Effective Field Theory for Lattice Nuclei

We show how nuclear effective field theory (EFT) and ab initio nuclear-structure methods can turn input from lattice quantum chromodynamics (LQCD) into predictions for the properties of nuclei. We argue that pionless EFT is the appropriate theory to describe the light nuclei obtained in LQCD simulations carried out at pion masses heavier than the physical pion mass. We solve the EFT using the effective-interaction hyperspherical harmonics and auxiliary-field diffusion Monte Carlo methods. Fitting the three leading-order EFT parameters to the deuteron, dineutron, and triton LQCD energies at $m_{\pi }\approx 800\mathrm{MeV}$, we reproduce the corresponding alpha-particle binding and predict the binding energies of mass-5 and mass-6 ground states.

Figure 1

${}^4\mathrm{He}$ binding energy $B_4$ [MeV] as a function of the momentum cutoff $\mathrm{\Lambda }$ [${\mathrm{fm}}^{-1}$]. The (magenta) horizontal line and the (pink) band give the LQCD central value and error. The (black and blue) solid lines are (respectively, the EIHH and AFMDC methods) LO EFT results.

Figure 2

Correlation between the ${}^4\mathrm{He}$ and ${}^3\mathrm{He}$ binding energies, $B_4$ [MeV] and $B_3$ [MeV]. Horizontal and vertical lines and bands represent LQCD results. The (blue) solid line is the Tjon line in LO EFT from the EIHH method at $\mathrm{\Lambda }=2{\mathrm{fm}}^{-1}$.