Production of $\varphi$ mesons in $\text{Au}+\text{Au}$ collisions at $11.7A\text{GeV}∕c$

We report on a measurement of $\varphi$-meson production in $\text{Au}+\text{Au}$ collisions at a beam momentum of $11.7A\text{GeV}∕c$ by experiment 917 at the alternating gradient synchroton. The measurement covers the midrapidity region $1.2<y<1.6$. Transverse-mass spectra and rapidity distributions are presented as functions of centrality characterized by the number of participant projectile nucleons. The yield of $\varphi$’s per participant projectile nucleon increases strongly in central collisions in a manner similar to that observed for kaons.

Figure 1

The experimental acceptance for $K^{+}{K}^{-}$ pairs in the space of transverse mass $\left(m_t\right)$ vs rapidity $\left(y\right)$ for the $19°$ and $14°$ spectrometer angle settings.

Figure 2

(Color online) The invariant-mass $\left(m_{inv}\right)$ distribution of $K^{+}{K}^{-}$ pairs for minimum-bias events, superimposed with a fit consisting of a relativistic Breit-Wigner distribution plus the background distribution from a mixed-event technique, as described in the text. In the inset, the $\varphi$ signal together with fit results from the first term in Eq. (1) is shown.

Figure 3

Dependence of $S$ on width of signal window for six bins in $y$ and $m_t$: (1a) $1.2<y<1.4$, $1.5<m_t<1.7\text{GeV}∕c^2$, (2a) $1.2<y<1.4$, $1.7<m_t<1.9\text{GeV}∕c^2$, (3a) $1.4<y<1.6$, $1.7<m_t<1.9\text{GeV}∕c^2$, (1b) $1.2<y<1.4$, $1.3<m_t<1.5\text{GeV}∕c^2$, (2b) $1.4<y<1.6$, $1.3<m_t<1.5\text{GeV}∕c^2$, and (3b) $1.4<y<1.6$, $1.5<m_t<1.7\text{GeV}∕c^2$. For panels (1a), (2a), and (3a), the spectrometer was at $19°$; for panels (1b), (2b), and (3b), the spectrometer was at $14°$. Minimum-bias data ($0–77\%$ central) are shown in each case. The abscissa is the half-width of the signal window expressed in units of the $\varphi$ width, ${\Gamma }_0=4.26\text{MeV}∕c^2$. The errors plotted are statistical only. The lines represent the results of linear, least-squares fits to the points, using uniform weights, and are used to obtain the estimate of the systematic error on $S$ for each bin.

Figure 4

The invariant yield of $\varphi$’s as a function of transverse mass $(m_t-m_0)$ in five centrality bins labeled by $\sigma ∕{\sigma }_{\text{tot}}$. In each panel, the top set of points (circles) is for $1.2<y<1.4$, while the second set of points (triangles) is for $1.4<y<1.6$ and is divided by 100 for presentation. The total errors are calculated as the quadrature sum of the systematic and statistical errors, while the magnitudes of the latter are indicated by the cross bars. The lines are the results of the exponential fits described in the text.

Figure 5

The inverse-slope parameters $T$ and rapidity density, $dN∕dy$, of $\varphi$ mesons as a function of centrality. The open symbols show the reflections of the data points about midrapidity $(y=1.6)$. The error bars have the same significance as in Fig. 4.

Figure 6

The fiducial $\varphi$ yield (left) and fiducial $\varphi$ yield per projectile participant, $⟨N_{\text{pp}}⟩$, as a function of $⟨N_{\text{pp}}⟩$ (right). The accepted rapidity region is $1.2<y<1.6$. The error bars have the same significance as in Fig. 4.

Figure 7

The mean transverse mass $\left(⟨m_t-m_0⟩\right)$ for various particle species as a function of the species mass at midrapidity for central $\text{Au}+\text{Au}$ collisions at $11.7\text{GeV}∕c$ per nucleon as measured by E866 and E917. The dashed line is a fit assuming exponential transverse-mass spectra and a linear relationship between inverse slope $\left(T\right)$ and particle mass $\left(m_0\right)$, as described in the text. Values of $T$ for particles other than the $\varphi$ are taken from Refs. [9, 12, 30, 46, 47]. The proton data point from E866 (E917) is presented with a shift of $-30\text{MeV}∕c^2\left(+30\text{MeV}∕c^2\right)$ in mass for clarity.

Figure 8

The $\varphi ∕\pi$ and $\varphi ∕K^{+}$ ratios as a function of $⟨N_{\text{pp}}⟩$. For the $\varphi$, the fiducial yields from E917 in the rapidity interval $1.2<y<1.6$ are used. For $\pi$’s, the data have been taken from Ref. [46], and represent fiducial yields in the rapidity interval $1.2<y<1.4$. The value used for the $\pi$ yield is 1.125 times the yield for ${\pi }^{+}$, which is essentially the average yield for ${\pi }^{+}$ and ${\pi }^{-}$ [52]. For $K^{+}$’s, the data have been taken from Ref. [9], and represent fiducial yields in the rapidity interval $1.2<y<1.6$.

Figure 9

The normalized fiducial yield of $\varphi$ mesons per number of binary collisions $⟨N_{\text{coll}}⟩$ as a function of $⟨N_{\text{coll}}⟩$. The accepted rapidity region is $1.2<y<1.6$.

Figure 10

Ratios of $\varphi ∕⟨\pi ⟩$ in central heavy-ion and $p+p$ interactions as a function of $\sqrt{s_{NN}}$ (top panel) and double ratios of $A+A$ over $p+p$ (bottom panel). For the E917 and STAR points, fiducial yield ratios are plotted; for the other two points, total yield ratios are shown instead. The hatched area represents the ratio of total yields in $p+p$ collisions, based on the parametrization discussed in the Appendix. The cross bars in the bottom panel indicate the contribution to the total errors from the uncertainty on $\varphi ∕⟨\pi ⟩$ in central heavy-ion interactions.

Figure 11

Same as Fig. 10 for the ratios of $\varphi ∕K^{+}$.

Figure 12

Same as Fig. 10 for the ratios of $\varphi ∕K^{-}$.

Figure 13

Same as Fig. 10 for the ratios of $\varphi ∕⟨N_{\text{coll}}⟩$, where $⟨N_{\text{coll}}⟩$ is the number of binary collisions. For the E917 data point, an estimated total $\varphi$ yield is plotted as described in the text.

Figure 14

Parametrization of the $\varphi$ yield in $p+p$ interactions. The data points are from Refs. [5, 48, 56]. The fit is discussed in the text.