Spectra and Scattering of Light Lattice Nuclei from Effective Field Theory

Abstract

An effective field theory is used to describe light nuclei, calculated from quantum chromodynamics on a lattice at unphysically large pion masses. The theory is calibrated at leading order to two available data sets on two- and three-body nuclei for two pion masses. At those pion masses we predict the quartet and doublet neutron-deuteron scattering lengths, and the alpha-particle binding energy. For $m_{\pi }=510$MeV we obtain, respectively, ${}^4{a}_{\mathrm{nD}}=2.3\pm 1.3$fm, ${}^2{a}_{\mathrm{nD}}=2.2\pm 2.1$fm, and $B_{\alpha }^{}=35\pm 22$MeV, while for $m_{\pi }=805$MeV ${}^4{a}_{\mathrm{nD}}=1.6\pm 1.3$fm, ${}^2{a}_{\mathrm{nD}}=0.62\pm 1.0$fm, and $B_{\alpha }^{}=94\pm 45$MeV are found. Phillips- and Tjon-like correlations to the triton binding energy are established. Higher-order effects on the respective correlation bands are found insensitive to the pion mass. As a benchmark, we present results for the physical pion mass, using experimental two-body scattering lengths and the triton binding energy as input. Hints of subtle changes in the structure of the triton and alpha particle are discussed.

19 pages, 8 figures, 4 tables, submitted to PRC

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