Extracting $p\mathrm{\Lambda }$ scattering lengths from heavy ion collisions

The source radii previously extracted by the STAR Collaboration from the $p-\mathrm{\Lambda }\oplus \overline{p}-\overline{\mathrm{\Lambda }}$ and $\overline{p}-\mathrm{\Lambda }\oplus p-\overline{\mathrm{\Lambda }}$ correlation functions measured in 10% most central Au+Au collisions at top Relativistic Heavy Ion Collider (RHIC) energy, $\sqrt{s_{NN}}=200$ GeV, differ by a factor of 2. The probable reason for this is the neglect of residual correlation effect in the STAR analysis. In the present paper we analyze baryon correlation functions within the Lednický and Lyuboshitz analytical model, extended to effectively account for the residual correlation contribution. Different analytical approximations for such a contribution are considered. We also use the averaged source radii extracted from hydrokinetic model (HKM) simulations to fit the experimental data. In contrast to the STAR experimental study, the calculations in HKM show both $p\mathrm{\Lambda }$ and $p\overline{\mathrm{\Lambda }}$ radii to be quite close, as expected from theoretical considerations. Using the effective Gaussian parametrization of residual correlations we obtain a satisfactory fit to the measured baryon-antibaryon correlation function with the HKM source radius value 3.28 fm. The baryon-antibaryon spin-averaged strong interaction scattering length is also extracted from the fit to the experimental correlation function.

Figure 1

The $p\mathrm{\Lambda }$ source function projections calculated in HKM (markers) and the Gaussian fits to them (lines). The simulations correspond to $10\%$ most central collisions at $\sqrt{s_{NN}}=200$ GeV in conditions of the STAR experiment at RHIC [4]. Pair transverse momentum and rapidity cuts correspond to those in the experiment. The cut $k^{*}<50$ MeV/$c$ is also applied to select the pairs from correlation effect domain, where the $r^{*}-k^{*}$ correlations are small.

Figure 2

The $p\mathrm{\Lambda }$ angle-averaged source function calculated in HKM (markers) and the Gaussian fit to it (line). The simulation conditions are the same as given in the caption of Fig. 1

Figure 3

The $p-\mathrm{\Lambda }\oplus \overline{p}-\overline{\mathrm{\Lambda }}$ correlation function measured by STAR (open markers), the corresponding fit according to (6) with parameters fixed as in the STAR paper [4] within the Lednický and Lyuboshitz analytical model [1] (light solid line) and our fit within the same model with the source radius $r_0$ extracted from the HKM calculations (dark dashed line).

Figure 4

The same as in Fig. 3 for the $\overline{p}-\mathrm{\Lambda }\oplus p-\overline{\mathrm{\Lambda }}$ correlation function.

Figure 5

Our fit (black line) to the STAR purity uncorrected $\overline{p}-\mathrm{\Lambda }\oplus p-\overline{\mathrm{\Lambda }}$ correlation function as presented in [14] (open markers) according to (10), (6), with $C_{\mathrm{res}}\left(k^{*}\right)$ term in the form (12). In this particular fitting the source radius $r_0$ is a free parameter. The extracted fit parameter values are $r_0=2.76\pm 0.13$ fm, $\text{Re}{f}_0=0.59\pm 0.19$ fm, $\text{Im}{f}_0=0.85\pm 0.14$ fm, with ${\chi }^2/\mathrm{ndf}=1.37$.

Figure 6

The purity uncorrected $\overline{p}-\mathrm{\Lambda }\oplus p-\overline{\mathrm{\Lambda }}$ correlation function measured by STAR [15] (open markers) and our fit to it according to (10) and (6) (black line), with the Gaussian parametrization (13) for the residual correlation term $C_{\mathrm{res}}\left(k^{*}\right)$. The source radius $r_0$ was fixed at a value extracted from the HKM calculations. The extracted fit parameters are $\text{Re}{f}_0=0.14\pm 0.66$ fm, $\text{Im}{f}_0=1.53\pm 1.31$ fm, $\beta =0.034\pm 0.005$, and $R=0.48\pm 0.05$ fm, with ${\chi }^2/\mathrm{ndf}=0.87$.