Bose-Einstein Correlations of Charged Pion Pairs in $\mathrm{A}\mathrm{u}+\mathrm{A}\mathrm{u}$ Collisions at $\sqrt{s_{NN}}=200\mathrm{G}\mathrm{e}\mathrm{V}$

Bose-Einstein correlations of identically charged pion pairs were measured by the PHENIX experiment at midrapidity in $\mathrm{A}\mathrm{u}+\mathrm{A}\mathrm{u}$ collisions at $\sqrt{s_{NN}}=200\mathrm{G}\mathrm{e}\mathrm{V}$. The Bertsch-Pratt radius parameters were determined as a function of the transverse momentum of the pair and as a function of the centrality of the collision. Using the standard core-halo partial Coulomb fits, and a new parametrization which constrains the Coulomb fraction as determined from the unlike-sign pion correlation, the ratio $R_{\mathrm{o}\mathrm{u}\mathrm{t}}/R_{\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}}$ is within 0.8–1.1 for $0.25<\langle k_{\mathrm{T}}\rangle <1.2\mathrm{G}\mathrm{e}\mathrm{V}/c$. The centrality dependence of all radii is well described by a linear scaling in $N_{\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t}}^{1/3}$, and $R_{\mathrm{o}\mathrm{u}\mathrm{t}}/R_{\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}}$ for $\langle k_{\mathrm{T}}\rangle \sim 0.45\mathrm{G}\mathrm{e}\mathrm{V}/c$ is approximately constant at unity as a function of centrality.

Figure 1

(a) The one-dimensional correlation function of unlike-sign pions for $0.2<k_{\mathrm{T}}<2.0\mathrm{G}\mathrm{e}\mathrm{V}/c$. The two overlaid histograms show calculations for the full (dashed) and the $50\%$ partial (solid) Coulomb corrections. (b)–(d) The three-dimensional ${\pi }^{-}{\pi }^{-}$ correlation function slices for $0.2<k_{\mathrm{T}}<2.0\mathrm{G}\mathrm{e}\mathrm{V}/c$ and $0\%–30\%$ centrality averaged over the lowest $40\mathrm{M}\mathrm{e}\mathrm{V}/c$ in the orthogonal directions. The full Coulomb corrected data (open circles) are fit to Eq. (1) (dashed lines), and the data without Coulomb correction (filled triangles) are fit to Eq. (2) (solid lines).

Figure 2

The $k_{\mathrm{T}}$ dependence of $\lambda$, $R_{\mathrm{o}\mathrm{u}\mathrm{t}}$, and $R_{\mathrm{o}\mathrm{u}\mathrm{t}}/R_{\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}}$ for ${\pi }^{-}{\pi }^{-}$ for $0\%–30\%$ centrality. Filled triangles show the results from fits to a core-halo structure by Eq. (2), with statistical error bars and systematic error bands. Open circles and squares show the results from the full and partial Coulomb corrections by Eqs. (1) and (3), respectively, with statistical error bars.

Figure 3

The $k_{\mathrm{T}}$ dependence of the Bertsch-Pratt parameters for ${\pi }^{+}{\pi }^{+}$ (blue square) and ${\pi }^{-}{\pi }^{-}$ (red triangle) for $0\%–30\%$ centrality, from fits to a core-halo structure by Eq. (2), with statistical error bars and systematic error bands. Results from STAR [28] and hydrodynamics models (Hirano [29], solid and dashed lines, and Soff [30], diamonds) are overlaid.

Figure 4

Bertsch-Pratt radius parameters versus the cube root of the number of participants ($N_{\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t}}^{1/3}$) for ${\pi }^{+}{\pi }^{+}$ (blue square) and ${\pi }^{-}{\pi }^{-}$ (red triangle) for the fits to a core-halo structure by Eq. (2) with statistical error bars and systematic error bands, in the $0.2<k_{\mathrm{T}}<2.0\mathrm{G}\mathrm{e}\mathrm{V}/c$ range, with $\langle k_{\mathrm{T}}\rangle \sim 0.45\mathrm{G}\mathrm{e}\mathrm{V}/c$. The solid line shows fits to $p_0+p_1*{\mathrm{N}}_{\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t}}^{1/3}$ for both signs.