GeV.

Figure 5

Yields of different hadronic resonances as a function of time and normalized to the initial yield at hadronization (Cooper-Frye). One clearly sees the lifetime hierarchy. The results are for central collisions of Au+Au at $\sqrt{s_{NN}}=200$ GeV.

Figure 6

Fraction of observable resonances which have decayed until a time $t$. The results are for central collisions of Au+Au at $\sqrt{s_{NN}}=200$ GeV.

Figure 7

Detection probability of different hadronic resonances as a function of the time of their decay. A resonance is detectable if none of their decay products rescatter in the hadronic phase. The results are for central collisions of Au+Au at $\sqrt{s_{NN}}=200$ GeV.

Figure 8

Detection probability of different hadronic resonances as a function of their transverse momentum. A resonance is detectable if none of their decay products rescatter in the hadronic phase. The results are for central collisions of Au+Au at $\sqrt{s_{NN}}=200$ GeV.

Figure 9

Ratios of detectable resonances to their ground state after the hadronic phase (red full circles) and before hadronic rescattering (red open circles), compared to data from the STAR experiment (green diamonds).

Figure 10

Ratios of detectable resonances to their ground state after the hadronic phase as a function of centrality (lines) compared to experimental data (symbols). The results are for collisions of Au+Au at $\sqrt{s_{NN}}=200$ GeV. The quoted temperature $T_{\mathrm{FO}}$ corresponds to the $\epsilon \approx 350$ MeV/${\mathrm{fm}}^3$ criterion.

Figure 11

Time dependence of the stable hadron yields (including their resonance feed-down), normalized to the final yields, during the hadronic phase. The results are for central collisions of Au+Au at $\sqrt{s_{NN}}=200$ GeV.

Figure 12

Change of the spectrum of stable hadrons from the final state rescattering. We compare two scenarios, one including the baryon+antibaryon annihilation and one excluding the annihilation reaction. The results are for central collisions of Au+Au at $\sqrt{s_{NN}}=200$ GeV.

Figure 13

Proton loss rate (by annihilation) as a function of the transverse momentum of the proton in the center-of-mass frame of the heavy ion collision. The results are for central collisions of Au+Au at $\sqrt{s_{NN}}=200$ GeV.

Figure 14

Proton loss rate (by annihilation) as a function of the invariant mass (minus the rest masses of the annihilating baryons $m_1$ and $m_2)$ of the baryon+antibaryon system in the center-of-mass frame of the annihilation reaction. The results are for central collisions of Au+Au at $\sqrt{s_{NN}}=200$ GeV.

Figure 15

Relative fraction of different baryonic species lost because of baryon+antibaryon annihilation in the hadronic phase. Only $42\%$ of all annihilated baryons are actual nucleons. The rest is composed of excited nucleonic states as well as hyperons and their resonance states. As a result less than 25% of all annihilations actually takes place between two nucleons in their ground state. The results are for central collisions of Au+Au at $\sqrt{s_{NN}}=200$ GeV.

Figure 16

The $p_T$-integrated elliptic flow $v_2$ for different hadronic particle species. We compare the elliptic flow of the hadrons at chemical freeze-out (Cooper-Frye) excluding (blue triangles) and including feed-down from the resonances (red circles) with the value after the hadronic phase (black squares). The results are for central collisions of Au+Au at $\sqrt{s_{NN}}=200$ GeV.

Figure 17

Relative change of the elliptic flow $v_2$ for different particle species as a function of the transverse mass $m_T$. We divided the elliptic flow of the hadrons at the chemical freeze-out (Cooper-Frye) excluding (short dashed lines) and including feed-down from the resonances (dashed lines) with the value after the hadronic phase. The results are for mid-central $(40\%–60\%)$ collisions of Au+Au at $\sqrt{s_{NN}}=200$ GeV.