Robustness of the baryon-stopping signal for the onset of deconfinement in relativistic heavy-ion collisions

The impact of the experimental acceptance, i.e. transverse-momentum $\left(p_T\right)$ cutoff and limited rapidity region, on the earlier predicted irregularity in the excitation function of the baryon stopping is studied. This irregularity is a consequence of the onset of deconfinement occurring in the compression stage of a nuclear collision and manifests itself as a wiggle in the excitation function of the reduced curvature $\left(C_y\right)$ of the net-proton rapidity distribution at midrapidity. It is demonstrated that the wiggle is a very robust signal of a first-order phase transition that survives even under conditions of a very limited acceptance. At the same time the $C_y$ for pure hadronic and crossover transition scenarios become hardly distinguishable, if the acceptance cuts off too much of the low-$p_T$ proton spectrum and/or puts a rapidity window that is too narrow around midrapidity. It is found that the shape of the net-proton rapidity distribution near midrapidity depends on the $p_T$ cutoff. This implies that the measurements should be taken at the same acceptance for all collision energies in order to reliably conclude the presence or absence of the irregularity.

Figure 1

Pressure scaled by the product of normal nuclear density $\left(n_0= 0.15 {\mathrm{fm}}^{-3}\right)$ and nucleon mass $\left(m_N\right)$ vs baryon density scaled by the normal nuclear density for three considered equations of state. Results are presented for three different temperatures $T=$ 10, 100, and 200 MeV (from bottom upwards for corresponding curves).

Figure 2

Midrapidity value of the net-proton rapidity distribution as a function of the collision energy in central ($b=$ 2 fm) Au+Au collisions in different windows of the transverse momentum $p_T$: (a) $0<p_T<2$ GeV/c, (b) $0.4<p_T<1$ GeV/c, (c) $1<p_T<2$ GeV/c, and (d) $0.4<p_T<3$ GeV/c. Results for the wide $p_T$ window ($0<p_T<2$ GeV/c) are also presented in panels (b)–(d) by the corresponding thin lines for the sake of comparison. Results of simulations with different EoS's are presented. Experimental data are from the collaborations E895 [19], E877 [20], E917 [21], E866 [22], NA49 [23, 24, 25, 26, 27], and STAR [28].

Figure 3

Midrapidity reduced curvature [see Eq. (2)] of the (net-)proton rapidity spectrum as a function of the center-of-mass energy of colliding nuclei as deduced from experimental data and predicted by 3FD calculations with different EoS's: the hadronic EoS (hadr. EoS) [10] (left column of panels), the EoS involving a first-order phase transition (2-ph. EoS, middle column of panels), and the EoS with a crossover transition (crossover EoS, right column of panels) into the quark-gluon phase [11]. Upper bounds of the shaded areas correspond to fits confined in the region of $\left|y\right|<0.7y_{\mathrm{beam}}$, and lower bounds correspond to $\left|y\right|<0.5y_{\mathrm{beam}}$. Results are presented for four different windows of the transverse momentum $p_T$: $0<p_T<2$ GeV/c (top row of panels), $0.4<p_T<1$ GeV/c (second row of panels), $1<p_T<2$ GeV/c (third row of panels), and $0.4<p_T<3$ GeV/c (bottom row of panels). Results for the $p_T$ window of the top panel with experimental data ($0<p_T<2$ GeV) are also presented in the lower panels with different restricted $p_T$ windows by shaded areas bounded by the corresponding thin lines for the sake of comparison. Results of fits within the range of $\left|y\right|<0.5$ are displayed by corresponding bold lines. In those cases, when $\left(\left|y\right|<0.5\right)$ fit substantially differs from that in the $\left|y\right|<0.9$ range, the $\left(\left|y\right|<0.9\right)$ results are also displayed by bold double-dash–triple-dotted lines.

Figure 4

Rapidity distribution of net protons in central ($b=$ 2 fm) Au+Au collisions at collision energies $\sqrt{s_{NN}}=$ 7.7 GeV (a) and 19.6 GeV (b) for the case of the $p_T$ range $0<p_T<2$ GeV/c.