Energy dependence of $\varphi$ meson production in central $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s_{\mathit{NN}}}=6$ to 17 GeV

$\varphi$ meson production is studied by the NA49 Collaboration in central $\mathrm{Pb}+\mathrm{Pb}$ collisions at $20A,30A,40A,80A$, and $158A$ GeV beam energy. The data are compared with measurements at lower and higher energies and with microscopic and thermal models. The energy dependence of yields and spectral distributions is compatible with the assumption that partonic degrees of freedom set in at low SPS energies.

Figure 1

$\mathit{dE}/\mathit{dx}$ parametrization for the data set at $80A$ GeV. (a) Mean $\mathit{dE}/\mathit{dx}$ as function of $\beta \gamma$ determined for TOF-identified pions, kaons, and protons; (b) $\mathit{dE}/\mathit{dx}$ resolution as function of momentum, obtained from the deconvolution of the energy loss spectra into the contributions of ${\pi }^{+},K^{+},$ and $p.$

Figure 2

$K^{+}{K}^{-}$ invariant-mass spectra after subtraction of the combinatorial background in the forward rapidity hemisphere for the five different beam momenta. The full lines show the Breit-Wigner fits to the signals as described in the text. The bin size is 4 MeV for $20A$ and $30A$ GeV and 2 MeV for the other beam energies.

Figure 3

$K^{+}{K}^{-}$ correlation function close to threshold in (a) $q_{\mathrm{inv}}$ and (b) $m_{\mathrm{inv}}$ [34].

Figure 4

Geometrical acceptance probability for $\varphi \to K^{+}{K}^{-}$ including kaon decay in flight for (a) $20A$ GeV and (b) $158A$ GeV.

Figure 5

$\varphi$ transverse momentum spectra integrated over the rapidity intervals given in Table 4. The full lines show the fits of thermal distributions (4). The squared symbols denote previously published results [23]. Only statistical errors are shown.

Figure 6

(a) $\varphi$ transverse mass spectra integrated over the rapidity intervals given in Table 4. The exponential fits indicated by the full lines correspond to the fits shown in Fig. 5. The spectra for different beam energies are scaled for better visibility. Only statistical errors are shown. The data at $158A$ GeV are compared with previously published results of NA49 [23] and CERES [25]. (b) Slope parameter as function of rapidity at $158A$ GeV. The values agree within errors with that obtained from the $y$-integrated $p_t$ spectrum, the latter indicated with its standard deviation by the shaded bar.

Figure 7

$\varphi$ rapidity distributions. The solid points refer to measured data, the open points are reflected at midrapidity. The full lines show the parametrization by a single Gaussian (5), the dashed lines that by the sum of two Gaussians (6). The data at $158A$ GeV are compared with previously published results of NA49 [23] and CERES [25]. Only statistical errors are shown.

Figure 8

$\varphi$ enhancement factor $E_{\varphi }$ [see Eq. (8)] as function of energy per nucleon pair. Data from the AGS [27] and the SPS refer to multiplicities in full phase space, data from the RHIC [29, 30] to midrapidity yields. The shaded boxes represent the systematic errors.

Figure 9

$\langle \varphi \rangle /\langle \pi \rangle$ ratio (a) in full phase space and (b) at midrapidity as function of energy per nucleon pair [$\langle \pi \rangle =1.5\hspace{0.5em}(\langle {\pi }^{+}\rangle +\langle {\pi }^{-}\rangle )$]. The CERES data point [25] was displaced horizontally for visibility. Note that the CERES measurement is at $y\approx y_{\mathrm{c}.\mathrm{m}.}-0.5$. The full line shows the predictions of the extended hadron gas model (HGM) with strangeness equilibration [37], the dashed curves those obtained with UrQMD 1.3 [17]. The shaded boxes represent the systematic errors.

Figure 10

$\varphi$ multiplicity in central $A+A$ collisions as function of energy per nucleon pair. The solid points denote the results of the statistical hadronization model (SHM) which allows a deviation from strangeness equilibrium [8]. They are connected by the solid line to guide the eye. The dotted curve shows the $\varphi$ yield predicted by the UrQMD 1.3 model [17]. The shaded boxes represent the systematic errors.

Figure 11

(a) Widths of the rapidity distributions of ${\pi }^{-},K^{+},K^{-}$, and $\varphi$ in central $\mathrm{Pb}+\mathrm{Pb}$ collisions at SPS energies as function of beam rapidity [38, 39]. The dashed lines are to guide the eye. The open star denotes the $\varphi$ rapidity width measured in $p+p$ collisions [23]. (b) Widths of the $\varphi$ rapidity distributions in central $\mathrm{Pb}+\mathrm{Pb}$ collisions compared with the expectations in a kaon coalescence picture [Eq. (9)]. The shaded boxes represent the systematic errors (shown only for $\varphi$ mesons).

Figure 12

(a) Inverse slope parameter $T$ and (b) average transverse mass $\langle m_t\rangle -m_0$ of the $\varphi$ meson in central $A+A$ collisions as function of energy per nucleon pair. The data from E917 [27] were averaged over the measured rapidity interval (see Table 4). Results from NA50 [24] and RHIC [28, 29, 30] were obtained at midrapidity, the result from CERES at $y=-0.71$. Data from NA49 are integrated over rapidity. The PHENIX data point was slightly displaced horizontally for visibility. For the NA49 data, $\langle m_t\rangle$ was calculated from the transverse momentum spectra using an exponential extrapolation to full $p_t$. For the other data sets, it was derived analytically from the exponential fit function. The shaded boxes represent the systematic errors.