Neutral kaon interferometry in Au+Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV

We present the first statistically meaningful results from two-$K_s^0$ interferometry in heavy-ion collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV. A model that takes the effect of the strong interaction into account has been used to fit the measured correlation function. The effects of single and coupled channels were explored. At the mean transverse mass $\langle m_T\rangle =1.07$ GeV, we obtain the values $R=4.09\pm 0.46(\mathrm{stat})\pm 0.31(\mathrm{sys})$ fm and $\lambda =0.92\pm 0.23(\mathrm{stat})\pm 0.13(\mathrm{sys})$, where $R$ and λ are the invariant radius and chaoticity parameters, respectively. The results are qualitatively consistent with $m_T$ systematics established with pions in a scenario characterized by a strong collective flow.

Figure 1

The $K_s^0$ invariant mass distribution from central Au+Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV. The range in transverse momentum is from $0.5$ to $3.5$ GeV/$c$ and rapidity is between $-1.5$ and 1.5. Kaon candidates falling in the mass range from $0.48$ to $0.51$ GeV/$c^2$, indicated by the shaded region, were selected for this correlation study. The corresponding mass is $495.6\pm 6.8$ MeV/$c^2$.

Figure 2

The $K_s^0$ signal to (signal+background) ratio as a function of the transverse momentum $p_T$. The data points correspond to a decay length (DL) greater than 6 cm. The kaons selected fall in the mass range from 0.48 to 0.51 GeV/$c^2$, which is also the mass range for the correlation analysis. The errors are only statistcal.

Figure 3

The $K_T$ distribution of the $K_s^0$ pairs. The range in transverse momentum of the single particles is from 0.5 to 3.5 GeV/$c$. The distribution in (a) corresponds to $Q<0.2$ GeV/$c$ and that in (b) is for $Q<0.1$ GeV/$c$, i.e., (b) is a subset of (a). The two histograms in each panel are for low (dashed) and high (full) pair purity.'

Figure 4

The $K_s^0{K}_s^0$ correlation function from central Au+Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV. The solid circles are for uncorrected data. The squares correspond to the case where the data have been corrected for pair purity. The triangles represent the data after correcting for pair purity and momentum resolution. The errors are ststistical only.

Figure 5

Theoretical correlation functions for input Gaussian sources of $R=6$ fm and $R=3$ fm with $\lambda =1,N=1$ The resonance masses and coupling constants are from Table 1.

Figure 6

Fits to the $K_s^0{K}_s^0$ experimental correlation function, including the strong interaction with resonance masses and coupling constants from Table 1. The confidence levels for the FSI fits are (a) $71\%$, (b) $70\%$, (c) $70\%$, and (d) $71\%$. A simple Gaussian fit, with a confidence level of $38\%$, is also shown for comparison. The errors are only statistical.

Figure 7

The extracted $R$ as a function of the pair purity (a) before correction for purity and (b) after correction for purity. The errors are only statistical.

Figure 8

The extracted λ as a function of the pair purity (a) before correction for purity and (b) after correction for purity. The errors are only statistical.

Figure 9

The extracted $R$ as a function of the mean $K_T$ of the pairs that go into the correlation function. The errors are only statistical.

Figure 10

$R$ as a function of $m_T$ in central Au+Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV. Statistical and systematic errors are shown. The FSI uncertainty measured by the spread of the fit results in rows (a)–(d) of Table 2 is substantially smaller than the statistical error.