Lévy-stable two-pion Bose-Einstein correlations in $\sqrt{s_{\mathit{NN}}}=200$ GeV $\mathrm{Au}+\mathrm{Au}$ collisions

We present a detailed measurement of charged two-pion correlation functions in 0–30% centrality $\sqrt{s_{{}_{\mathit{NN}}}}=200$ GeV $\mathrm{Au}+\mathrm{Au}$ collisions by the PHENIX experiment at the Relativistic Heavy Ion Collider. The data are well described by Bose-Einstein correlation functions stemming from Lévy-stable source distributions. Using a fine transverse momentum binning, we extract the correlation strength parameter $\lambda$, the Lévy index of stability $\alpha$, and the Lévy length scale parameter $R$ as a function of average transverse mass of the pair $m_T$. We find that the positively and the negatively charged pion pairs yield consistent results, and their correlation functions are represented, within uncertainties, by the same Lévy-stable source functions. The $\lambda \left(m_T\right)$ measurements indicate a decrease of the strength of the correlations at low $m_T$. The Lévy length scale parameter $R\left(m_T\right)$ decreases with increasing $m_T$, following a hydrodynamically predicted type of scaling behavior. The values of the Lévy index of stability $\alpha$ are found to be significantly lower than the Gaussian case of $\alpha =2$, but also significantly larger than the conjectured value that may characterize the critical point of a second-order quark-hadron phase transition.

Figure 1

View of the PHENIX central arm spectrometer detector setup during the 2010 run.

Figure 2

Lévy-stable source distributions with (a) $S_{\mathrm{core}}\left(\mathit{r}\right)=\mathcal{L}(\alpha ,R,\mathit{r})$ and $r=\left|\mathit{r}\right|$ for $\alpha =1$, 1.2, and 2. (b) Radial source distributions $4\pi r^2{S}_{\mathrm{core}}$ for $\alpha =1$, 1.2, and 2. In these plots, the dependence of the source distribution on Lévy scale $R$ is scaled out by using $r\to r/R$ and $S_{\mathrm{core}}\to R^3{S}_{\mathrm{core}}$. With this transformation, source distributions coincide for any $R$.

Figure 3

Example fits of Bose-Einstein correlation functions of (a) ${\pi }^{-}{\pi }^{-}$ pair with $m_T$ between 0.331 and 0.349 $\mathrm{GeV}/c^2$ and of (b) ${\pi }^{+}{\pi }^{+}$ pair with $m_T$ between 0.655 and 0.675 $\mathrm{GeV}/c^2$, as a function $Q\equiv |{\mathit{q}}_{\mathrm{LCMS}}|$, defined in Eq. (26). Both fits show the measured correlation function and the complete fit function (described in Sec. 6a), while a Bose-Einstein fit function $C_2^{\left(0\right)}\left(Q\right)$ is also shown, with the Coulomb-corrected data, i.e., the raw data multiplied by $C_2^{\left(0\right)}\left(Q\right)/C_2\left(Q\right)$. In this analysis, we measured 62 such correlation functions (for $++$ and $--$ pairs, in 31 $m_T$ bins), and fitted all of them with the method described in Sec. 6a. The first visible point on both panels corresponds to $Q$ values below the accessible range (based on an evaluation of the two-track cuts); these were not taken into account in the fitting.

Figure 4

Correlation strength parameter $\lambda$ vs average $m_T$ of the pair, for 0–30% centrality collisions. Statistical and systematic uncertainties are shown as bars and boxes.

Figure 5

Lévy scale parameter $R$ vs average $m_T$ of the pair. The graphical representation of statistical and systematic uncertainties is the same as in Fig. 4.

Figure 6

Lévy index parameter $\alpha$ vs average $m_T$ of the pair. Statistical and systematic uncertainties are indicated similarly to Fig. 4. The horizontal line, $\alpha =1.207$, represents the 0–30% centrality average value of $\alpha$.

Figure 7

Contour lines of the ${\chi }^2$ map in the (a) $\lambda ,R$, (b) $\lambda ,\alpha$, and (c) $R,\alpha$ planes for fits to ${\pi }^{-}{\pi }^{-}$ correlation functions of pairs with $m_T$ between 0.331 and 0.349 $\mathrm{GeV}/c^2$. The horizontal and vertical lines represent the MINOS fit uncertainties.

Figure 8

Inverse square of the Lévy scale parameter $1/R^2$ vs average $m_T$ of the pair. Statistical and systematic uncertainties shown as bars and boxes, respectively.

Figure 9

Contour lines of the ${\chi }^2$ map in the (a) $\lambda ,\widehat{R}$, (b) $\lambda ,\alpha$, and (c) $\widehat{R},\alpha$ planes for fits to ${\pi }^{-}{\pi }^{-}$ correlation functions of pairs with $m_T$ between 0.331 and 0.349 $\mathrm{GeV}/c^2$. The horizontal and vertical lines represent the MINOS fit uncertainties.

Figure 10

New scale parameter $\widehat{R}$ vs average $m_T$ of the pair, with a linear fit. Statistical and systematic uncertainties shown as bars and boxes, respectively.

Figure 11

Normalized correlation strength parameter $\lambda /{\lambda }_{\max }$ vs average $m_T$ of the pair. The data are compared with parameter scans from Refs. [58, 59] using different values of in-medium ${\eta }^{\prime }$ mass $m_{{\eta }^{\prime }}^{*}$ and slope parameter $B_{{\eta }^{\prime }}^{-1}$. A best fit with Eq. (63) and the resulting $H$ and $\sigma$ parameters are also shown.