Centrality dependence of proton and antiproton spectra in Pb$+$Pb collisions at $40A$ GeV and $158A$ GeV measured at the CERN Super Proton Synchrotron

The yields of (anti)protons were measured by the NA49 Collaboration in centrality-selected Pb $+$ Pb collisions at $40A$ and $158A$ GeV. Particle identification was obtained in the laboratory momentum range from 5 to 63 GeV$/c$ by measuring the energy loss $dE/dx$ in the time projection chamber detector gas. The corresponding rapidity coverage extends 1.6 units from midrapidity into the forward hemisphere. Transverse-mass spectra, the rapidity dependences of the average transverse mass, and rapidity density distributions were studied as a function of collision centrality. The values of the average transverse mass as well as the midrapidity yields of protons normalized to the number of wounded nucleons show only modest centrality dependences. In contrast, the shape of the rapidity distribution changes significantly with collision centrality, especially at $40A$ GeV. The experimental results are compared to calculations of the hadron-string dynamics and the ultrarelativistic quantum-molecular-dynamics transport models.

Figure 1

(a) The most probable specific energy loss $\mathrm{ê}$ for particle species $\pi {}^{+}$, $K^{+}$, and $p$ as a function of total momentum $p$. The points show results extracted from data, whereas the lines indicate the Bethe-Bloch parametrizations optimized for the NA49 measurement. (b) The ratios of the Bethe-Bloch parametrizations (${\mathrm{ê}}_{\mathrm{B}-\mathrm{B}\mathrm{param}.}$) to $\mathrm{ê}$ from fits to the data are shown as a function of laboratory momentum.

Figure 2

Raw yields per event of protons at (a) $40A$ GeV, (b) protons, and (c) antiprotons at $158A$ GeV are shown as a function of c.m. rapidity $y$ and $p_{\mathrm{T}}$ for centrality class C2.

Figure 3

Invariant $m_{\mathrm{T}}$ spectra of protons at (a) $40A$ GeV and (b) $158A$ GeV as well as antiprotons at (c) $158A$ GeV for five centrality bins in Pb $+$ Pb collisions. The respective c.m. rapidity intervals are $-0.02<y<0.18$, $-0.12<y<0.08$, $-0.12<y<0.08$. The data at different centralities are scaled down by the factors indicated in the figures. The new NA49 measurements (filled symbols) are compared, whenever available, to results of an earlier analysis using TOF information for particle identification [6] (open symbols). Only statistical errors are shown if larger than the symbol size. For the systematic errors, see Sec. 3c.

Figure 4

$\langle m_{\mathrm{T}}\rangle -m_0$ for (anti)protons as function of rapidity for five centrality intervals in Pb $+$ Pb collisions. We show in the upper row (a) protons at $40A$ GeV, in the middle row (b) protons at $158A$ GeV, and in the lower row (c) antiprotons at $158A$ GeV. The open symbols are obtained by reflection at midrapidity. Asterisks refer to results of an earlier analysis using TOF information for particle identification [6]. Only statistical errors are shown (if larger than the symbol size). For the systematic errors, see Sec. 3c.

Figure 5

$\langle m_{\mathrm{T}}\rangle -m_0$ near midrapidity as function of $\langle N_{\mathrm{w}}\rangle$ in Pb $+$ Pb collisions. The leftmost panel (a) shows the proton data at $40A$ GeV, the middle panel (b) the proton data at $158A$ GeV, and the right panel (c) the antiproton data at $158A$ GeV. The results of this analysis (labeled $dE/dx$) are compared to previously published Pb $+$ Pb data (labeled TOF) [6]. The ordinate has a suppressed zero. Only statistical errors are shown (if larger than the symbol size). For the systematic errors, see Sec. 3c.

Figure 6

$dn/dy$ of (net) protons for five different centralities. We show in (a) the proton distributions at $40A$ GeV and in (b) the difference between proton and antiproton spectra (i.e., the net-proton spectra) at $158A$ GeV. The open symbols are obtained by reflection at midrapidity. Also shown are the results from an earlier analysis labeled TOF [6]. Only statistical errors are shown (if larger than the symbol size). For the systematic errors, see Sec. 3c.

Figure 7

Rapidity density distributions per wounded nucleon are shown for protons at $40A$ GeV (top row), protons at $158A$ GeV (middle row), and antiprotons at $158A$ GeV (bottom row) for five centralities in Pb $+$ Pb collisions. The open symbols are obtained by reflection at midrapidity. The solid lines represent results of single Gaussian fits. For the statistical errors see Fig. 6. For the systematic errors, see Sec. 3c.

Figure 8

The total multiplicities (per wounded nucleon) of $\mathrm{p̄}$ and $\mathrm{\Lambda ̄}$ (upper panel) and the RMS${}_y$ widths of the $dn/dy$ distributions of $\mathrm{p̄}$ and $\mathrm{\Lambda ̄}$ (lower panel) for five centralities as a function of the number of wounded nucleons $\langle N_{\mathrm{w}}\rangle$ in Pb $+$ Pb collisions at $158A$ GeV. The $\mathrm{\Lambda ̄}$ data are from Ref. [24]. Also shown are results on antiprotons and $\mathrm{\Lambda ̄}$ obtained from p $+$ p interactions (for references see the text). Only statistical errors are shown (if larger than the symbol size). For the systematic errors, see Sec. 3c.

Figure 9

The net-proton rapidity distribution at $158A$ GeV for centrality bin C0 is compared with previously published data [3]. The full circles indicate results from the analysis presented in this paper, whereas the full squares show the previously published data. The open points result from reflection of the data points at midrapidity. The shaded bars represent the sytematic uncertainties. Error bars represent statistical errors.

Figure 10

Rapidity distribution of net protons from p $+$ p collisions at 158 GeV$/c$ beam momentum [25]. The solid line represents the HSD [26] and the dashed line the UrQMD [27] calculation.

Figure 11

The rapidity distributions scaled with 1/$\langle N_{\mathrm{w}}\rangle$ of net protons for five different centralities at $40A$ GeV are shown together with results of HSD (top) [26] and UrQMD (bottom) [27] calculations. For the statistical errors see Fig. 6. For the systematic errors, see Sec. 3c.

Figure 12

The rapidity distributions scaled with 1/$\langle N_{\mathrm{w}}\rangle$ of net protons for five different centralities at $158A$ GeV are shown together with results of HSD (top) [26] and UrQMD (bottom) [27] calculations. For the statistical errors see Fig. 6. For the systematic errors, see Sec. 3c.