Proton-$\Lambda$ correlations in central Pb$+$Pb collisions at $\sqrt{s_{\mathit{NN}}}=17.3$ GeV

The momentum correlation between protons and $\Lambda$ particles emitted from central Pb$+$Pb collisions at $\sqrt{s_{\mathit{NN}}}=17.3$ GeV was studied by the NA49 experiment at the CERN Super Proton Synchrotron. A clear enhancement is observed for small relative momenta ($q_{\text{inv}}<0.2$ GeV). By fitting a theoretical model, which uses the strong interaction between the proton and the $\Lambda$ in a given pair, to the measured data, a value for the effective source size is deduced. Assuming a static Gaussian source distribution, we derive an effective radius parameter of $R_G=3.02\pm 0.20$(stat.)${}_{-0.16}^{+0.44}$(syst.) fm.

Figure 1

Invariant mass distribution of $\Lambda$ candidates in two exemplary phase-space bins [(a) $-1.2<y<-0.4$ and $0.6<p_t<1.2$ GeV$/c$, and (b) $-0.4<y<0.4$ and $1.8<p_t<2.4$ GeV$/c$] for central Pb$+$Pb reactions at $\sqrt{s_{\mathit{NN}}}=17.3$ GeV. The two vertical lines indicate the mass windows used to define $\Lambda$ candidates.

Figure 2

Purity $P_{\Lambda }(y,p_t)$ of the selected $\Lambda$ candidates as function of rapidity $y$ and transverse momentum $p_t$.

Figure 3

$\mathit{dE}/\mathit{dx}$ spectra in two exemplary total momentum bins [(a) $4.0<p<5.0$ GeV$/c$, and (b) $12.6<p<15.9$ GeV$/c$] together with their decomposition into contributions from protons, kaons, pions, and electrons (from left to right). Shown is the measured energy loss normalized to the minimum ionizing value $\mathit{dE}/{\mathit{dx}}_{\text{MIP}}$. The vertical lines represent the upper $\mathit{dE}/\mathit{dx}$ cuts that result in a purity of $P_p=0.8$.

Figure 4

Phase-space population of (a) protons and (b) $\Lambda$ as a function of rapidity $y$ and transverse momentum $p_t$. (c) Distribution for the resulting $p-\Lambda$ pairs vs pair rapidity $y_{p\Lambda }=\frac{1}{2}\ln \frac{E_p+E_{\Lambda }+p_{z,p}+p_{z,\Lambda }}{E_p+E_{\Lambda }-p_{z,p}-p_{z,\Lambda }}$ and $k_t=\frac{1}{2}|{\mathrm{p⃗}}_{t,p}+{\mathrm{p⃗}}_{t,\Lambda }|$.

Figure 5

Fraction of (a) protons $F_p(y,p_t)$ and (b) $\Lambda$ $F_{\Lambda }(y,p_t)$ originating from feed-down as a function of $y$ and $p_t$.

Figure 6

Corrected $p-\Lambda$ correlation function for central Pb$+$Pb reactions at $\sqrt{s_{\mathit{NN}}}=17.3$ GeV, shown as a function of the invariant relative momentum $q_{\text{inv}}$. The data represent an average over the whole acceptance of the NA49 experiment. The lines display results of the fit with a theoretical correlation function[35, 38] (see text for details). Only statistical errors are shown.

Figure 7

Corrected $p-\Lambda$ correlation function $C_{\text{corr}}(q_{\text{inv}})$ for central Pb$+$Pb reactions at $\sqrt{s_{\mathit{NN}}}=17.3$ GeV as a function of the invariant relative momentum $q_{\text{inv}}$ for different purities of (a) protons and (b) $\Lambda$ as well as for different feed-down contributions to (c) protons and (d) $\Lambda$ (see text). The lines display the results of fits with a theoretical correlation function[35, 38].

Figure 8

Effective radius parameter $R_G$ for $p-\Lambda$ correlations as a function of center-of-mass energy $\sqrt{s_{\mathit{NN}}}$. The figure also includes data on Ar$+$KCl collisions by the HADES Collaboration[28] and on central Au$+$Au collisions by the E895[7] and STAR[29] experiments. The systematic errors are represented by the brackets. Please note that the STAR result corresponds to a slightly higher pair $\langle m_t\rangle$ than for the NA49 measurement. Assuming the $m_t$ dependence shown in Fig. 9, the STAR data point would move up by $\approx 6\%$, if it was measured at the same $\langle m_t\rangle$.

Figure 9

Effective radius parameter $R_G$ extracted from the correlation functions of $\pi {}^{-}$$\pi {}^{-}$[3], $K^{+}$$K^{+}$ and $K^{-}$$K^{-}$[8], $\mathit{pp}$[4], and $p-\Lambda$ pairs vs $\langle m_t\rangle$ as measured by NA49 for central Pb$+$Pb collisions at $\sqrt{s_{\mathit{NN}}}$$=$ 17.3 GeV. The systematic errors are represented by the brackets. For explanation of curves, see text.