Dibaryon with Highest Charm Number near Unitarity from Lattice QCD

A pair of triply charmed baryons, ${\mathrm{\Omega }}_{ccc}{\mathrm{\Omega }}_{ccc}$, is studied as an ideal dibaryon system by ($2+1$)-flavor lattice QCD with nearly physical light-quark masses and the relativistic heavy-quark action with the physical charm quark mass. The spatial baryon-baryon correlation is related to their scattering parameters on the basis of the HAL QCD method. The ${\mathrm{\Omega }}_{ccc}{\mathrm{\Omega }}_{ccc}$ in the ${}^1{S}_0$ channel, taking into account the Coulomb repulsion with the charge form factor of ${\mathrm{\Omega }}_{ccc}$, leads to the scattering length $a_0^{\mathrm{C}}\simeq -19\mathrm{fm}$ and the effective range $r_{\mathrm{eff}}^{\mathrm{C}}\simeq 0.45\mathrm{fm}$. The ratio $r_{\mathrm{eff}}^{\mathrm{C}}/a_0^{\mathrm{C}}\simeq -0.024$, whose magnitude is considerably smaller than that of the dineutron ($-0.149$), indicates that ${\mathrm{\Omega }}_{ccc}{\mathrm{\Omega }}_{ccc}$ is located in the unitary regime.

Figure 1

The ${\mathrm{\Omega }}_{ccc}{\mathrm{\Omega }}_{ccc}$ potential $V(r)$ in the ${}^1{S}_0$ channel as a function of separation $r$ at Euclidean time $t/a=25$ (red square), 26 (blue diamond), and 27 (green circle).

Figure 2

The ${\mathrm{\Omega }}_{ccc}{\mathrm{\Omega }}_{ccc}$ scattering phase shifts ${\delta }_0$ in the ${}^1{S}_0$ channel obtained from the potential $V(r)$ at $t/a=25$, 26, and 27 as a function of the center of mass kinetic energy $E_{\mathrm{CM}}$.

Figure 3

The inverse of the scattering length $1/a_0^{\mathrm{C}}$ as a function of ${\alpha }_e/{\alpha }_e^{\mathrm{phys}.}$. The red solid line is the central values for $r_d=0.410\mathrm{fm}$. The statistical errors are shown by the inner band (red), while the outer band (gray) corresponds to the statistical and systematic errors added in quadrature. The blue dashed line corresponds to the central values for $r_d=0\mathrm{fm}$.

Figure 4

The dimensionless ratio of the effective range $r_{\mathrm{eff}}$ and the scattering length $a_0$ as a function of $r_{\mathrm{eff}}$. The red up(down)-pointing triangle and the blue right(left)-pointing triangle correspond to ${\mathrm{\Omega }}_{ccc}{\mathrm{\Omega }}_{ccc}$ system and $\mathrm{\Omega }\mathrm{\Omega }$ system in the ${}^1{S}_0$ channel with (without) the Coulomb repulsion, respectively. The black circle represents $NN$ system in the ${}^3{S}_1\text{−}{}^3{D}_1$ channel. The green square ($nn$) and diamond ($pp$) correspond to $NN$ system in the ${}^1{S}_0$ channel. The error bars for ${\mathrm{\Omega }}_{ccc}{\mathrm{\Omega }}_{ccc}$ are the quadrature of the statistical and systematic errors in Eqs. (4) and (8).