Probing $\mathrm{\Omega }\mathrm{\Omega }$ and $p\mathrm{\Omega }$ dibaryons with femtoscopic correlations in relativistic heavy-ion collisions

The momentum correlation functions of baryon pairs, which reflects the baryon-baryon interaction at low energies, are investigated for multistrangeness pairs ($\mathrm{\Omega }\mathrm{\Omega }$ and $N\mathrm{\Omega }$) produced in relativistic heavy-ion collisions. We calculate the correlation functions based on an expanding source model constrained by single-particle distributions. The interaction potentials are taken from those obtained from recent lattice QCD calculations at nearly physical quark masses. Experimental measurements of these correlation functions for different system sizes will help to disentangle the strong interaction between baryons and to unravel the possible existence of strange dibaryons.

Figure 1

The correlation function $C^{\left(\text{LL}\right)}\left(q\right)$ with $r_{\mathrm{eff}}=0$ as a function of $R/a_0$ for different $qR$ (a) and as a function of $qR$ for different $R/a_0$ value (b). In the present sign convention, $a_0>0$ corresponds to the existence of a bound state.

Figure 2

Transverse-momentum spectra of (a) $\mathrm{\Omega }$ and (b) $p$. Experimental data are taken from Refs. [27] and [28] for $\mathrm{\Omega }$ and protons, respectively. Two most central events are scaled by factor 3 and 1.5 for better comparison.

Figure 3

The $\mathrm{\Omega }\mathrm{\Omega }$ potential in $J=0$ channel from lattice QCD simulations [12]. The lattice data are fitted by the form, $V_{\text{fit}}\left(r\right)={\sum }_{j=1,2,3}{c}_j{e}^{-{(r/d_j)}^2}$.

Figure 4

$\mathrm{\Omega }\mathrm{\Omega }$ correlation function $C\left(q\right)$ from central (0–10%) to peripheral (60–80%) Pb-Pb collisions, as well as the small-to-large ratio $C_{\text{SL}}\left(q\right)$.

Figure 5

The $S$-wave $N\mathrm{\Omega }$ potential with $J=2$ from lattice QCD simulations [13]. The lattice data are fitted by the form $V_{\text{fit}}\left(r\right)=b_1{e}^{-b_2{r}^2}+b_3(1-e^{-b_4{r}^2}){(e^{-m_{\pi }r}/r)}^2$ with $m_{\pi }=146$ MeV.

Figure 6

$p\mathrm{\Omega }$ correlation function from central (0–10%) to peripheral (60–80%) Pb-Pb collisions (a), as well as from peripheral to central collisions and the small-to-large ratio (b).

Figure 7

$p\mathrm{\Omega }$ correlation function calculated with the static Gaussian source function employing the $t/a=12$ potential. The purple solid line denotes the result with ${\chi }_0^{C,J=1}=0$, and blue dashed line denotes the result with the assumption of ${\chi }_0^{C,J=1}={\chi }_0^{C,J=2}$. Gaussian source size is chosen to be in the range $R=0.8$–$4\mathrm{fm}$. The error of each correlation estimated with the Jackknife method is shown by the colored shadow.

Figure 8

Comparison of the $S$-wave $N\mathrm{\Omega }$ potentials with $J=2$ in Refs. [13] and [17]. The solid curve show the $N\mathrm{\Omega }$ potential with nearly physical quark masses [13] at $t/a=12$. The dashed, dotted, and dash-dotted curves show the $J=2N\mathrm{\Omega }$ potentials, $V_{\mathrm{I}}$, $V_{\mathrm{II}}$, and $V_{\mathrm{III}}$, given in Ref. [17].