Bound $H$ Dibaryon in Flavor SU(3) Limit of Lattice QCD

The flavor-singlet $H$ dibaryon, which has strangeness $-2$ and baryon number 2, is studied by the approach recently developed for the baryon-baryon interactions in lattice QCD. The flavor-singlet central potential is derived from the spatial and imaginary-time dependence of the Nambu-Bethe-Salpeter wave function measured in $N_f=3$ full QCD simulations with the lattice size of $L\simeq 2,3,4\mathrm{fm}$. The potential is found to be insensitive to the volume, and it leads to a bound $H$ dibaryon with the binding energy of 30–40 MeV for the pseudoscalar meson mass of 673–1015 MeV.

Figure 1

Flavor 27-plet potential $V_C^{(27)}(r)$ obtained for lattice sizes $L=1.94,2.90,3.87\mathrm{fm}$ at $m_{\mathrm{ps}}=1015\mathrm{MeV}$ and $(t-t_0)/a=10$. Inset shows a magnification.

Figure 2

Flavor-singlet potential $V_C^{(1)}(r)$ at $(t-t_0)/a=10$. (a) Results for $L=1.94,2.90,3.87\mathrm{fm}$ at $m_{\mathrm{ps}}=1015\mathrm{MeV}$. (b) Results for $L=3.87\mathrm{fm}$ at $m_{\mathrm{ps}}=1015,837,673\mathrm{MeV}$. Insets show a magnification.

Figure 3

Bound state energy $E_0\equiv -{\tilde{B}}_H$ and the rms distance $\sqrt{⟨r^2⟩}$ of the $H$ dibaryon obtained from the potential at $L=3.87\mathrm{fm}$. (a) Imaginary-time dependence at $m_{\mathrm{ps}}=673\mathrm{MeV}$. (b) Quark mass dependence at $(t-t_0)/a=10$.